THE STORY OF BURIDAN'S ASS.
Questiones Morales, folio, 1489 [Paris]. By T. Buridan.
This is the title from the Hartwell Catalogue of Law Books. I suppose
it is what is elsewhere called the "Commentary on the Ethics of
Aristotle," printed in 1489.[13] Buridan[14] (died about 1358) is the creator of the
famous ass which, as Burdin's[15] ass, was current in Burgundy, perhaps
is, as a vulgar proverb. Spinoza[16] says it was a jenny ass, and that a man
would not have been so foolish; but whether the compliment is paid to
human or to masculine character does not appear—perhaps to both in
one. The story told about the famous paradox is very curious. The
Queen of France, Joanna or Jeanne, was in the habit of sewing her lovers
up in sacks, and throwing them into the Seine; not for blabbing, but that
they might not blab—certainly the safer plan. Buridan was exempted,
and, in gratitude, invented the sophism. What it has to do with the
matter has never been explained. Assuredly qui
facit per alium facit per se will convict Buridan of prating. The
argument is as follows, and is seldom told in full. Buridan was for
free-will—that is, will which determines conduct, let motives be
ever so evenly balanced. An ass is equally pressed by hunger and
by thirst; a bundle of hay is on one side, a pail of water on the other.
Surely, you will say, he will not be ass enough to die for want of food
or drink; he will then make a choice—that is, will choose between
alternatives of equal force. The problem became famous in the schools;
some allowed the poor donkey to die of indecision; some denied the
possibility of the balance, which was no answer at all.
MICHAEL SCOTT'S DEVILS.
The following question is more difficult, and involves free-will to
all who answer—"Which you please." If the northern hemisphere were
land, and all the southern hemisphere water, ought we to call the
northern hemisphere an island, or the southern hemisphere a lake? Both
the questions would be good exercises for paradoxers who must be kept
employed, like Michael Scott's[17] devils. The wizard knew nothing
about squaring the circle, etc., so he set them to make ropes out of sea
sand, which puzzled them. Stupid devils; much of our glass is sea sand,
and it makes beautiful thread. Had Michael set them to square the circle
or to find a perpetual motion, he would have done his work much better.
But all this is conjecture: who knows that I have not hit on the very
plan he adopted? Perhaps the whole race of paradoxers on hopeless
subjects are Michael's subordinates, condemned to transmigration after
transmigration, until their task is done.
The above was not a bad guess. A little after the time when the famous
Pascal papers[18] were
produced, I came into possession of a correspondence which, but for these
papers, I should have held too incredible to be put before the world. But
when one sheep leaps the ditch, another will follow: so I gave the
following account in the Athenæum of October 5, 1867:
"The recorded story is that Michael Scott, being bound by contract to
produce perpetual employment for a number of young demons, was worried
out of his life in inventing jobs for them, until at last he set them to
make ropes out of sea sand, which they never could do. We have obtained a
very curious correspondence between the wizard Michael and his
demon-slaves; but we do not feel at liberty to say how it came into our
hands. We much regret that we did not receive it in time for the British
Association. It appears that the story, true as far as it goes, was never
finished. The demons easily conquered the rope difficulty, by the simple
process of making the sand into glass, and spinning the glass into
thread, which they twisted. Michael, thoroughly disconcerted, hit upon
the plan of setting some to square the circle, others to find the
perpetual motion, etc. He commanded each of them to transmigrate from one
human body into another, until their tasks were done. This explains the
whole succession of cyclometers, and all the heroes of the Budget. Some
of this correspondence is very recent; it is much blotted, and we are not
quite sure of its meaning: it is full of figurative allusions to driving
something illegible down a steep into the sea. It looks like a humble
petition to be allowed some diversion in the intervals of transmigration;
and the answer is—
Rumpat et serpens iter institutum,[19]
—a line of Horace, which the demons interpret as a direction to
come athwart the proceedings of the Institute by a sly trick. Until we
saw this, we were suspicious of M. Libri,[20] the unvarying blunders of the
correspondence look like knowledge. To be always out of the road requires
a map: genuine ignorance occasionally lapses into truth. We thought it
possible M. Libri might have played the trick to show how easily the
French are deceived; but with our present information, our minds are at
rest on the subject. We see M. Chasles does not like to avow the real
source of information: he will not confess himself a spiritualist."
PHILO OF GADARA.
Philo of Gadara[21] is
asserted by Montucla,[22]
on the authority of Eutocius,[23] the commentator on Archimedes, to have
squared the circle within the ten-thousandth part of a unit, that
is, to four places of decimals. A modern classical dictionary
represents it as done by Philo to ten thousand places of decimals.
Lacroix comments on Montucla to the effect that myriad (in Greek
ten thousand) is here used as we use it, vaguely, for an immense
number. On looking into Eutocius, I find that not one definite word is
said about the extent to which Philo carried the matter. I give a
translation of the passage:
"We ought to know that Apollonius Pergæus, in his Ocytocium [this work
is lost], demonstrated the same by other numbers, and came nearer, which
seems more accurate, but has nothing to do with Archimedes; for, as
before said, he aimed only at going near enough for the wants of life.
Neither is Porus of Nicæa fair when he takes Archimedes to task for not
giving a line accurately equal to the circumference. He says in his Cerii
that his teacher, Philo of Gadara, had given a more accurate
approximation (εἰς
ἀκριβεστέρους
ἀριθμοὺς
ἀγάγειν) than that of
Archimedes, or than 7 to 22. But all these [the rest as well as Philo]
miss the intention. They multiply and divide by tens of thousands,
which no one can easily do, unless he be versed in the logistics
[fractional computation] of Magnus [now unknown]."
Montucla, or his source, ought not to have made this mistake. He had
been at the Greek to correct Philo Gadetanus, as he had often been
called, and he had brought away and quoted ἀπὸ
Γάδαρων. Had he read two
sentences further, he would have found the mistake.
We here detect a person quite unnoticed hitherto by the moderns,
Magnus the arithmetician. The phrase is ironical; it is as if we should
say, "To do this a man must be deep in Cocker."[24] Accordingly, Magnus, Baveme,[25] and Cocker, are three
personifications of arithmetic; and there may be more.
ON SQUARING THE CIRCLE.
Aristotle, treating of the category of relation, denies that the
quadrature has been found, but appears to assume that it can be done.
Boethius,[26] in his
comment on the passage, says that it has been done since Aristotle, but
that the demonstration is too long for him to give. Those who have no
notion of the quadrature question may look at the English
Cyclopædia, art. "Quadrature of the Circle."
Tetragonismus. Id est circuli quadratura per Campanum, Archimedem
Syracusanum, atque Boetium mathematicæ perspicacissimos
adinventa.—At the end, Impressum Venetiis per Ioan. Bapti. Sessa.
Anno ab incarnatione Domini, 1503. Die 28 Augusti.
This book has never been noticed in the history of the subject, and I
cannot find any mention of it. The quadrature of Campanus[27] takes the ratio of Archimedes,[28] 7 to 22 to be absolutely
correct; the account given of Archimedes is not a translation of his
book; and that of Boetius has more than is in Boethius. This book
must stand, with the next, as the earliest in print on the subject, until
further showing: Murhard[29] and Kastner[30] have nothing so early. It is edited by
Lucas Gauricus,[31] who has
given a short preface. Luca Gaurico, Bishop of Civita Ducale, an
astrologer of astrologers, published this work at about thirty years of
age, and lived to eighty-two. His works are collected in folios, but I do
not know whether they contain this production. The poor fellow could
never tell his own fortune, because his father neglected to note the hour
and minute of his birth. But if there had been anything in astrology, he
could have worked back, as Adams[32] and Leverrier[33] did when they caught Neptune: at
sixty he could have examined every minute of his day of birth, by the
events of his life, and so would have found the right minute. He could
then have gone on, by rules of prophecy. Gauricus was the mathematical
teacher of Joseph Scaliger,[34] who did him no credit, as we shall
see.
BOVILLUS ON THE QUADRATURE PROBLEM.
In hoc opere contenta Epitome.... Liber de quadratura Circuli....
Paris, 1503, folio.
The quadrator is Charles Bovillus,[35] who adopted the views of Cardinal
Cusa,[36] presently
mentioned. Montucla is hard on his compatriot, who, he says, was only
saved from the laughter of geometers by his obscurity. Persons must guard
against most historians of mathematics in one point: they frequently
attribute to his own age the obscurity which a writer has in
their own time. This tract was printed by Henry Stephens,[37] at the instigation of
Faber Stapulensis,[38] and is
recorded by Dechales,[39]
etc. It was also introduced into the Margarita Philosophica of
1815,[40] in the same
appendix with the new perspective from Viator. This is not extreme
obscurity, by any means. The quadrature deserved it; but that is another
point.
It is stated by Montucla that Bovillus makes π = √10. But Montucla cites a work of 1507,
Introductorium Geometricum, which I have never seen.[41] He finds in it an account
which Bovillus gives of the quadrature of the peasant laborer, and
describes it as agreeing with his own. But the description makes π = 3-1/8, which it thus appears Bovillus could not
distinguish from √10. It seems also that this 3-1/8, about which we
shall see so much in the sequel, takes its rise in the thoughtful head of
a poor laborer. It does him great honor, being so near the truth, and he
having no means of instruction. In our day, when an ignorant person
chooses to bring his fancy forward in opposition to demonstration which
he will not study, he is deservedly laughed at.
THE STORY OF LACOMME'S ATTEMPT AT QUADRATURE.
Mr. James Smith,[42] of
Liverpool—hereinafter notorified—attributes the first
announcement of 3-1/8 to M. Joseph Lacomme, a French well-sinker, of whom
he gives the following account:
"In the year 1836, at which time Lacomme could neither read nor write,
he had constructed a circular reservoir and wished to know the quantity
of stone that would be required to pave the bottom, and for this purpose
called on a professor of mathematics. On putting his question and giving
the diameter, he was surprised at getting the following answer from the
Professor: 'Qu'il lui était impossible de le lui dire au juste,
attendu que personne n'avait encore pu trouver d'une manière exacte le
rapport de la circonférence au diametre.'[43] From this he was led to attempt the
solution of the problem. His first process was purely mechanical, and he
was so far convinced he had made the discovery that he took to educating
himself, and became an expert arithmetician, and then found that
arithmetical results agreed with his mechanical experiments. He appears
to have eked out a bare existence for many years by teaching arithmetic,
all the time struggling to get a hearing from some of the learned
societies, but without success. In the year 1855 he found his way to
Paris, where, as if by accident, he made the acquaintance of a young
gentleman, son of M. Winter, a commissioner of police, and taught him his
peculiar methods of calculation. The young man was so enchanted that he
strongly recommended Lacomme to his father, and subsequently through M.
Winter he obtained an introduction to the President of the Society of
Arts and Sciences of Paris. A committee of the society was appointed to
examine and report upon his discovery, and the society at its
séance of March 17, 1856, awarded a silver medal of the first
class to M. Joseph Lacomme for his discovery of the true ratio of
diameter to circumference in a circle. He subsequently received three
other medals from other societies. While writing this I have his likeness
before me, with his medals on his breast, which stands as a frontispiece
to a short biography of this extraordinary man, for which I am indebted
to the gentleman who did me the honor to publish a French translation of
the pamphlet I distributed at the meeting of the British Association for
the Advancement of Science, at Oxford, in
1860."—Correspondent, May 3, 1866.
My inquiries show that the story of the medals is not incredible.
There are at Paris little private societies which have not so much claim
to be exponents of scientific opinion as our own Mechanics' Institutes.
Some of them were intended to give a false lustre: as the "Institut
Historique," the members of which are "Membre de l'Institut Historique."
That M. Lacomme should have got four medals from societies of this class
is very possible: that he should have received one from any society at
Paris which has the least claim to give one is as yet simply
incredible.
NICOLAUS OF CUSA'S ATTEMPT.
Nicolai de Cusa Opera Omnia. Venice, 1514. 3 vols. folio.
The real title is "Hæc accurata recognitio trium voluminum operum
clariss. P. Nicolai Cusæ ... proxime sequens pagina monstrat."[44] Cardinal Cusa, who died
in 1464, is one of the earliest modern attempters. His quadrature is
found in the second volume, and is now quite unreadable.
In these early days every quadrator found a geometrical opponent, who
finished him. Regimontanus[45] did this office for the Cardinal.
HENRY CORNELIUS AGRIPPA.
De Occulta Philosophia libri III. By Henry Cornelius Agrippa. Lyons,
1550, 8vo.
De incertitudine et vanitate scientiarum. By the same. Cologne, 1531,
8vo.
The first editions of these works were of 1530, as well as I can make
out; but the first was in progress in 1510.[46] In the second work Agrippa repents of
having wasted time on the magic of the first; but all those who actually
deal with demons are destined to eternal fire with Jamnes and Mambres and
Simon Magus. This means, as is the fact, that his occult philosophy did
not actually enter upon black magic, but confined itself to the
power of the stars, of numbers, etc. The fourth book, which appeared
after the death of Agrippa, and really concerns dealing with evil
spirits, is undoubtedly spurious. It is very difficult to make out what
Agrippa really believed on the subject. I have introduced his books as
the most marked specimens of treatises on magic, a paradox of our day,
though not far from orthodoxy in his; and here I should have ended my
notice, if I had not casually found something more interesting to the
reader of our day.
WHICH LEADS TO WALTER SCOTT.
Walter Scott, it is well known, was curious on all matters connected
with magic, and has used them very widely. But it is hardly known how
much pains he has taken to be correct, and to give the real thing. The
most decided detail of a magical process which is found in his writings
is that of Dousterswivel in The Antiquary; and it is obvious, by
his accuracy of process, that he does not intend the adept for a mere
impostor, but for one who had a lurking belief in the efficacy of his own
processes, coupled with intent to make a fraudulent use of them. The
materials for the process are taken from Agrippa. I first quote Mr.
Dousterswivel:
"... I take a silver plate when she [the moon] is in her fifteenth
mansion, which mansion is in de head of Libra, and I engrave upon
one side de worts Schedbarschemoth Schartachan [ch
should be t]—dat is, de Intelligence of de Intelligence of
de moon—and I make his picture like a flying serpent with a
turkey-cock's head—vary well—Then upon this side I make de
table of de moon, which is a square of nine, multiplied into itself, with
eighty-one numbers [nine] on every side and diameter nine...."
In the De Occulta Philosophia, p. 290, we find that the
fifteenth mansion of the moon incipit capite Libræ, and is good
pro extrahendis thesauris, the object being to discover hidden
treasure. In p. 246, we learn that a silver plate must be used
with the moon. In p. 248, we have the words which denote the
Intelligence, etc. But, owing to the falling of a number into a wrong
line, or the misplacement of a line, one or other—which takes place
in all the editions I have examined—Scott has, sad to say, got hold
of the wrong words; he has written down the demon of the demons of
the moon. Instead of the gibberish above, it should have been Malcha
betarsisim hed beruah schenhakim. In p. 253, we have the magic square
of the moon, with eighty-one numbers, and the symbol for the
Intelligence, which Scott likens to a flying serpent with a
turkey-cock's head. He was obliged to say something; but I will stake my
character—and so save a woodcut—on the scratches being more
like a pair of legs, one shorter than the other, without a body, jumping
over a six-barred gate placed side uppermost. Those who thought that
Scott forged his own nonsense, will henceforth stand corrected. As to the
spirit Peolphan, etc., no doubt Scott got it from the authors he
elsewhere mentions, Nicolaus Remigius[47] and Petrus Thyracus; but this last word
should be Thyræus.
The tendency of Scott's mind towards prophecy is very marked, and it
is always fulfilled. Hyder, in his disguise, calls out to Tippoo: "Cursed
is the prince who barters justice for lust; he shall die in the gate by
the sword of the stranger." Tippoo was killed in a gateway at
Seringapatam.[48]
FINAEUS ON CIRCLE SQUARING.
Orontii Finaei ... Quadratura Circuli. Paris, 1544, 4to.
Orontius[49] squared the
circle out of all comprehension; but he was killed by a feather from his
own wing. His former pupil, John Buteo,[50] the same who—I believe for the
first time—calculated the question of Noah's ark, as to its power
to hold all the animals and stores, unsquared him completely. Orontius
was the author of very many works, and died in 1555. Among the laudatory
verses which, as was usual, precede this work, there is one of a rare
character: a congratulatory ode to the wife of the author. The French now
call this writer Oronce Finée; but there is much difficulty about
delatinization. Is this more correct than Oronce Fine, which the
translator of De Thou uses? Or than Horonce Phine, which older writers
give? I cannot understand why M. de Viette[51] should be called Viète, because his
Latin name is Vieta. It is difficult to restore Buteo; for not only now
is butor a blockhead as well as a bird, but we really cannot know
what kind of bird Buteo stood for. We may be sure that Madame Fine was
Denise Blanche; for Dionysia Candida can mean nothing else. Let her shade
rejoice in the fame which Hubertus Sussannæus has given her.
I ought to add that the quadrature of Orontius, and solutions of all
the other difficulties, were first published in De Rebus Mathematicis
Hactenus Desideratis,[52] of which I have not the date.
DUCHESNE, AND A DISQUISITION ON ETYMOLOGY.
Nicolai Raymari Ursi Dithmarsi Fundamentum Astronomicum, id est, nova
doctrina sinuum et triangulorum.... Strasburg, 1588, 4to.[53]
People choose the name of this astronomer for themselves: I take
Ursus, because he was a bear. This book gave the quadrature
of Simon Duchesne,[54] or à
Quercu, which excited Peter Metius,[55] as presently noticed. It also gave that
unintelligible reference to Justus Byrgius which has been used in the
discussion about the invention of logarithms.[56]
The real name of Duchesne is Van der Eycke. I have met with a tract in
Dutch, Letterkundige Aanteekeningen, upon Van Eycke, Van Ceulen,[57] etc., by J. J. Dodt van
Flensburg,[58] which I make
out to be since 1841 in date. I should much like a translation
of this tract to be printed, say in the Phil. Mag. Dutch would be
clear English if it were properly spelt. For example, learn-master
would be seen at once to be teacher; but they will spell it
leermeester. Of these they write as van deze;
widow they make weduwe. All this is plain to me, who never
saw a Dutch dictionary in my life; but many of their misspellings are
quite unconquerable.
FALCO'S RARE TRACT.
Jacobus Falco Valentinus, miles Ordinis Montesiani, hanc circuli
quadraturam invenit. Antwerp, 1589, 4to.[59]
The attempt is more than commonly worthless; but as Montucla and
others have referred to the verses at the end, and as the tract is of the
rarest, I will quote them:
Circulus loquitur.
Vocabar ante circulus
Eramque curvus undique
Ut alta solis orbita
Et arcus ille nubium.
Eram figura nobilis
Carensque sola origine
Carensque sola termino.
Modo indecora prodeo
Novisque fœdor angulis.
Nec hoc peregit Archytas[60]
Neque Icari pater neque
Tuus, Iapete, filius.
Quis ergo casus aut Deus
Meam quadravit aream?
Respondet auctor.
Ad alta Turiæ ostia
Lacumque limpidissimum
Sita est beata civitas
Parum Saguntus abfuit
Abestque Sucro plusculum.
Hic est poeta quispiam
Libenter astra consulens
Sibique semper arrogans
Negata doctioribus,
Senex ubique cogitans
Sui frequenter immemor
Nec explicare circinum
Nec exarare lineas
Sciens ut ipse prædicat.
Hic ergo bellus artifex
Tuam quadravit aream.[61]
Falco's verses are pretty, if the ˘-mysteries be correct; but of
these things I have forgotten—what I knew. [One mistake has been
pointed out to me: it is Archytas].
As a specimen of the way in which history is written, I copy the
account which Montucla—who is accurate when he writes about what he
has seen—gives of these verses. He gives the date 1587; he places
the verses at the beginning instead of the end; he says the circle thanks
its quadrator affectionately; and he says the good and modest chevalier
gives all the glory to the patron saint of his order. All of little
consequence, as it happens; but writing at second-hand makes as complete
mistakes about more important matters.
BUNGUS ON THE MYSTERY OF NUMBER.
Petri Bungi Bergomatis Numerorum mysteria. Bergomi [Bergamo], 1591,
4to. Second Edition.
The first edition is said to be of 1585;[62] the third, Paris, 1618. Bungus is not
for my purpose on his own score, but those who gave the numbers their
mysterious characters: he is but a collector. He quotes or uses 402
authors, as we are informed by his list; this just beats Warburton,[63] whom some eulogist or
satirist, I forget which, holds up as having used 400 authors in some one
work. Bungus goes through 1, 2, 3, etc., and gives the account of
everything remarkable in which each number occurs; his accounts not being
always mysterious. The numbers which have nothing to say for themselves
are omitted: thus there is a gap between 50 and 60. In treating 666,
Bungus, a good Catholic, could not compliment the Pope with it, but he
fixes it on Martin Luther with a little forcing. If from A to I represent
1-10, from K to S 10-90, and from T to Z 100-500, we see:
| M |
A |
R |
T |
I |
N |
|
L |
U |
T |
E |
R |
A |
| 30 |
1 |
80 |
100 |
9 |
40 |
|
20 |
200 |
100 |
5 |
80 |
1 |
which gives 666. Again, in Hebrew, Lulter does the same:
| ר |
ת |
ל |
ו |
ל |
| 200 |
400 |
30 |
6 |
30 |
And thus two can play at any game. The second is better than the
first: to Latinize the surname and not the Christian name is very
unscholarlike. The last number mentioned is a thousand millions; all
greater numbers are dismissed in half a page. Then follows an accurate
distinction between number and multitude—a thing much
wanted both in arithmetic and logic.
WHICH LEADS TO A STORY ABOUT THE ROYAL SOCIETY.
What may be the use of such a book as this? The last occasion on which
it was used was the following. Fifteen or sixteen years ago the Royal
Society determined to restrict the number of yearly admissions to fifteen
men of science, and noblemen ad libitum; the men of science being
selected and recommended by the Council, with a power, since practically
surrendered, to the Society to elect more. This plan appears to me to be
directly against the spirit of their charter, the true intent of which
is, that all who are fit should be allowed to promote natural knowledge
in association, from and after the time at which they are both fit and
willing. It is also working more absurdly from year to year; the tariff
of fifteen per annum will soon amount to the practical exclusion of many
who would be very useful. This begins to be felt already, I suspect. But,
as appears above, the body of the Society has the remedy in its own
hands. When the alteration was discussed by the Council, my friend the
late Mr. Galloway,[64] then
one of the body, opposed it strongly, and inquired particularly into the
reason why fifteen, of all numbers, was the one to be selected.
Was it because fifteen is seven and eight, typifying the Old Testament
Sabbath, and the New Testament day of the resurrection following? Was it
because Paul strove fifteen days against Peter, proving that he was a
doctor both of the Old and New Testament? Was it because the prophet
Hosea bought a lady for fifteen pieces of silver? Was it
because, according to Micah, seven shepherds and eight chiefs should
waste the Assyrians? Was it because Ecclesiastes commands equal reverence
to be given to both Testaments—such was the interpretation—in
the words "Give a portion to seven, and also to eight"? Was it because
the waters of the Deluge rose fifteen cubits above the
mountains?—or because they lasted fifteen decades of days? Was it
because Ezekiel's temple had fifteen steps? Was it because Jacob's ladder
has been supposed to have had fifteen steps? Was it because fifteen years
were added to the life of Hezekiah? Was it because the feast of
unleavened bread was on the fifteenth day of the month? Was it because
the scene of the Ascension was fifteen stadia from Jerusalem? Was it
because the stone-masons and porters employed in Solomon's temple
amounted to fifteen myriads? etc. The Council were amused and astounded
by the volley of fifteens which was fired at them; they knowing nothing
about Bungus, of which Mr. Galloway—who did not, as the French say,
indicate his sources—possessed the copy now before me. In giving
this anecdote I give a specimen of the book, which is exceedingly rare.
Should another edition ever appear, which is not very probable, he would
be but a bungling Bungus who should forget the fifteen of the
Royal Society.
AND ALSO TO A QUESTION OF EVIDENCE.
[I make a remark on the different colors which the same person gives
to one story, according to the bias under which he tells it. My friend
Galloway told me how he had quizzed the Council of the Royal Society, to
my great amusement. Whenever I am struck by the words of any one, I carry
away a vivid recollection of position, gestures, tones, etc. I do not
know whether this be common or uncommon. I never recall this joke without
seeing before me my friend, leaning against his bookcase, with Bungus
open in his hand, and a certain half-depreciatory tone which he often
used when speaking of himself. Long after his
death, an F.R.S. who was present at the discussion, told me the story. I
did not say I had heard it, but I watched him, with Galloway at the
bookcase before me. I wanted to see whether the two would agree as to the
fact of an enormous budget of fifteens having been fired at the Council,
and they did agree perfectly. But when the paragraph of the Budget
appeared in the Athenæum, my friend, who seemed rather to object
to the showing-up, assured me that the thing was grossly
exaggerated; there was indeed a fifteen or two, but nothing like the
number I had given. I had, however, taken sharp note of the previous
narration.
AND TO ANOTHER QUESTION OF EVIDENCE.
I will give another instance. An Indian officer gave me an account of
an elephant, as follows. A detachment was on the march, and one of the
gun-carriages got a wheel off the track, so that it was also off the
ground, and hanging over a precipice. If the bullocks had moved a step,
carriages, bullocks, and all must have been precipitated. No one knew
what could be done until some one proposed to bring up an elephant, and
let him manage it his own way. The elephant took a moment's survey of the
fix, put his trunk under the axle of the free wheel, and waited. The
surrounders, who saw what he meant, moved the bullocks gently forward,
the elephant followed, supporting the axle, until there was ground under
the wheel, when he let it quietly down. From all I had heard of the
elephant, this was not too much to believe. But when, years afterwards, I
reminded my friend of his story, he assured me that I had misunderstood
him, that the elephant was directed to put his trunk under the
wheel, and saw in a moment why. This is reasonable sagacity, and very
likely the correct account; but I am quite sure that, in the fit of
elephant-worship under which the story was first told, it was told as I
have first stated it.]
GIORDANO BRUNO AND HIS PARADOXES.
[Jordani Bruni Nolani de Monade, Numero et Figura ... item de
Innumerabilibus, Immenso, et Infigurabili ... Frankfort, 1591, 8vo.[65]
I cannot imagine how I came to omit a writer whom I have known so many
years, unless the following story will explain it. The officer reproved
the boatswain for perpetual swearing; the boatswain answered that he
heard the officers swear. "Only in an emergency," said the officer.
"That's just it," replied the other; "a boatswain's life is a life of
'mergency." Giordano Bruno was all paradox; and my mind was not alive to
his paradoxes, just as my ears might have become dead to the boatswain's
oaths. He was, as has been said, a vorticist before Descartes,[66] an optimist before
Leibnitz, a Copernican before Galileo. It would be easy to collect a
hundred strange opinions of his. He was born about 1550, and was roasted
alive at Rome, February 17, 1600, for the maintenance and defence of the
holy Church, and the rights and liberties of the same. These last words
are from the writ of our own good James I, under which Leggatt[67] was roasted at
Smithfield, in March 1612; and if I had a copy of the instrument under
which Wightman[68] was
roasted at Lichfield, a month afterwards, I daresay I should find something
quite as edifying. I extract an account which I gave of Bruno in the
Comp. Alm. for 1855:
"He was first a Dominican priest, then a Calvinist; and was roasted
alive at Rome, in 1600, for as many heresies of opinion, religious and
philosophical, as ever lit one fire. Some defenders of the papal cause
have at least worded their accusations so to be understood as imputing to
him villainous actions. But it is positively certain that his death was
due to opinions alone, and that retractation, even after sentence, would
have saved him. There exists a remarkable letter, written from Rome on
the very day of the murder, by Scioppius[69] (the celebrated scholar, a waspish
convert from Lutheranism, known by his hatred to Protestants and Jesuits)
to Rittershusius,[70] a
well-known Lutheran writer on civil and canon law, whose works are in the
index of prohibited books. This letter has been reprinted by Libri (vol.
iv. p. 407). The writer informs his friend (whom he wished to convince
that even a Lutheran would have burnt Bruno) that all Rome would tell him
that Bruno died for Lutheranism; but this is because the Italians do not
know the difference between one heresy and another, in which simplicity
(says the writer) may God preserve them. That is to say, they knew the
difference between a live heretic and a roasted one by actual inspection,
but had no idea of the difference between a Lutheran and a Calvinist. The
countrymen of Boccaccio would have smiled at the idea which the German
scholar entertained of them. They said Bruno was burnt for Lutheranism, a
name under which they classed all Protestants: and they are better
witnesses than Schopp, or Scioppius. He then proceeds to describe to his
Protestant friend (to whom he would certainly not have omitted any act
which both their churches would have condemned) the mass of opinions with
which Bruno was charged; as that there are innumerable worlds,
that souls migrate, that Moses was a magician, that the Scriptures are a
dream, that only the Hebrews descended from Adam and Eve, that the devils
would be saved, that Christ was a magician and deservedly put to death,
etc. In fact, says he, Bruno has advanced all that was ever brought
forward by all heathen philosophers, and by all heretics, ancient and
modern. A time for retractation was given, both before sentence and
after, which should be noted, as well for the wretched palliation which
it may afford, as for the additional proof it gives that opinions, and
opinions only, brought him to the stake. In this medley of charges the
Scriptures are a dream, while Adam, Eve, devils, and salvation are
truths, and the Saviour a deceiver. We have examined no work of Bruno
except the De Monade, etc., mentioned in the text. A strong though
strange theism runs through the whole, and Moses, Christ, the
Fathers, etc., are cited in a manner which excites no remark either way.
Among the versions of the cause of Bruno's death is atheism: but
this word was very often used to denote rejection of revelation, not
merely in the common course of dispute, but by such writers, for
instance, as Brucker[71]
and Morhof.[72] Thus Morhof
says of the De Monade, etc., that it exhibits no manifest signs of
atheism. What he means by the word is clear enough, when he thus speaks
of a work which acknowledges God in hundreds of places, and rejects
opinions as blasphemous in several. The work of Bruno in which his
astronomical opinions are contained is De Monade, etc. (Frankfort,
1591, 8vo). He is the most thorough-going Copernican possible, and throws
out almost every opinion, true or false, which has ever been discussed by
astronomers, from the theory of innumerable inhabited worlds and systems
to that of the planetary nature of comets. Libri
(vol. iv)[73] has reprinted
the most striking part of his expressions of Copernican opinion."
THIS LEADS TO THE CHURCH QUESTION.
The Satanic doctrine that a church may employ force in aid of its
dogma is supposed to be obsolete in England, except as an individual
paradox; but this is difficult to settle. Opinions are much divided as to
what the Roman Church would do in England, if she could: any one who
doubts that she claims the right does not deserve an answer. When the
hopes of the Tractarian section of the High Church were in bloom, before
the most conspicuous intellects among them had transgressed their
ministry, that they might go to their own place, I had the curiosity to
see how far it could be ascertained whether they held the only doctrine
which makes me the personal enemy of a sect. I found in one of their
tracts the assumption of a right to persecute, modified by an asserted
conviction that force was not efficient. I cannot now say that this tract
was one of the celebrated ninety; and on looking at the collection I find
it so poorly furnished with contents, etc., that nothing but searching
through three thick volumes would decide. In these volumes I find,
augmenting as we go on, declarations about the character and power of
"the Church" which have a suspicious appearance. The suspicion is
increased by that curious piece of sophistry, No. 87, on religious
reserve. The queer paradoxes of that tract leave us in doubt as to
everything but this, that the church(man) is not bound to give his whole
counsel in all things, and not bound to say what the things are in which
he does not give it. It is likely enough that some of the "rights and
liberties" are but scantily described. There is now no fear; but the time
was when, if not fear, there might be a looking for of fear to come;
nobody could then be so sure as we now are that the lion was only
asleep. There was every appearance of a harder fight at hand than was
really found needful.
Among other exquisite quirks of interpretation in the No. 87 above
mentioned is the following. God himself employs reserve; he is said to be
decked with light as with a garment (the old or prayer-book version of
Psalm civ. 2). To an ordinary apprehension this would be a strong image
of display, manifestation, revelation; but there is something more. "Does
not a garment veil in some measure that which it clothes? Is not that
very light concealment?"
This No. 87, admitted into a series, fixes upon the managers of the
series, who permitted its introduction, a strong presumption of that
underhand intent with which they were charged. At the same time it is
honorable to our liberty that this series could be published: though its
promoters were greatly shocked when the Essayists and Bishop Colenso[74] took a swing on the other
side. When No. 90 was under discussion, Dr. Maitland,[75] the librarian at Lambeth, asked
Archbishop Howley[76] a
question about No. 89. "I did not so much as know there was a No.
89," was the answer. I am almost sure I have seen this in print, and
quite sure that Dr. Maitland told it to me. It is creditable that there
was so much freedom; but No. 90 was too bad, and was stopped.
The Tractarian mania has now (October 1866) settled down into a
chronic vestment disease, complicated with fits of transubstantiation,
which has taken the name of Ritualism. The common sense of our
national character will not put up with a continuance of this grotesque
folly; millinery in all its branches will at last be advertised only over
the proper shops. I am told that the Ritualists give short and practical
sermons; if so, they may do good in the end. The English Establishment
has always contained those who want an excitement; the New Testament, in
its plain meaning, can do little for them. Since the Revolution,
Jacobitism, Wesleyanism, Evangelicism, Puseyism,[77] and Ritualism, have come on in turn,
and have furnished hot water for those who could not wash without it. If
the Ritualists should succeed in substituting short and practical
teaching for the high-spiced lectures of the doctrinalists, they will be
remembered with praise. John the Baptist would perhaps not have brought
all Jerusalem out into the wilderness by his plain and good sermons: it
was the camel's hair and the locusts which got him a congregation, and
which, perhaps, added force to his precepts. When at school I heard a
dialogue, between an usher and the man who cleaned the shoes, about Mr.
——, a minister, a very corporate body with due area of
waistcoat. "He is a man of great erudition," said the first. "Ah, yes
sir," said Joe; "any one can see that who looks at that silk
waistcoat."]
OF THOMAS GEPHYRANDER SALICETUS.
[When I said at the outset that I had only taken books from my own
store, I should have added that I did not make any search for information
given as part of a work. Had I looked through all my books,
I might have made some curious additions. For instance, in Schott's
Magia Naturalis[78]
(vol. iii. pp. 756-778) is an account of the
quadrature of Gephyrauder, as he is misprinted in Montucla. He was
Thomas Gephyrander Salicetus; and he published two editions, in 1608 and
1609.[79] I never even
heard of a copy of either. His work is of the extreme of absurdity: he
makes a distinction between geometrical and arithmetical fractions, and
evolves theorems from it. More curious than his quadrature is his name;
what are we to make of it? If a German, he is probably a German form of
Bridgeman. and Salicetus refers him to Weiden. But
Thomas was hardly a German Christian name of his time; of 526
German philosophers, physicians, lawyers, and theologians who were
biographed by Melchior Adam,[80] only two are of this name. Of these one
is Thomas Erastus,[81] the
physician whose theological writings against the Church as a separate
power have given the name of Erastians to those who follow his doctrine,
whether they have heard of him or not. Erastus is little known;
accordingly, some have supposed that he must be Erastus, the friend of
St. Paul and Timothy (Acts xix. 22; 2 Tim. iv. 20; Rom. xvi. 23), but
what this gentleman did to earn the character is not hinted at. Few words
would have done: Gaius (Rom. xvi. 23) has an immortality which many more
noted men have missed, given by John Bunyan, out of seven words of St.
Paul. I was once told that the Erastians got their name from
Blastus, and I could not solve bl = er: at last I
remembered that Blastus was a chamberlain[82] as well as Erastus; hence the
association which caused the mistake. The real heresiarch was
a physician who died in 1583; his heresy was promulgated in a work,
published immediately after his death by his widow, De
Excommunicatione Ecclesiastica. He denied the power of
excommunication on the principle above stated; and was answered by
Besa.[83] The work was
translated by Dr. R. Lee[84] (Edinb. 1844, 8vo). The other is Thomas
Grynæus,[85] a theologian,
nephew of Simon, who first printed Euclid in Greek; of him Adam says that
of works he published none, of learned sons four. If Gephyrander were a
Frenchman, his name is not so easily guessed at; but he must have been of
La Saussaye. The account given by Schott is taken from a certain Father
Philip Colbinus, who wrote against him.
In some manuscripts lately given to the Royal Society, David
Gregory,[86] who seems to
have seen Gephyrander's work, calls him Salicetus Westphalus,
which is probably on the title-page. But the only Weiden I can find is in
Bavaria. Murhard has both editions in his Catalogue, but had plainly
never seen the books: he gives the author as Thomas Gep. Hyandrus,
Salicettus Westphalus. Murhard is a very old referee of mine; but who the
non nominandus was to see Montucla's Gephyrander in
Murhard's Gep. Hyandrus, both writers being usually accurate?]
NAPIER ON REVELATIONS.
A plain discoverie of the whole Revelation of St. John ... whereunto
are annexed certain oracles of Sibylla.... Set Foorth by John Napeir L.
of Marchiston. London, 1611, 4to.[87]
The first edition was Edinburgh, 1593,[88] 4to. Napier[89] always believed that his great mission
was to upset the Pope, and that logarithms, and such things, were merely
episodes and relaxations. It is a pity that so many books have been
written about this matter, while Napier, as good as any, is forgotten and
unread. He is one of the first who gave us the six thousand years. "There
is a sentence of the house of Elias reserved in all ages, bearing these
words: The world shall stand six thousand years, and then it shall be
consumed by fire: two thousand yeares voide or without lawe, two thousand
yeares under the law, and two thousand yeares shall be the daies of the
Messias...."
I give Napier's parting salute: it is a killing dilemma:
"In summar conclusion, if thou o Rome aledges thyselfe
reformed, and to beleeue true Christianisme, then beleeue Saint
John the Disciple, whome Christ loued, publikely here in this
Reuelation proclaiming thy wracke, but if thou remain Ethnick in thy
priuate thoghts, beleeuing[90] the old Oracles of the Sibyls
reuerently keeped somtime in thy Capitol: then doth here this
Sibyll proclame also thy wracke. Repent therefore alwayes, in this
thy latter breath, as thou louest thine Eternall salvation.
Amen."
—Strange that Napier should not have seen that this appeal could
not succeed, unless the prophecies of the Apocalypse were no true
prophecies at all.
OF GILBERT'S DE MAGNETE.
De Magnete magneticisque corporibus, et de magno magnete tellure. By
William Gilbert. London, 1600, folio.—There is a second edition;
and a third, according to Watt.[91]
Of the great work on the magnet there is no need to speak, though it
was a paradox in its day. The posthumous work of Gilbert, "De Mundo
nostro sublunari philosophia nova" (Amsterdam, 1651, 4to)[92] is, as the title indicates, confined to
the physics of the globe and its atmosphere. It has never excited
attention: I should hope it would be examined with our present
lights.
OF GIOVANNI BATISTA PORTA.
Elementorum Curvilineorium Libri tres. By John Baptista Porta. Rome,
1610, 4to.[93]
This is a ridiculous attempt, which defies description, except that it
is all about lunules. Porta was a voluminous writer. His printer
announces fourteen works printed, and four to come, besides thirteen
plays printed, and eleven waiting. His name is, and will be, current in
treatises on physics for more reasons than one.
CATALDI ON THE QUADRATURE.
Trattato della quadratura del cerchio. Di Pietro Antonio Cataldi.
Bologna, 1612, folio.[94]
Rheticus,[95] Vieta, and
Cataldi are the three untiring computers of Germany, France, and Italy;
Napier in Scotland, and Briggs[96] in England, come just after them. This
work claims a place as beginning with the quadrature of Pellegrino
Borello[97] of Reggio, who
will have the circle to be exactly 3 diameters and 69/484 of a diameter.
Cataldi, taking Van Ceulen's approximation, works hard at the finding of
integers which nearly represent the ratio. He had not then the
continued fraction, a mode of representation which he gave the
next year in his work on the square root. He has but twenty of Van
Ceulen's thirty places, which he takes from Clavius[98]: and any one might be puzzled to know
whence the Italians got the result; Van Ceulen, in 1612, not having been
translated from Dutch. But Clavius names his comrade Gruenberger, and
attributes the approximation to them jointly; "Lud. a Collen
et Chr. Gruenbergerus[99]
invenerunt," which he had no right to do, unless, to his private
knowledge, Gruenberger had verified Van Ceulen. And Gruenberger only
handed over twenty of the places. But here is one instance, out of many,
of the polyglot character of the Jesuit body, and its advantages in
literature.
OF LANSBERGIUS.
Philippi Lausbergii Cyclometriæ Novæ Libri Duo. Middleburg, 1616,
4to.[100]
This is one of the legitimate quadratures, on which I shall here only
remark that by candlelight it is quadrature under difficulties, for all
the diagrams are in red ink.
A TEXT LEADING TO REMARKS ON PRESTER JOHN.
Recherches Curieuses des Mesures du Monde. By S. C. de V. Paris, 1626,
8vo (pp. 48).[101]
It is written by some Count for his son; and if all the French
nobility would have given their sons the same kind of instruction about
rank, the old French aristocracy would have been as prosperous at this
moment as the English peerage and squireage. I sent the tract to Capt.
Speke,[102] shortly after
his arrival in England, thinking he might like to see the old names of
the Ethiopian provinces. But I first made a copy of all that relates to
Prester John,[103]
himself a paradox. The tract contains, inter alia, an account of
the four empires; of the great Turk, the great Tartar, the great Sophy,
and the great Prester John. This word great (grand), which
was long used in the phrase "the great Turk," is a generic adjunct to an
emperor. Of the Tartars it is said that "c'est vne nation prophane et
barbaresque, sale et vilaine, qui mangent la chair demie cruë, qui
boiuent du laict de jument, et qui n'vsent de nappes et seruiettes que
pour essuyer leurs bouches et leurs mains."[104] Many persons have heard of Prester
John, and have a very indistinct idea of him. I give all that is said
about him, since the recent discussions about the Nile may give an
interest to the old notions of geography.
"Le grand Prestre Jean qui est le quatriesme en rang, est Empereur
d'Ethiopie, et des Abyssins, et se vante d'estre issu de la race de
Dauid, comme estant descendu de la Royne de Saba, Royne d'Ethiopie,
laquelle estant venuë en Hierusalem pour voir la sagesse de Salomon,
enuiron l'an du monde 2952, s'en retourna grosse d'vn fils qu'ils nomment
Moylech, duquel ils disent estre descendus en ligne directe. Et ainsi il
se glorifie d'estre le plus ancien Monarque de la terre, disant que son
Empire a duré plus de trois mil ans, ce que nul autre Empire ne peut
dire. Aussi met-il en ses tiltres ce qui s'ensuit: Nous, N. Souuerain en
mes Royaumes, vniquement aymé de Dieu, colomne de la foy, sorty de la
race de Inda, etc. Les limites de cet Empire touchent à la mer Rouge, et
aux montagnes d'Azuma vers l'Orient, et du costé de l'Occident, il est
borné du fleuue du Nil, qui le separe de la Nubie, vers le Septentrion il
a l'Ægypte, et au Midy les Royaumes de Congo, et de Mozambique, sa
longueur contenant quarante degré, qui font mille vingt cinq lieuës, et
ce depuis Congo ou Mozambique qui sont au Midy, iusqu'en Ægypte qui est
au Septentrion, et sa largeur contenant depuis le Nil qui est à
l'Occident, iusqu'aux montagnes d'Azuma, qui sont à l'Orient, sept cens
vingt cinq lieues, qui font vingt neuf degrez. Cét empire a sous soy
trente grandes Prouinces, sçavoir, Medra, Gaga, Alchy, Cedalon, Mantro,
Finazam, Barnaquez, Ambiam, Fungy, Angoté, Cigremaon, Gorga, Cafatez,
Zastanla, Zeth, Barly, Belangana, Tygra, Gorgany, Barganaza, d'Ancut,
Dargaly, Ambiacatina, Caracogly, Amara, Maon (sic), Guegiera,
Bally, Dobora et Macheda. Toutes ces Prouinces cy dessus sont situées
iustement sous la ligne equinoxiale, entres les Tropiques de Capricorne,
et de Cancer. Mais elles s'approchent de nostre Tropique, de deux cens
cinquante lieuës plus qu'elles ne font de l'autre Tropique. Ce mot de
Prestre Jean signifie grand Seigneur, et n'est pas Prestre comme
plusieurs pense, il a esté tousiours Chrestien, mais souuent
Schismatique: maintenant il est Catholique, et reconnaist le Pape pour
Souuerain Pontife. I'ay veu quelqu'vn des ses Euesques, estant en
Hierusalem, auec lequel i'ay conferé souuent par le moyen de nostre
trucheman: il estoit d'vn port graue et serieux, succiur (sic) en
son parler, mais subtil à merueilles en tout ce qu'il disoit. Il prenoit
grand plaisir au recit que je luy faisais de nos belles ceremonies, et de
la grauité de nos Prelats en leurs habits Pontificaux, et autres choses
que je laisse pour dire, que l'Ethiopien est ioyoux et gaillard, ne
ressemblant en rien a la saleté du Tartare, ny à l'affreux regard du
miserable Arabe, mais ils sont fins et cauteleux, et ne se fient en
personne, soupçonneux à merueilles, et fort devotieux, ils ne sont du
tout noirs comme l'on croit, i'entens parler de ceux qui ne sont pas sous
la ligne Equinoxiale, ny trop proches d'icelle, car ceux qui
sont dessous sont les Mores que nous voyons."[105]
It will be observed that the author speaks of his conversation with an
Ethiopian bishop, about that bishop's sovereign. Something must have
passed between the two which satisfied the writer that the bishop
acknowledged his own sovereign under some title answering to Prester
John.
CONCERNING A TRACT BY FIENUS.
De Cometa anni 1618 dissertationes Thomæ Fieni[106] et Liberti Fromondi[107] ... Equidem Thomæ Fieni epistolica
quæstio, An verum sit Cœlum moveri et Terram quiescere? London,
1670, 8vo.
This tract of Fienus against the motion of the earth is a reprint of
one published in 1619.[108] I have given an account of it as a
good summary of arguments of the time, in the Companion to the
Almanac for 1836.
ON SNELL'S WORK.
Willebrordi Snellii. R. F. Cyclometricus. Leyden, 1621, 4to.
This is a celebrated work on the approximative quadrature, which,
having the suspicious word cyclometricus, must be noticed here for
distinction.[109]
ON BACON'S NOVUM ORGANUM.
1620. In this year, Francis Bacon[110] published his Novum Organum,[111] which was long held in
England—but not until the last century—to be the work which
taught Newton and all his successors how to philosophize. That Newton
never mentions Bacon, nor alludes in any way to his works, passed for
nothing. Here and there a paradoxer ventured not to find all this
teaching in Bacon, but he was pronounced blind. In our day it begins to
be seen that, great as Bacon was, and great as his book really is, he is
not the philosophical father of modern discovery.
But old prepossession will find reason for anything. A learned friend
of mine wrote to me that he had discovered proof that Newton owned Bacon
for his master: the proof was that Newton, in some of his earlier
writings, used the phrase experimentum crucis, which is
Bacon's. Newton may have read some of Bacon, though no proof of it
appears. I have a dim idea that I once saw the two words attributed to
the alchemists: if so, there is another explanation; for Newton was
deeply read in the alchemists.
I subjoin a review which I wrote of the splendid edition of Bacon by
Spedding,[112] Ellis,[113] and Heath.[114] All the opinions
therein expressed had been formed by me long before: most of the
materials were collected for another purpose.
The Works of Francis Bacon. Edited by James Spedding, R. Leslie Ellis,
and Douglas D. Heath. 5 vols.[115]
No knowledge of nature without experiment and observation: so said
Aristotle, so said Bacon, so acted Copernicus, Tycho Brahé,[116] Gilbert, Kepler,
Galileo, Harvey, etc., before Bacon wrote.[117] No derived knowledge until
experiment and observation are concluded: so said Bacon, and no one else.
We do not mean to say that he laid down his principle in these words, or
that he carried it to the utmost extreme: we mean that Bacon's ruling
idea was the collection of enormous masses of facts, and
then digested processes of arrangement and elimination, so artistically
contrived, that a man of common intelligence, without any unusual
sagacity, should be able to announce the truth sought for. Let Bacon
speak for himself, in his editor's English:
"But the course I propose for the discovery of sciences is such as
leaves but little to the acuteness and strength of wits, but places all
wits and understandings nearly on a level. For, as in the drawing of a
straight line or a perfect circle, much depends on the steadiness and
practice of the hand, if it be done by aim of hand only, but if with the
aid of rule or compass little or nothing, so it is exactly with my
plan.... For my way of discovering sciences goes far to level men's wits,
and leaves but little to individual excellence; because it performs
everything by the surest rules and demonstrations."
To show that we do not strain Bacon's meaning, we add what is said by
Hooke,[118] whom we have
already mentioned as his professed disciple, and, we believe, his only
disciple of the day of Newton. We must, however, remind the reader that
Hooke was very little of a mathematician, and spoke of algebra from his
own idea of what others had told him:
"The intellect is not to be suffered to act without its helps, but is
continually to be assisted by some method or engine, which shall be as a
guide to regulate its actions, so as that it shall not be able to act
amiss. Of this engine, no man except the incomparable Verulam hath had
any thoughts and he indeed hath promoted it to a very good pitch; but
there is yet somewhat more to be added, which he seemed to want time to
complete. By this, as by that art of algebra in geometry, 'twill be very
easy to proceed in any natural inquiry, regularly and certainly.... For
as 'tis very hard for the most acute wit to find out any difficult
problem in geometry without the help of algebra ... and altogether as
easy for the meanest capacity acting by that method to complete and
perfect it, so will it be in the inquiry after natural knowledge."
Bacon did not live to mature the whole of this plan. Are we really to
believe that if he had completed the Instauratio we who write
this—and who feel ourselves growing bigger as we write
it—should have been on a level with Newton in physical discovery?
Bacon asks this belief of us, and does not get it. But it may be said,
Your business is with what he did leave, and with its
consequences. Be it so. Mr. Ellis says: "That his method is impracticable
cannot, I think, be denied, if we reflect not only that it never has
produced any result, but also that the process by which scientific truths
have been established cannot be so presented as even to appear to be in
accordance with it." That this is very true is well known to all who have
studied the history of discovery: those who deny it are bound to
establish either that some great discovery has been made by Bacon's
method—we mean by the part peculiar to Bacon—or, better
still, to show that some new discovery can be made, by actually making
it. No general talk about induction: no reliance upon the mere
fact that certain experiments or observations have been made; let us see
where Bacon's induction has been actually used or can be used.
Mere induction, enumeratio simplex, is spoken of by himself with
contempt, as utterly incompetent. For Bacon knew well that a thousand
instances may be contradicted by the thousand and first: so that no
enumeration of instances, however large, is "sure demonstration," so long
any are left.
The immortal Harvey, who was inventing—we use the word in
its old sense—the circulation of the blood, while Bacon was in the
full flow of thought upon his system, may be trusted to say whether, when
the system appeared, he found any likeness in it to his own processes, or
what would have been any help to him, if he had waited for the Novum
Organum. He said of Bacon, "He writes philosophy like a Lord
Chancellor." This has been generally supposed to be only a sneer at the
sutor ultra crepidam; but we cannot help suspecting that there was
more intended by it. To us, Bacon is eminently the philosopher of
error prevented, not of progress facilitated. When we throw
off the idea of being led right, and betake ourselves to that of
being kept from going wrong, we read his writings with a sense of
their usefulness, his genius, and their probable effect upon purely
experimental science, which we can be conscious of upon no other
supposition. It amuses us to have to add that the part of Aristotle's
logic of which he saw the value was the book on refutation of
fallacies. Now is this not the notion of things to which the bias of
a practised lawyer might lead him? In the case which is before the Court,
generally speaking, truth lurks somewhere about the facts, and the
elimination of all error will show it in the residuum. The two senses of
the word law come in so as to look almost like a play upon words.
The judge can apply the law so soon as the facts are settled: the
physical philosopher has to deduce the law from the facts. Wait, says the
judge, until the facts are determined: did the prisoner take the goods
with felonious intent? did the defendant give what amounts to a warranty?
or the like. Wait, says Bacon, until all the facts, or all the obtainable
facts, are brought in: apply my rules of separation to the facts, and the
result shall come out as easily as by ruler and compasses. We think it
possible that Harvey might allude to the legal character of Bacon's
notions: we can hardly conceive so acute a man, after seeing what manner
of writer Bacon was, meaning only that he was a lawyer and had better
stick to his business. We do ourselves believe that Bacon's philosophy
more resembles the action of mind of a
common-law judge—not a Chancellor—than that of the physical
inquirers who have been supposed to follow in his steps. It seems to us
that Bacon's argument is, there can be nothing of law but what must be
either perceptible, or mechanically deducible, when all the results of
law, as exhibited in phenomena, are before us. Now the truth is, that the
physical philosopher has frequently to conceive law which never was in
his previous thought—to educe the unknown, not to choose among the
known. Physical discovery would be very easy work if the inquirer could
lay down his this, his that, and his t'other, and say, "Now, one of these
it must be; let us proceed to try which." Often has he done this, and
failed; often has the truth turned out to be neither this, that, nor
t'other. Bacon seems to us to think that the philosopher is a judge who
has to choose, upon ascertained facts, which of known statutes is to rule
the decision: he appears to us more like a person who is to write the
statute-book, with no guide except the cases and decisions presented in
all their confusion and all their conflict.
Let us take the well-known first aphorism of the Novum
Organum:
"Man being the servant and interpreter of nature, can do and
understand so much, and so much only, as he has observed in fact or in
thought of the course of nature: beyond this he neither knows anything
nor can do anything."
This aphorism is placed by Sir John Herschel[119] at the head of his Discourse on
the Study of Natural Philosophy: a book containing notions of
discovery far beyond any of which Bacon ever dreamed; and this because it
was written after discovery, instead of before. Sir John
Herschel, in his version, has avoided the translation of re vel mente
observaverit, and gives us only "by his observation of the order of
nature." In making this the opening of an excellent sermon, he has
imitated the theologians, who often employ the whole time of the
discourse in stuffing matter into the text, instead of drawing matter out
of it. By observation he (Herschel) means the whole course of
discovery, observation, hypothesis, deduction, comparison, etc. The type
of the Baconian philosopher as it stood in his mind, had been derived
from a noble example, his own father, William Herschel,[120] an inquirer whose processes would
have been held by Bacon to have been vague, insufficient, compounded of
chance work and sagacity, and too meagre of facts to deserve the name of
induction. In another work, his treatise on Astronomy,[121] Sir John Herschel, after noting that
a popular account can only place the reader on the threshold, proceeds to
speak as follows of all the higher departments of science. The italics
are his own:
"Admission to its sanctuary, and to the privileges and feelings of a
votary, is only to be gained by one means—sound and sufficient
knowledge of mathematics, the great instrument of all exact inquiry,
without which no man can ever make such advances in this or any other of
the higher departments of science as can entitle him to form an
independent opinion on any subject of discussion within their
range."
How is this? Man can know no more than he gets from observation, and
yet mathematics is the great instrument of all exact inquiry. Are the
results of mathematical deduction results of observation? We think it
likely that Sir John Herschel would reply that Bacon, in
coupling together observare re and observare mente, has
done what some wags said Newton afterwards did in his
study-door—cut a large hole of exit for the large cat, and a little
hole for the little cat.[122] But Bacon did no such thing: he never
included any deduction under observation. To mathematics he had a
dislike. He averred that logic and mathematics should be the handmaids,
not the mistresses, of philosophy. He meant that they should play a
subordinate and subsequent part in the dressing of the vast mass of facts
by which discovery was to be rendered equally accessible to Newton and to
us. Bacon himself was very ignorant of all that had been done by
mathematics; and, strange to say, he especially objected to astronomy
being handed over to the mathematicians. Leverrier and Adams, calculating
an unknown planet into visible existence by enormous heaps of algebra,
furnish the last comment of note on this specimen of the goodness of
Bacon's views. The following account of his knowledge of what had been
done in his own day or before it, is Mr. Spedding's collection of casual
remarks in Mr. Ellis's several prefaces:
"Though he paid great attention to astronomy, discussed carefully the
methods in which it ought to be studied, constructed for the satisfaction
of his own mind an elaborate theory of the heavens, and listened eagerly
for the news from the stars brought by Galileo's telescope, he appears to
have been utterly ignorant of the discoveries which had just been made by
Kepler's calculations. Though he complained in 1623 of the want of
compendious methods for facilitating arithmetical computations,
especially with regard to the doctrine of Series, and fully recognized
the importance of them as an aid to physical inquiries—he does not
say a word about Napier's Logarithms, which had been published only nine
years before and reprinted more than once in the interval. He complained
that no considerable advance had made in geometry beyond Euclid, without
taking any notice of what had been done by Archimedes and Apollonius. He
saw the importance of determining accurately the specific gravity of
different substances, and himself attempted to form a table of them by a
rude process of his own, without knowing of the more scientific though
still imperfect methods previously employed by Archimedes, Ghetaldus,[123] and Porta. He speaks
of the εὕρηκα of Archimedes in a
manner which implies that he did not clearly apprehend either the nature
of the problem to be solved or the principles upon which the solution
depended. In reviewing the progress of mechanics, he makes no mention of
Archimedes himself, or of Stevinus,[124] Galileo, Guldinus,[125] or Ghetaldus. He makes no allusion to
the theory of equilibrium. He observes that a ball of one pound weight
will fall nearly as fast through the air as a ball of two, without
alluding to the theory of the acceleration of falling bodies, which had
been made known by Galileo more than thirty years before. He proposes an
inquiry with regard to the lever—namely, whether in a balance with
arms of different length but equal weight the distance from the fulcrum
has any effect upon the inclination,—though the theory of the lever
was as well understood in his own time as it is now. In making an
experiment of his own to ascertain the cause of the
motion of a windmill, he overlooks an obvious circumstance which makes
the experiment inconclusive, and an equally obvious variation of the same
experiment which would have shown him that his theory was false. He
speaks of the poles of the earth as fixed, in a manner which seems to
imply that he was not acquainted with the precession of the equinoxes;
and in another place, of the north pole being above and the south pole
below, as a reason why in our hemisphere the north winds predominate over
the south."
Much of this was known before, but such a summary of Bacon's want of
knowledge of the science of his own time was never yet collected in one
place. We may add, that Bacon seems to have been as ignorant of
Wright's[126] memorable
addition to the resources of navigation as of Napier's addition to the
means of calculation. Mathematics was beginning to be the great
instrument of exact inquiry: Bacon threw the science aside, from
ignorance, just at the time when his enormous sagacity, applied to
knowledge, would have made him see the part it was to play. If Newton had
taken Bacon for his master, not he, but somebody else, would have been
Newton.[127]
ON METEOROLOGICAL OBSERVATORIES.
There is an attempt at induction going on, which has yielded little or
no fruit, the observations made in the meteorological observatories. This
attempt is carried on in a manner which would have caused Bacon to dance
for joy; for he lived in times when Chancellors did dance. Russia, says M.
Biot,[128] is covered by
an army of meteorographs, with generals, high officers, subalterns, and
privates with fixed and defined duties of observation. Other countries
have also their systematic observations. And what has come of it?
Nothing, says M. Biot, and nothing will ever come of it; the veteran
mathematician and experimental philosopher declares, as does Mr. Ellis,
that no single branch of science has ever been fruitfully explored in
this way. There is no special object, he says. Any one would
suppose that M. Biot's opinion, given to the French Government upon the
proposal to construct meteorological observatories in Algeria (Comptes
Rendus, vol. xli, Dec. 31, 1855), was written to support the mythical
Bacon, modern physics, against the real Bacon of the Novum
Organum. There is no special object. In these words lies the
difference between the two methods.
[In the report to the Greenwich Board of Visitors for 1867 Mr. Airy,[129] speaking of the
increase of meteorological observatories, remarks, "Whether the effect of
this movement will be that millions of useless observations will be added
to the millions that already exist, or whether something may be expected
to result which will lead to a meteorological theory, I cannot hazard a
conjecture." This is a conjecture, and a very obvious one: if Mr.
Airy would have given 2-3/4d. for the chance of a meteorological
theory formed by masses of observations, he would never have said what I
have quoted.]
BASIS OF MODERN DISCOVERY.
Modern discoveries have not been made by large collections of facts,
with subsequent discussion, separation, and resulting deduction of a
truth thus rendered perceptible. A few facts have suggested an
hypothesis, which means a supposition, proper to explain
them. The necessary results of this supposition are worked out, and then,
and not till then, other facts are examined to see if these ulterior
results are found in nature. The trial of the hypothesis is the
special object: prior to which, hypothesis must have been started,
not by rule, but by that sagacity of which no description can be given,
precisely because the very owners of it do not act under laws perceptible
to themselves.[130] The
inventor of hypothesis, if pressed to explain his method, must answer as
did Zerah Colburn,[131]
when asked for his mode of instantaneous calculation. When the poor boy
had been bothered for some time in this manner, he cried out in a huff,
"God put it into my head, and I can't put it into yours."[132] Wrong hypotheses, rightly
worked from, have produced more useful results than unguided observation.
But this is not the Baconian plan. Charles the Second, when informed of
the state of navigation, founded a Baconian observatory at Greenwich, to
observe, observe, observe away at the moon, until her motions were known
sufficiently well to render her useful in guiding the seaman. And no
doubt Flamsteed's[133]
observations, twenty or thirty of them at least, were of signal use. But
how? A somewhat fanciful thinker, one Kepler, had hit upon the
approximate orbits of the planets by trying one hypothesis after another:
he found the ellipse, which the Platonists, well despised of
Bacon, and who would have despised him as heartily if they had known him,
had investigated and put ready to hand nearly 2000 years before.[134] The sun in the focus,
the motions of the planet more and more rapid as they approach the sun,
led Kepler—and Bacon would have reproved him for his
rashness—to imagine that a force residing in the sun might move the
planets, a force inversely as the distance. Bouillaud,[135] upon a fanciful analogy, rejected the
inverse distance, and, rejecting the force altogether,
declared that if such a thing there were, it would be as the inverse
square of the distance. Newton, ready prepared with the
mathematics of the subject, tried the fall of the moon towards the earth,
away from her tangent, and found that, as compared with the fall of a
stone, the law of the inverse square did hold for the moon. He deduced
the ellipse, he proceeded to deduce the effect of the disturbance of the
sun upon the moon, upon the assumed theory of universal
gravitation. He found result after result of his theory in conformity
with observed fact: and, by aid of Flamsteed's observations, which
amended what mathematicians call his constants, he constructed his
lunar theory. Had it not been for Newton, the whole dynasty of Greenwich
astronomers, from Flamsteed of happy memory, to Airy whom Heaven
preserve,[136] might have
worked away at nightly observation and daily reduction, without any
remarkable result: looking forward, as to a millennium, to the time when
any man of moderate intelligence was to see the whole explanation. What
are large collections of facts for? To make theories from, says
Bacon: to try ready-made theories by, says the history of
discovery: it's all the same, says the idolater: nonsense, say we!
Time and space run short: how odd it is that of the three leading
ideas of mechanics, time, space, and matter, the first two should always
fail a reviewer before the third. We might dwell upon many points,
especially if we attempted a more descriptive account of the valuable
edition before us. No one need imagine that the editors, by their
uncompromising attack upon the notion of Bacon's influence common even
among mathematicians and experimental philosophers, have lowered the
glory of the great man whom it was, many will think, their business to
defend through thick and thin. They have given a clearer notion of his
excellencies, and a better idea of the power
of his mind, than ever we saw given before. Such a correction as theirs
must have come, and soon, for as Hallam says—after noting that the
Novum Organum was never published separately in England,
Bacon has probably been more read in the last thirty years—now
forty—than in the two hundred years which preceded. He will now be
more read than ever he was. The history of the intellectual world is the
history of the worship of one idol after another. No sooner is it clear
that a Hercules has appeared among men, than all that imagination can
conceive of strength is attributed to him, and his labors are recorded in
the heavens. The time arrives when, as in the case of Aristotle, a new
deity is found, and the old one is consigned to shame and reproach. A
reaction may afterwards take place, and this is now happening in the case
of the Greek philosopher. The end of the process is, that the opposing
deities take their places, side by side, in a Pantheon dedicated not to
gods, but to heroes.
THE REAL VALUE OF BACON'S WORKS.
Passing over the success of Bacon's own endeavors to improve the
details of physical science, which was next to nothing, and of his method
as a whole, which has never been practised, we might say much of the good
influence of his writings. Sound wisdom, set in sparkling wit, must
instruct and amuse to the end of time: and, as against error, we repeat
that Bacon is soundly wise, so far as he goes. There is hardly a form of
human error within his scope which he did not detect, expose, and attach
to a satirical metaphor which never ceases to sting. He is largely
indebted to a very extensive reading; but the thoughts of others fall
into his text with such a close-fitting compactness that he can make even
the words of the Sacred Writers pass for his own. A saying of the prophet
Daniel, rather a hackneyed quotation in our day, Multi pertransibunt,
et augebitur scientia, stands in the title-page of the first edition
of
Montucla's History of Mathematics as a quotation from
Bacon—and it is not the only place in which this mistake occurs.
When the truth of the matter, as to Bacon's system, is fully recognized,
we have little fear that there will be a reaction against the man. First,
because Bacon will always live to speak for himself, for he will not
cease to be read: secondly, because those who seek the truth will find it
in the best edition of his works, and will be most ably led to know what
Bacon was, in the very books which first showed at large what he was
not.
THE CONGREGATION OF THE INDEX, ON COPERNICUS.
In this year (1620) appeared the corrections under which the
Congregation of the Index—i.e., the Committee of Cardinals which
superintended the Index of forbidden books—proposed to allow
the work of Copernicus to be read. I insert these conditions in full,
because they are often alluded to, and I know of no source of reference
accessible to a twentieth part of those who take interest in the
question.
By a decree of the Congregation of the Index, dated March 5, 1616, the
work of Copernicus, and another of Didacus Astunica,[137] are suspended donec
corrigantur, as teaching:
"Falsam illam doctrinam Pythagoricam, divinæ que Scripturæ omnino
adversantem, de mobilitate Terræ et immobilitate Solis."[138]
But a work of the Carmelite Foscarini[139] is:
"Omnino prohibendum atque damnandum," because "ostendere conatur
præfatam doctrinam ... consonam esse veritati et non adversari Sacræ
Scripturæ."[140]
Works which teach the false doctrine of the earth's motion are to be
corrected; those which declare the doctrine conformable to Scripture are
to be utterly prohibited.
In a "Monitum ad Nicolai Copernici lectorem, ejusque emendatio,
permissio, et correctio," dated 1620 without the month or day, permission
is given to reprint the work of Copernicus with certain alterations; and,
by implication, to read existing copies after correction in writing. In
the preamble the author is called nobilis astrologus; not a
compliment to his birth, which was humble, but to his fame. The
suspension was because:
"Sacræ Scripturæ, ejusque veræ et Catholicæ interpretationi
repugnantia (quod in homine Christiano minime tolerandum) non per
hypothesin tractare, sed ut verissima adstruere non
dubitat!"[141]
And the corrections relate:
"Locis in quibus non ex hypothesi, sed asserendo de situ
et motu Terræ disputat."[142]
That is, the earth's motion may be an hypothesis for elucidation of
the heavenly motions, but must not be asserted as a fact.
(In Pref. circa finem.) "Copernicus. Si fortasse erunt ματαιόλογοι,
qui cum omnium Mathematum ignari sint, tamen de illis judicium sibi
summunt, propter aliquem locum scripturæ, male ad suum propositum
detortum, ausi fuerint meum hoc institutum reprehendere ac insectari:
illos nihil moror adeo ut etiam illorum judicium tanquam temerarium
contemnam. Non enim obscurum est Lactantium, celebrem alioqui scriptorem,
sed Mathematicum parum, admodum pueriliter de forma terræ loqui, cum
deridet eos, qui terram globi formam habere prodiderunt. Itaque non debet
mirum videri studiosis, si qui tales nos etiam videbunt. Mathemata
Mathematicis scribuntur, quibus et hi nostri labores, si me non fallit
opinio, videbuntur etiam Reipub. ecclesiasticæ conducere aliquid....
Emend. Ibi si fortasse dele omnia, usque ad verbum hi
nostri labores et sic accommoda—Cœterum hi nostri
labores."[143]
All the allusion to Lactantius, who laughed at the notion of the earth
being round, which was afterwards found true, is to be struck out.
(Cap. 5. lib. i. p. 3) "Copernicus. Si tamen attentius rem
consideremus, videbitur hæc quæstio nondum absoluta, et ideireo minime
contemnenda. Emend. Si tamen attentius rem consideremus, nihil
refert an Terram in medio Mundi, an extra Medium existere, quoad
solvendas cœlestium motuum apparentias existimemus."[144]
We must not say the question is not yet settled, but only that it may
be settled either way, so far as mere explanation of the celestial
motions is concerned.
(Cap. 8. lib. i.) "Totum hoc caput potest expungi, quia ex professo
tractat de veritate motus Terræ, dum solvit veterum rationes probantes
ejus quietem. Cum tamen problematice videatur loqui; ut studiosis
satisfiat, seriesque et ordo libri integer maneat; emendetur ut infra."[145]
A chapter which seems to assert the motion should perhaps be expunged;
but it may perhaps be problematical; and, not to break up the book, must
be amended as below.
(p. 6.) "Copernicus. Cur ergo hesitamus adhuc, mobilitatem illi
formæ suæ a natura congruentem concedere, magisquam quod totus labatur
mundus, cujus finis ignoratur, scirique nequit, neque fateamur ipsius
cotidianæ revolutionis in cœlo apparentiam esse, et in terra
veritatem? Et hæc perinde se habere, ac si diceret Virgilianus Æneas:
Provehimur portu ... Emend. Cur ergo non possum mobilitatem illi
formæ suæ concedere, magisque quod totus labatur mundus, cujus finis
ignoratur scirique nequit, et quæ apparent in cœlo, perinde se
habere ac si ..."[146]
"Why should we hesitate to allow the earth's motion," must be altered
into "I cannot concede the earth's motion."
(p. 7.) "Copernicus. Addo etiam, quod satis absurdum videretur,
continenti sive locanti motum adscribi, et non potius contento et locato,
quod est terra. Emend. Addo etiam difficilius non esse contento et
locato, quod est Terra, motum adscribere, quam continenti."[147]
We must not say it is absurd to refuse motion to the contained
and located, and to give it to the containing and locating; say
that neither is more difficult than the other.
(p. 7.) "Copernicus. Vides ergo quod ex his omnibus probabilior
sit mobilitas Terræ, quam ejus quies, præsertim in cotidiana revolutione,
tanquam terræ maxime propria. Emend. Vides ... delendus est
usque ad finem capitis."[148]
Strike out the whole of the chapter from this to the end; it says that
the motion of the earth is the most probable hypothesis.
(Cap. 9. lib. i. p. 7.) "Copernicus. Cum igitur nihil prohibeat
mobilitatem Terræ, videndum nunc arbitror, an etiam plures illi motus
conveniant, ut possit una errantium syderum existimari. Emend. Cum
igitur Terram moveri assumpserim, videndum nunc arbitror, an etiam illi
plures possint convenire motus."[149]
We must not say that nothing prohibits the motion of the earth, only
that having assumed it, we may inquire whether our explanations
require several motions.
(Cap. 10. lib. i. p. 9.) "Copernicus. Non pudet nos fateri ...
hoc potius in mobilitate terræ verificari. Emend. Non pudet nos
assumere ... hoc consequenter in mobilitate verificari."[150]
(Cap. 10. lib. i. p. 10.) "Copernicus. Tanta nimirum est divina
hæc. Opt. Max. fabrica. Emend. Dele illa verba postrema."[151]
(Cap. ii. lib. i.[152]) "Copernicus. De triplici motu
telluris demonstratio. Emend. De hypothesi triplicis motus Terræ,
ejusque demonstratione."[153]
(Cap. 10. lib. iv. p. 122.[154]) "Copernicus. De magnitudine
horum trium siderum, Solis, Lunæ, et Terræ. Emend. Dele verba
horum trium siderum, quia terra non est sidus, ut facit eam
Copernicus."[155]
We must not say we are not ashamed to acknowledge;
assume is the word. We must not call this assumption a Divine
work. A chapter must not be headed demonstration, but
hypothesis. The earth must not be called a star; the word
implies motion.
It will be seen that it does not take much to reduce Copernicus to
pure hypothesis. No personal injury being done to the author—who
indeed had been 17 years out of reach—the treatment of his book is now
an excellent joke. It is obvious that the Cardinals of the Index were a
little ashamed of their position, and made a mere excuse of a few
corrections. Their mode of dealing with chap. 8, this problematice
videtur loqui, ut studiosis satisfiat,[156] is an excuse to avoid corrections.
But they struck out the stinging allusion to Lactantius[157] in the preface, little thinking,
honest men, for they really believed what they said—that the light
of Lactantius would grow dark before the brightness of their own.
THE CONVOCATION AT OXFORD EQUALLY AT FAULT.
1622. I make no reference to the case of Galileo, except this. I have
pointed out (Penny Cycl. Suppl. "Galileo"; Engl. Cycl.
"Motion of the Earth") that it is clear the absurdity was the act of the
Italian Inquisition—for the private and personal pleasure of
the Pope, who knew that the course he took would not commit him as
Pope—and not of the body which calls itself the
Church. Let the dirty proceeding have its right name. The Jesuit
Riccioli,[158] the
stoutest and most learned Anti-Copernican in Europe, and the Puritan
Wilkins, a strong Copernican and Pope-hater, are equally positive that
the Roman Church never pronounced any decision: and this in the
time immediately following the ridiculous proceeding of the Inquisition.
In like manner a decision of the Convocation of Oxford is not a law of
the English Church; which is fortunate, for that Convocation, in
1622, came to a decision quite as absurd, and a great deal more wicked than
the declaration against the motion of the earth. The second was a foolish
mistake; the first was a disgusting surrender of right feeling. The story
is told without disapprobation by Anthony Wood, who never exaggerated
anything against the university of which he is writing eulogistic
history.
In 1622, one William Knight[159] put forward in a sermon preached
before the University certain theses which, looking at the state of the
times, may have been improper and possibly of seditious intent. One of
them was that the bishop might excommunicate the civil magistrate: this
proposition the clerical body could not approve, and designated it by the
term erronea,[160]
the mildest going. But Knight also declared as follows:
"Subditis mere privatis, si Tyrannus tanquam latro aut stuprator in
ipsos faciat impetum, et ipsi nec potestatem ordinariam implorare, nec
alia ratione effugere periculum possint, in presenti periculo se et suos
contra tyrannum, sicut contra privatum grassatorem, defendere licet."[161]
That is, a man may defend his purse or a woman her honor, against the
personal attack of a king, as against that of a private person, if no
other means of safety can be found. The Convocation sent Knight to
prison, declared the proposition "falsa, periculosa, et
impia," and enacted that all applicants for degrees should
subscribe this censure, and make oath that they would neither hold,
teach, nor defend Knight's opinions.
The thesis, in the form given, was unnecessary and improper. Though
strong opinions of the king's rights were advanced at the time, yet no
one ventured to say that, ministers and advisers apart, the king might
personally break the law; and we know that the first and only
attempt which his successor made brought on the crisis which cost him his
throne and his head. But the declaration that the proposition was
false far exceeds in all that is disreputable the decision of the
Inquisition against the earth's motion. We do not mention this little
matter in England. Knight was a Puritan, and Neal[162] gives a short account of his sermon.
From comparison with Wood,[163] I judge that the theses, as given,
were not Knight's words, but the digest which it was customary to make in
criminal proceedings against opinion. This heightens the joke, for it
appears that the qualifiers of the Convocation took pains to present
their condemnation of Knight in the terms which would most unequivocally
make their censure condemn themselves. This proceeding took place in the
interval between the two proceedings against Galileo: it is left
undetermined whether we must say pot-kettle-pot or kettle-pot-kettle.
Liberti Fromondi.... Ant-Aristarchus, sive orbis terræ immobilis.
Antwerp, 1631, 8vo.[164]
This book contains the evidence of an ardent opponent of Galileo to
the fact, that Roman Catholics of the day did not consider the decree of
the Index or of the Inquisition as a declaration of their
Church. Fromond would have been glad to say as much, and tries to
come near it, but confesses he must abstain. See Penny Cyclop.
Suppl. "Galileo," and Eng. Cycl. "Motion of the Earth." The
author of a celebrated article in the Dublin Review, in defence of
the Church of Rome, seeing that Drinkwater
Bethune[165] makes use of
the authority of Fromondus, but for another purpose, sneers at him for
bringing up a "musty old Professor." If he had known Fromondus, and used
him he would have helped his own case, which is very meagre for want of
knowledge.[166]
Advis à Monseigneur l'eminentissime Cardinal Duc de Richelieu, sur la
Proposition faicte par le Sieur Morin pour l'invention des longitudes.
Paris, 1634, 8vo.[167]
This is the Official Report of the Commissioners appointed by the
Cardinal, of whom Pascal is the one now best known, to consider Morin's
plan. See the full account in Delambre, Hist. Astr. Mod. ii. 236,
etc.
THE METIUS APPROXIMATION.
Arithmetica et Geometria practica. By Adrian Metius. Leyden, 1640,
4to.[168]
This book contains the celebrated approximation guessed at by
his father, Peter Metius,[169] namely that the diameter is to the
circumference as 113 to 355. The error is at the rate of about a foot in 2,000
miles. Peter Metius, having his attention called to the subject by the
false quadrature of Duchesne, found that the ratio lay between 333/106
and 377/120. He then took the liberty of taking the mean of both
numerators and denominators, giving 355/113. He had no right to presume
that this mean was better than either of the extremes; nor does it appear
positively that he did so. He published nothing; but his son Adrian,[170] when Van Ceulen's work
showed how near his father's result came to the truth, first made it
known in the work above. (See Eng. Cyclop., art.
"Quadrature.")
ON INHABITABLE PLANETS.
A discourse concerning a new world and another planet, in two books.
London, 1640, 8vo.[171]
Cosmotheoros: or conjectures concerning the planetary worlds and their
inhabitants. Written in Latin, by Christianus Huyghens. This translation
was first published in 1698. Glasgow, 1757, 8vo. [The original is also of
1698.][172]
The first work is by Bishop Wilkins, being the third edition, [first
in 1638] of the first book, "That the Moon may be a Planet"; and the
first edition of the second work, "That the Earth may be
a Planet." [See more under the reprint of 1802.] Whether other planets be
inhabited or not, that is, crowded with organisations some of them having
consciousness, is not for me to decide; but I should be much surprised
if, on going to one of them, I should find it otherwise. The whole
dispute tacitly assumes that, if the stars and planets be inhabited, it
must be by things of which we can form some idea. But for aught we know,
what number of such bodies there are, so many organisms may there be, of
which we have no way of thinking nor of speaking. This is seldom
remembered. In like manner it is usually forgotten that the matter
of other planets may be of different chemistry from ours. There may be no
oxygen and hydrogen in Jupiter, which may have gens of its own.[173] But this must not be
said: it would limit the omniscience of the a priori school of
physical inquirers, the larger half of the whole, and would be very
unphilosophical. Nine-tenths of my best paradoxers come out from
among this larger half, because they are just a little more than of it at
their entrance.
There was a discussion on the subject some years ago, which began
with
The plurality of worlds: an Essay. London, 1853, 8vo. [By Dr. Wm.
Whewell, Master of Trinity College, Cambridge]. A dialogue on the
plurality of worlds, being a supplement to the Essay on that subject.
[First found in the second edition, 1854; removed to the end in
subsequent editions, and separate copies issued.][174]
A work of skeptical character, insisting on analogies which prohibit
the positive conclusion that the planets, stars, etc., are what we should
call inhabited worlds. It produced several works and a
large amount of controversy in reviews. The last predecessor of whom I
know was
Plurality of Worlds.... By Alexander Maxwell. Second Edition. London,
1820, 8vo.
This work is directed against the plurality by an author who does not
admit modern astronomy. It was occasioned by Dr. Chalmers's[175] celebrated discourses
on religion in connection with astronomy. The notes contain many
citations on the gravity controversy, from authors now very little read:
and this is its present value. I find no mention of Maxwell, not even in
Watt.[176] He
communicated with mankind without the medium of a publisher; and, from
Vieta till now, this method has always been favorable to loss of
books.
A correspondent informs me that Alex. Maxwell, who wrote on the
plurality of worlds, in 1820, was a law-bookseller and publisher
(probably his own publisher) in Bell Yard. He had peculiar notions, which
he was fond of discussing with his customers. He was a bit of a
Swedenborgian.
INHABITED PLANETS IN FICTION.
There is a class of hypothetical creations which do not belong to my
subject, because they are acknowledged to be fictions, as those of
Lucian,[177] Rabelais,[178] Swift, Francis Godwin,[179] Voltaire, etc. All who have more
positive notions as to either the composition or organization of other
worlds, than the reasonable conclusion that our Architect must be quite
able to construct millions of other buildings on millions of other plans,
ought to rank with the writers just mentioned, in all but self-knowledge.
Of every one of their systems I say, as the Irish Bishop said of
Gulliver's book,—I don't believe half of it. Huyghens had been
preceded by Fontenelle,[180] who attracted more attention.
Huyghens is very fanciful and very positive; but he gives a true account
of his method. "But since there's no hopes of a Mercury to carry us such
a journey, we shall e'en be contented with what's in our power: we shall
suppose ourselves there...." And yet he says, "We have proved that they
live in societies, have hands and feet...." Kircher[181] had gone to the stars before him, but
would not find any life in them, either animal or vegetable.
The question of the inhabitants of a particular planet is one which
has truth on one side or the other: either there are some inhabitants, or
there are none. Fortunately, it is of no consequence which is true. But
there are many cases where the balance is equally one of truth and
falsehood, in which the choice is a matter of importance. My work
selects, for the most part, sins against demonstration: but the world is
full of questions of fact or opinion, in which a struggling minority will
become a majority, or else will be gradually annihilated: and each of the
cases subdivides into results of good, and results of evil. What is to be
done?
"Periculosum est credere et non credere;
Hippolitus obiit quia novercæ creditum est;
Cassandræ quia non creditum ruit Ilium:
Ergo exploranda est veritas multum prius
Quam stulta prove judicet sententia."[182]
Nova Demonstratio immobilitatis terræ petita ex virtute magnetica. By
Jacobus Grandamicus. Flexiae (La Flèche), 1645, 4to.[183]
No magnetic body can move about its poles: the earth is a magnetic
body, therefore, etc. The iron and its magnetism are typical of two
natures in one person; so it is said, "Si exaltatus fuero à terra, omnia
traham ad me ipsum."[184]
A VENETIAN BUDGET OF PARADOXES.
Le glorie degli incogniti, o vero gli huomini illustri dell' accademia
de' signori incogniti di Venetia. Venice, 1647, 4to.
This work is somewhat like a part of my own: it is a budget of
Venetian nobodies who wished to be somebodies; but paradox is not the
only means employed. It is of a serio-comic character, gives genuine
portraits in copperplate, and grave lists of works; but satirical
accounts. The astrologer Andrew Argoli[185] is there, and his son; both of whom,
with some of the others, have place in modern works on biography.
Argoli's discovery that logarithms facilitate easy processes, but
increase the labor of difficult ones, is worth recording.
Controversiæ de vera circuli mensura ... inter ... C. S. Longomontanum
et Jo. Pellium.[186]
Amsterdam, 1647, 4to.
Longomontanus,[187] a
Danish astronomer of merit, squared the circle in 1644: he found out that
the diameter 43 gives the square root of 18252 for the circumference;
which gives 3.14185... for the ratio. Pell answered him, and being a kind
of circulating medium, managed to engage in the controversy names known
and unknown, as Roberval, Hobbes, Carcavi, Lord Charles Cavendish,
Pallieur, Mersenne, Tassius, Baron Wolzogen, Descartes, Cavalieri and
Golius.[188] Among them,
of course, Longomontanus was made mincemeat: but he is
said to have insisted on the discovery of his epitaph.[189]
THE CIRCULATING MEDIA OF MATHEMATICS.
The great circulating mediums, who wrote to everybody, heard from
everybody, and sent extracts to everybody else, have been Father
Mersenne, John Collins, and the late Professor Schumacher: all "late" no
doubt, but only the last recent enough to be so styled. If M.C.S. should
ever again stand for "Member of the Corresponding Society," it should
raise an acrostic thought of the three. There is an allusion to
Mersenne's occupation in Hobbes's reply to him. He wanted to give Hobbes,
who was very ill at Paris, the Roman Eucharist: but Hobbes said, "I have
settled all that long ago; when did you hear from Gassendi?" We are
reminded of William's answer to Burnet. John Collins disseminated Newton,
among others. Schumacher ought to have been called the postmaster-general
of astronomy, as Collins was called the attorney-general of
mathematics.[190]
THE SYMPATHETIC POWDER.
A late discourse ... by Sir Kenelme Digby.... Rendered into English by
R. White. London, 1658, 12mo.
On this work see Notes and Queries, 2d series, vii. 231, 299,
445, viii. 190. It contains the celebrated sympathetic powder. I am still
in much doubt as to the connection of Digby with this tract.[191] Without entering on
the subject here, I observe that in Birch's History of the Royal
Society,[192] to
which both Digby and White belonged, Digby, though he brought many things
before the Society, never mentioned the powder, which is connected only
with the names of Evelyn[193] and Sir Gilbert Talbot.[194] The sympathetic powder
was that which cured by anointing the weapon with its salve instead of
the wound. I have long been convinced that it was efficacious. The
directions were to keep the wound clean and cool, and to take care of
diet, rubbing the salve on the knife or sword.[195] If we remember the dreadful notions
upon drugs which prevailed, both as to quantity and quality, we shall
readily see that any way of not dressing the wound would have been
useful. If the physicians had taken the hint, had been careful of diet
etc., and had poured the little barrels of medicine down the throat of a
practicable doll, they would have had their magical cures as well
as the surgeons.[196]
Matters are much improved now; the quantity of medicine given, even by
orthodox physicians, would have been called infinitesimal by their
professional ancestors. Accordingly, the College of Physicians has a
right to abandon its motto, which is Ars longa, vita brevis,
meaning Practice is long, so life is short.
HOBBES AS A MATHEMATICIAN.
Examinatio et emendatio Mathematicæ Hodiernæ. By Thomas Hobbes.
London, 1666, 4to.
In six dialogues: the sixth contains a quadrature of the circle.[197] But there is another
edition of this work, without place or date on the title-page, in which
the quadrature is omitted. This seems to be connected with the
publication of another quadrature, without date, but
about 1670, as may be judged from its professing to answer a tract of
Wallis, printed in 1669.[198] The title is "Quadratura circuli,
cubatio sphæræ, duplicatio cubi," 4to.[199] Hobbes, who began in 1655, was very
wrong in his quadrature; but, though not a Gregory St. Vincent,[200] he was not the
ignoramus in geometry that he is sometimes supposed. His writings,
erroneous as they are in many things, contain acute remarks on points of
principle. He is wronged by being coupled with Joseph Scaliger, as the
two great instances of men of letters who have come into geometry to help
the mathematicians out of their difficulty. I have never seen Scaliger's
quadrature,[201] except
in the answers of Adrianus Romanus,[202] Vieta and Clavius, and in the
extracts of Kastner.[203]
Scaliger had no right to such strong opponents: Erasmus or Bentley might
just as well have tried the problem, and either would have done much
better in any twenty minutes of his life.[204]
AN ESTIMATE OF SCALIGER.
Scaliger inspired some mathematicians with great respect for his
geometrical knowledge. Vieta, the first man of his time, who answered
him, had such regard for his opponent as made him conceal
Scaliger's name. Not that he is very respectful in his manner of
proceeding: the following dry quiz on his opponent's logic must have been
very cutting, being true. "In grammaticis, dare navibus Austros, et dare
naves Austris, sunt æque significantia. Sed in Geometricis, aliud est
adsumpsisse circulum BCD non esse majorem
triginta sex segmentis BCDF, aliud circulo
BCD non esse majora triginta sex segmenta BCDF. Illa adsumptiuncula vera est, hæc falsa."[205] Isaac Casaubon,[206] in one of his letters
to De Thou,[207] relates
that, he and another paying a visit to Vieta, the conversation fell upon
Scaliger, of whom the host said that he believed Scaliger was the only
man who perfectly understood mathematical writers, especially the Greek
ones: and that he thought more of Scaliger when wrong than of many others
when right; "pluris se Scaligerum vel errantem facere quam multos κατορθούντας."[208] This must have been
before Scaliger's quadrature (1594). There is an old story of some one
saying, "Mallem cum Scaligero errare, quam cum Clavio recte sapere."[209] This I cannot help
suspecting to have been a version of Vieta's speech with Clavius
satirically inserted, on account of the great hostility which Vieta
showed towards Clavius in the latter years of his life.
Montucla could not have read with care either Scaliger's quadrature or
Clavius's refutation. He gives the first a wrong date: he assures the
world that there is no question about Scaliger's quadrature being wrong,
in the eyes of geometers at least: and he states that Clavius mortified
him extremely by showing that it made the
circle less than its inscribed dodecagon, which is, of course, equivalent
to asserting that a straight line is not always the shortest distance
between two points. Did Clavius show this? No, it was Scaliger
himself who showed it, boasted of it, and declared it to be a "noble
paradox" that a theorem false in geometry is true in arithmetic; a thing,
he says with great triumph, not noticed by Archimedes himself! He says in
so many words that the periphery of the dodecagon is greater than that of
the circle; and that the more sides there are to the inscribed figure,
the more does it exceed the circle in which it is. And here are
the words, on the independent testimonies of Clavius and Kastner:
"Ambitus dodecagoni circulo inscribendi plus potest quam circuli
ambitus. Et quanto deinceps plurium laterum fuerit polygonum circulo
inscribendum, tanto plus poterit ambitus polygoni quam ambitus
circuli."[210]
There is much resemblance between Joseph Scaliger and William
Hamilton,[211] in a
certain impetuousity of character, and inaptitude to think of quantity.
Scaliger maintained that the arc of a circle is less than its chord in
arithmetic, though greater in geometry; Hamilton arrived at two
quantities which are identical, but the greater the one the less the
other. But, on the whole, I liken Hamilton rather to Julius than to
Joseph. On this last hero of literature I repeat Thomas Edwards,[212] who says that a man is
unlearned who, be his other knowledge what it may, does not understand the
subject he writes about. And now one of many instances in which
literature gives to literature character in science. Anthony Teissier,[213] the learned annotator
of De Thou's biographies, says of Finæus, "Il se vanta sans raison avoir
trouvé la quadrature du cercle; la gloire de cette admirable découverte
était réservée à Joseph Scalinger, comme l'a écrit Scévole de St.
Marthe."[214]
JOHN GRAUNT AS A PARADOXER.
Natural and Political Observations ... upon the Bills of Mortality. By
John Graunt, citizen of London. London, 1662, 4to.[215]
This is a celebrated book, the first great work upon mortality. But
the author, going ultra crepidam, has attributed to the motion of
the moon in her orbit all the tremors which she gets from a shaky
telescope.[216] But there
is another paradox about this book: the above absurd opinion is
attributed to that excellent mechanist, Sir William Petty, who passed his
days among the astronomers. Graunt did not write his own book! Anthony
Wood[217] hints that
Petty "assisted, or put into a way" his old benefactor: no doubt the two
friends talked the matter over many a time. Burnet and Pepys[218] state that Petty wrote
the book. It is enough for me that Graunt, whose honesty
was never impeached, uses the plainest incidental professions of
authorship throughout; that he was elected into the Royal Society because
he was the author; that Petty refers to him as author in scores of
places, and published an edition, as editor, after Graunt's death, with
Graunt's name of course. The note on Graunt in the Biographia
Britannica may be consulted; it seems to me decisive. Mr. C. B.
Hodge, an able actuary, has done the best that can be done on the other
side in the Assurance Magazine, viii. 234. If I may say what is in
my mind, without imputation of disrespect, I suspect some actuaries have
a bias: they would rather have Petty the greater for their Coryphæus than
Graunt the less.[219]
Pepys is an ordinary gossip: but Burnet's account has an animus which
is of a worse kind. He talks of "one Graunt, a Papist, under whose name
Sir William Petty[220]
published his observations on the bills of mortality." He then gives the
cock without a bull story of Graunt being a trustee of the New River
Company, and shutting up the cocks and carrying off their keys, just
before the fire of London, by which a supply of water was delayed.[221] It was one of the
first objections made to Burnet's work, that Graunt was not a
trustee at the time; and Maitland, the historian of London, ascertained
from the books of the Company that he was not admitted until twenty-three
days after the breaking out of the fire. Graunt's first admission to
the Company took place on the very day on which a committee was appointed
to inquire into the cause of the fire. So much for Burnet. I incline to
the view that Graunt's setting London on fire strongly corroborates his
having written on the bills of mortality: every practical man takes stock
before he commences a grand operation in business.
MANKIND A GULLIBLE LOT.
De Cometis: or a discourse of the natures and effects of Comets, as
they are philosophically, historically, and astrologically considered.
With a brief (yet full) account of the III late Comets, or blazing stars,
visible to all Europe. And what (in a natural way of judicature) they
portend. Together with some observations on the nativity of the Grand
Seignior. By John Gadbury, Φιλομαθηματικός.
London, 1665, 4to.
Gadbury, though his name descends only in astrology, was a
well-informed astronomer.[222] D'Israeli[223] sets down Gadbury, Lilly, Wharton,
Booker, etc., as rank rogues: I think him quite wrong. The easy belief in
roguery and intentional imposture which prevails in educated society is,
to my mind, a greater presumption against the honesty of mankind than all
the roguery and imposture itself. Putting aside mere swindling for the
sake of gain, and looking at speculation and paradox, I find very little
reason to suspect wilful deceit.[224] My opinion of mankind is founded upon
the mournful fact that, so far as I can see,
they find within themselves the means of believing in a thousand times as
much as there is to believe in, judging by experience. I do not say
anything against Isaac D'Israeli for talking his time. We are all in the
team, and we all go the road, but we do not all draw.
A FORERUNNER OF A WRITTEN ESPERANTO.
An essay towards a real character and a philosophical language. By
John Wilkins [Dean of Ripon, afterwards Bishop of Chester].[225] London, 1668,
folio.
This work is celebrated, but little known. Its object gives it a right
to a place among paradoxes. It proposes a language—if that be the
proper name—in which things and their relations shall be
denoted by signs, not words: so that any person, whatever may be
his mother tongue, may read it in his own words. This is an obvious
possibility, and, I am afraid, an obvious impracticability. One man may
construct such a system—Bishop Wilkins has done it—but where
is the man who will learn it? The second tongue makes a language, as the
second blow makes a fray. There has been very little curiosity about his
performance, the work is scarce; and I do not know where to refer the
reader for any account of its details, except, to the partial reprint of
Wilkins presently mentioned under 1802, in which there is an
unsatisfactory abstract. There is nothing in the Biographia
Britannica, except discussion of Anthony Wood's statement that the
hint was derived from Dalgarno's book, De Signis,
1661.[226] Hamilton
(Discussions, Art. 5, "Dalgarno") does not say a word on this
point, beyond quoting Wood; and Hamilton, though he did now and then
write about his countrymen with a rough-nibbed pen, knew perfectly well
how to protect their priorities.
GREGOIRE DE ST. VINCENT.
Problema Austriacum. Plus ultra Quadratura Circuli. Auctore P.
Gregorio a Sancto Vincentio Soc. Jesu., Antwerp, 1647, folio.—Opus
Geometricum posthumum ad Mesolabium. By the same. Gandavi [Ghent], 1668,
folio.[227]
The first book has more than 1200 pages, on all kinds of geometry.
Gregory St. Vincent is the greatest of circle-squarers, and his
investigations led him into many truths: he found the property of the
area of the hyperbola[228] which led to Napier's logarithms
being called hyperbolic. Montucla says of him, with sly truth,
that no one has ever squared the circle with so much genius, or,
excepting his principal object, with so much success.[229] His reputation, and the many merits
of his work, led to a sharp controversy on his quadrature, which ended in
its complete exposure by Huyghens and others. He had a small school of
followers, who defended him in print.
RENE DE SLUSE.
Renati Francisci Slusii Mesolabum. Leodii Eburonum [Liège], 1668,
4to.[230]
The Mesolabum is the solution of the problem of finding two mean
proportionals, which Euclid's geometry does not attain. Slusius is a true
geometer, and uses the ellipse, etc.: but he is sometimes ranked with the
trisecters, for which reason I place him here, with this explanation.
The finding of two mean proportionals is the preliminary to the famous
old problem of the duplication of the cube, proposed by Apollo (not
Apollonius) himself. D'Israeli speaks of the "six follies of
science,"—the quadrature, the duplication, the perpetual motion,
the philosopher's stone, magic, and astrology. He might as well have
added the trisection, to make the mystic number seven: but had he done
so, he would still have been very lenient; only seven follies in all
science, from mathematics to chemistry! Science might have said to such a
judge—as convicts used to say who got seven years, expecting it for
life, "Thank you, my Lord, and may you sit there till they are
over,"—may the Curiosities of Literature outlive the Follies of
Science!
JAMES GREGORY.
1668. In this year James Gregory, in his Vera Circuli et Hyperbolæ
Quadratura,[231] held
himself to have proved that the geometrical quadrature of the
circle is impossible. Few mathematicians read this very abstruse
speculation, and opinion is somewhat divided. The regular circle-squarers
attempt the arithmetical quadrature, which has long been proved to
be impossible. Very few attempt the geometrical quadrature. One of the
last is Malacarne, an Italian, who published his Solution
Géométrique, at Paris, in 1825. His method would make the
circumference less than three times the diameter.
BEAULIEU'S QUADRATURE.
La Géométrie Françoise, ou la Pratique aisée.... La quadracture du
cercle. Par le Sieur de Beaulieu, Ingénieur, Géographe du Roi ... Paris,
1676, 8vo. [not Pontault de Beaulieu, the celebrated topographer; he died
in 1674].[232]
If this book had been a fair specimen, I might have pointed to it in
connection with contemporary English works, and made a scornful
comparison. But it is not a fair specimen. Beaulieu was attached to the
Royal Household, and throughout the century it may be suspected that the
household forced a royal road to geometry. Fifty years before, Beaugrand,
the king's secretary, made a fool of himself, and [so?] contrived to pass
for a geometer. He had interest enough to get Desargues, the most
powerful geometer of his time,[233] the teacher and friend of Pascal,
prohibited from lecturing. See some letters on the History
of Perspective, which I wrote in the Athenæum, in October and
November, 1861. Montucla, who does not seem to know the true secret of
Beaugrand's greatness, describes him as "un certain M. de Beaugrand,
mathématicien, fort mal traité par Descartes, et à ce qu'il paroit avec
justice."[234]
Beaulieu's quadrature amounts to a geometrical construction[235] which gives π = √10. His depth may be ascertained from
the following extracts. First on Copernicus:
"Copernic, Allemand, ne s'est pas moins rendu illustre par ses doctes
écrits; et nous pourrions dire de luy, qu'il seroit le seul et unique en
la force de ses Problèmes, si sa trop grande présomption ne l'avoit porté
à avancer en cette Science une proposition aussi absurde, qu'elle est
contre la Foy et raison, en faisant la circonférence d'un Cercle fixe,
immobile, et le centre mobile, sur lequel principe Géométrique, il a
avancé en son Traitté Astrologique le Soleil fixe, et la Terre mobile."[236]
I digress here to point out that though our quadrators, etc., very
often, and our historians sometimes, assert that men of the character of
Copernicus, etc., were treated with contempt and abuse until their day of
ascendancy came, nothing can be more incorrect. From Tycho Brahé[237] to Beaulieu, there is
but one expression of admiration for the genius of Copernicus. There is
an exception, which, I believe, has been quite misunderstood.
Maurolycus,[238] in his
De Sphæra, written many years before its posthumous publication in
1575, and which it is not certain he would have published, speaking of
the safety with which various authors may be read after his cautions,
says, "Toleratur et Nicolaus Copernicus qui Solem fixum et Terram in
girum circumverti posuit: et scutica potius, aut flagello, quam
reprehensione dignus est."[239] Maurolycus was a mild and somewhat
contemptuous satirist, when expressing disapproval: as we should now say,
he pooh-poohed his opponents; but, unless the above be an instance, he
was never savage nor impetuous. I am fully satisfied that the meaning of
the sentence is, that Copernicus, who turned the earth like a boy's top,
ought rather to have a whip given him wherewith to keep up his plaything
than a serious refutation. To speak of tolerating a person as
being more worthy of a flogging than an argument, is almost a
contradiction.
I will now extract Beaulieu's treatise on algebra, entire.
"L'Algebre est la science curieuse des Sçavans et specialement d'un
General d'Armée ou Capitaine, pour promptement ranger une Armée en
bataille, et nombre de Mousquetaires et Piquiers qui composent les
bataillons d'icelle, outre les figures de l'Arithmetique. Cette science a
5 figures particulieres en cette sorte. P signifie plus au
commerce, et à l'Armée Piquiers. M signifie moins, et
Mousquetaire en l'Art des bataillons. [It is quite true that P and
M were used for plus and minus in a great many old works.]
R signifie racine en la mesure du Cube, et en l'Armée rang.
Q signifie quaré en l'un et l'autre usage. C signifie cube
en la mesure, et Cavallerie en la composition des bataillons et
escadrons. Quant à l'operation de cette science, c'est d'additionner
un plus d'avec plus, la somme sera plus, et
moins d'avec plus, on soustrait le moindre du plus,
et la reste est la somme requise ou nombre trouvé. Je dis seulement cecy
en passant pour ceux qui n'en sçavent rien du tout."[240]
This is the algebra of the Royal Household, seventy-three years after
the death of Vieta. Quære, is it possible that the fame of Vieta, who
himself held very high stations in the household all his life, could have
given people the notion that when such an officer chose to declare
himself an algebraist, he must be one indeed? This would explain
Beaugrand, Beaulieu, and all the beaux. Beaugrand—not only
secretary to the king, but "mathematician" to the Duke of Orleans—I
wonder what his "fool" could have been like, if indeed he kept the
offices separate,—would have been in my list if I had possessed his
Geostatique, published about 1638.[241] He makes bodies diminish in weight as
they approach the earth, because the effect of a weight on a lever is
less as it approaches the fulcrum.
SIR MATTHEW HALE.
Remarks upon two late ingenious discourses.... By Dr. Henry More.[242] London, 1676, 8vo.
In 1673 and 1675, Matthew Hale,[243] then Chief Justice, published two
tracts, an "Essay touching Gravitation," and "Difficiles Nugæ" on the
Torricellian experiment. Here are the answers by the learned and
voluminous Henry More. The whole would be useful to any one engaged in
research about ante-Newtonian notions of gravitation.
Observations touching the principles of natural motions; and
especially touching rarefaction and condensation.... By the author of
Difficiles Nugæ. London, 1677, 8vo.
This is another tract of Chief Justice Hale, published the year after
his death. The reader will remember that motion, in old
philosophy, meant any change from state to state: what we now describe as
motion was local motion. This is a very philosophical book,
about flux and materia prima, virtus activa and
essentialis, and other fundamentals. I think Stephen Hales, the
author of the "Vegetable Statics," has the writings of the Chief Justice
sometimes attributed to him, which is very puny justice indeed.[244] Matthew Hale died in
1676, and from his devotion to science it probably arose that his famous
Pleas of the Crown[245] and other law works did not appear
until after his death. One of his contemporaries was the
astronomer Thomas Street, whose Caroline Tables[246] were several times printed: another
contemporary was his brother judge, Sir Thomas Street.[247] But of the astronomer absolutely
nothing is known: it is very unlikely that he and the judge were the same
person, but there is not a bit of positive evidence either for or
against, so far as can be ascertained. Halley[248]—no less a
person—published two editions of the Caroline Tables, no
doubt after the death of the author: strange indeed that neither Halley
nor any one else should leave evidence that Street was born or died.
Matthew Hale gave rise to an instance of the lengths a lawyer will go
when before a jury who cannot detect him. Sir Samuel Shepherd,[249] the Attorney General,
in opening Hone's[250]
first trial, calls him "one who was the most learned man that ever
adorned the Bench, the most even man that ever blessed domestic life, the
most eminent man that ever advanced the progress of science, and
one of the [very moderate] best and most purely religious men that ever
lived."
ON THE DISCOVERY OF ANTIMONY.
Basil Valentine his triumphant Chariot of Antimony, with annotations
of Theodore Kirkringius, M.D. With the true book of the learned Synesius,
a Greek abbot, taken out of the Emperour's library, concerning the
Philosopher's Stone. London, 1678, 8vo.[251]
There are said to be three Hamburg editions of the collected works of
Valentine, who discovered the common antimony, and is said to have given
the name antimoine, in a curious way. Finding that the pigs of his
convent throve upon it, he gave it to his brethren, who died of it.[252] The impulse given to
chemistry by R. Boyle[253] seems to have brought out a vast
number of translations, as in the following tract:
ON ALCHEMY.
Collectanea Chymica: A collection of ten several treatises in
chymistry, concerning the liquor Alkehest, the Mercury of Philosophers,
and other curiosities worthy the perusal. Written by Eir. Philaletha,[254] Anonymus, J. B.
Van-Helmont,[255] Dr. Fr.
Antonie,[256] Bernhard Earl of Trevisan,[257] Sir Geo. Ripley,[258] Rog. Bacon,[259] Geo. Starkie,[260] Sir Hugh Platt,[261] and the Tomb of
Semiramis. See more in the contents. London, 1684, 8vo.
In the advertisements at the ends of these tracts there are upwards of
a hundred English tracts, nearly all of the period, and most of them
translations. Alchemy looks up since the chemists have found perfectly
different substances composed of the same elements and proportions. It is
true the chemists cannot yet transmute; but they may in time: they
poke about most assiduously. It seems, then, that the conviction that
alchemy must be impossible was a delusion: but we do not mention
it.
The astrologers and the alchemists caught it in company in the
following, of which I have an unreferenced note.
"Mendacem et futilem hominem nominare qui volunt, calendariographum
dicunt; at qui sceleratum simul ac impostorem, chimicum.[262]
"Crede ratem ventis corpus ne crede chimistis;
Est quævis chimica tutior aura fide."[263]
Among the smaller paradoxes of the day is that of the Times
newspaper, which always spells it chymistry: but so, I believe, do
Johnson, Walker, and others. The Arabic work is very likely formed from
the Greek: but it may be connected either with χημεια or with χυμεια.
Lettre d'un gentil-homme de province à une dame de qualité, sur le
sujet de la Comète. Paris, 1681, 4to.
An opponent of astrology, whom I strongly suspect to have been one of
the members of the Academy of Sciences under the name of a country
gentleman,[264] writes
very good sense on the tremors excited by comets.
The Petitioning-Comet: or a brief Chronology of all the famous Comets
and their events, that have happened from the birth of Christ to this
very day. Together with a modest enquiry into this present comet, London,
1681, 4to.
A satirical tract against the cometic prophecy:
"This present comet (it's true) is of a menacing aspect, but if the
new parliament (for whose convention so many good men pray)
continue long to sit, I fear not but the star will lose its virulence and
malignancy, or at least its portent be averted from this our nation;
which being the humble request to God of all good men, makes me thus
entitle it, a Petitioning-Comet."
The following anecdote is new to me:
"Queen Elizabeth (1558) being then at Richmond, and being disswaded
from looking on a comet which did then appear, made answer, jacta est
alea, the dice are thrown; thereby intimating that the pre-order'd
providence of God was above the influence of any star or comet."
The argument was worth nothing: for the comet might have been on
the dice with the event; the astrologers said no more, at least the
more rational ones, who were about half of the whole.
An astrological and theological discourse upon this present great
conjunction (the like whereof hath not (likely) been in some ages)
ushered in by a great comet. London, 1682, 4to. By C. N.[265]
The author foretells the approaching "sabbatical jubilee," but will
not fix the date: he recounts the failures of his predecessors.
A judgment of the comet which became first generally visible to us in
Dublin, December 13, about 15 minutes before 5 in the evening, A.D. 1680. By a person of quality. Dublin, 1682,
4to.
The author argues against cometic astrology with great ability.
A prophecy on the conjunction of Saturn and Jupiter in this present
year 1682. With some prophetical predictions of what is likely to ensue
therefrom in the year 1684. By John Case, Student in physic and
astrology.[266] London,
1682, 4to.
According to this writer, great conjunctions of Jupiter and Saturn
occur "in the fiery trigon," about once in 800 years. Of these there are
to be seven: six happened in the several times of Enoch, Noah, Moses,
Solomon, Christ, Charlemagne. The seventh, which is to happen at "the
lamb's marriage with the bride," seems to be that of 1682; but this is
only vaguely hinted.
De Quadrature van de Circkel. By Jacob Marcelis. Amsterdam, 1698,
4to.
Ampliatie en demonstratie wegens de Quadrature ... By Jacob Marcelis.
Amsterdam, 1699, 4to.
Eenvoudig vertoog briev-wys geschrevem am J. Marcelis ... Amsterdam,
1702, 4to.
De sleutel en openinge van de quadrature ... Amsterdam, 1704, 4to.
Who shall contradict Jacob Marcelis?[267] He says the circumference contains
the diameter exactly times
1008449087377541679894282184894
3 ————————————————
6997183637540819440035239271702
But he does not come very near, as the young arithmetician will
find.
MATHEMATICAL THEOLOGY.
Theologiæ Christianæ Principia Mathematica. Auctore Johanne Craig.[268] London, 1699, 4to.
This is a celebrated speculation, and has been reprinted abroad, and
seriously answered. Craig is known in the early history of fluxions, and
was a good mathematician. He professed to calculate, on the
hypothesis that the suspicions against historical evidence increase with
the square of the time, how long it will take the evidence of
Christianity to die out. He finds, by formulæ, that had it been oral
only, it would have gone out A.D. 800; but, by aid of the written
evidence, it will last till A.D. 3150. At this period he places the
second coming, which is deferred until the extinction of evidence, on the
authority of the question "When the Son of Man cometh, shall he find
faith on the earth?" It is a pity that Craig's theory was not adopted: it
would have spared a hundred treatises on the end of the world, founded on
no better knowledge than his, and many of them falsified by the event.
The most recent (October, 1863) is a tract in proof of Louis Napoleon
being Antichrist, the Beast, the eighth Head, etc.; and the present
dispensation is to close soon after 1864.
In order rightly to judge Craig, who added speculations on the
variations of pleasure and pain treated as functions of time, it is
necessary to remember that in Newton's day the idea of force, as a
quantity to be measured, and as following a law of variation, was very
new: so likewise was that of probability, or belief, as an object of
measurement.[269] The
success of the Principia of Newton put it into many heads to
speculate about applying notions of quantity to other things not then
brought under measurement. Craig imitated Newton's title, and evidently
thought he was making a step in advance: but it is not every one who can
plough with Samson's heifer.
It is likely enough that Craig took a hint, directly or indirectly,
from Mohammedan writers, who make a reply to the argument that the Koran
has not the evidence derived from miracles. They say that, as evidence
of Christian miracles is daily becoming weaker, a time must at last
arrive when it will fail of affording assurance that they were miracles
at all: whence would arise the necessity of another prophet and other
miracles. Lee,[270] the
Cambridge Orientalist, from whom the above words are taken, almost
certainly never heard of Craig or his theory.
THE ARISTOCRAT AS A SCIENTIST.
Copernicans of all sorts convicted ... to which is added a Treatise of
the Magnet. By the Hon. Edw. Howard, of Berks. London, 1705, 8vo.
Not all the blood of all the Howards will gain respect for a writer
who maintains that eclipses admit no possible explanation under the
Copernican hypothesis, and who asks how a man can "go 200 yards to any
place if the moving superficies of the earth does carry it from him?"
Horace Walpole, at the beginning of his Royal and Noble Authors,
has mottoed his book with the Cardinal's address to Ariosto, "Dove
diavolo, Messer Ludovico, avete pigliato tante coglionerie?"[271] Walter Scott says you
could hardly pick out, on any principle of selection—except badness
itself, he means of course—the same number of plebeian authors
whose works are so bad. But his implied satire on aristocratic writing
forgets two points. First, during a large period of our history, when
persons of rank condescended to write, they veiled themselves under "a
person of honor," "a person of quality," and the like, when not wholly
undescribed. Not one of these has Walpole got; he omits, for instance,
Lord Brounker's[272]
translation of Descartes on Music. Secondly, Walpole only takes the heads
of houses: this cuts both ways; he equally eliminates the Hon. Robert
Boyle and the precious Edward Howard. The last writer is hardly out of
the time in which aristocracy suppressed its names; the avowal was then
usually meant to make the author's greatness useful to the book. In our
day, literary peers and honorables are very favorably known, and contain
an eminent class.[273]
They rough it like others, and if such a specimen as Edw. Howard were now
to appear, he would be greeted with
"Hereditary noodle! knowest thou not
Who would be wise, himself must make him so?"
THE LONGITUDE PROBLEM.
A new and easy method to find the longitude at land or sea. London,
1710, 4to.
This tract is a little earlier than the great epoch of such
publications (1714), and professes to find the longitude by the observed
altitudes of the moon and two stars.[274]
A new method for discovering the longitude both at sea and land,
humbly proposed to the consideration of the public.[275] By Wm. Whiston[276] and Humphry Ditton.[277] London, 1714, 8vo.
This is the celebrated tract, written by the two Arian heretics.
Swift, whose orthodoxy was as undoubted as his meekness, wrote upon it
the epigram—if, indeed, that be epigram of which the point is pious
wish—which has been so often recited for the purity of its style, a
purity which transcends modern printing. Perhaps some readers may think
that Swift cared little for Whiston and Ditton, except as a chance
hearing of their plan pointed them out as good marks. But it was not so:
the clique had their eye on the guilty pair before the publication of the
tract. The preface is dated July 7; and ten days afterwards Arbuthnot[278] writes as follows to
Swift:
"Whiston has at last published his project of the longitude; the most
ridiculous thing that ever was thought on. But a pox on him! he has
spoiled one of my papers of Scriblerus, which was a proposition for the
longitude not very unlike his, to this purpose; that since there was no
pole for east and west, that all the princes of Europe should join and
build two prodigious poles, upon high mountains, with a vast lighthouse
to serve for a polestar. I was thinking of a calculation of the time,
charges, and dimensions. Now you must understand his project is by
lighthouses, and explosion of bombs at a certain hour."
The plan was certainly impracticable; but Whiston and Ditton might
have retorted that they were nearer to the longitude than their satirist
to the kingdom of heaven, or even to a bishopric. Arbuthnot, I think,
here and elsewhere, reveals himself as the calculator who kept Swift
right in his proportions in the matter of the Lilliputians,
Brobdingnagians, etc. Swift was very ignorant about things connected with
number. He writes to Stella that he has discovered that leap-year comes
every four years, and that all his life he had thought it came every
three years. Did he begin with the mistake of Cæsar's priests? Whether or
no, when I find the person who did not understand leap-year inventing
satellites of Mars in correct accordance with Kepler's third law, I feel
sure he must have had help.
THE AURORA BOREALIS.
An essay concerning the late apparition in the heavens on the 6th of
March. Proving by mathematical, logical, and moral arguments, that it
cou'd not have been produced meerly by the ordinary course of nature, but
must of necessity be a prodigy. Humbly offered to the consideration of
the Royal Society. London, 1716, 8vo.
The prodigy, as described, was what we should call a very decided and
unusual aurora borealis. The inference was, that men's sins were bringing
on the end of the world. The author thinks that if one of the old
"threatening prophets" were then alive, he would give "something like the
following." I quote a few sentences of the notion which the author had of
the way in which Ezekiel, for instance, would have addressed his Maker in
the reign of George the First:
"Begin! Begin! O Sovereign, for once, with an effectual clap of
thunder.... O Deity! either thunder to us no more, or when you thunder,
do it home, and strike with vengeance to the mark.... 'Tis not enough to
raise a storm, unless you follow it with a blow, and the thunder without
the bolt, signifies just nothing at all.... Are then your lightnings of
so short a sight, that they don't know how to hit, unless a mountain
stands like a barrier in their way? Or perhaps so many eyes open in the
firmament make you lose your aim when you shoot the arrow? Is it this?
No! but, my dear Lord, it is your custom never to take hold of your arms
till you have first bound round your majestic countenance with gathered
mists and clouds."
The principles of the Philosophy of the Expansive and Contractive
Forces ... By Robert Greene,[279] M.A., Fellow of Clare Hall.
Cambridge, 1727, folio.
Sanderson[280] writes
to Jones,[281] "The
gentleman has been reputed mad for these two years last past, but never
gave the world such ample testimony of it before." This was said of a
former work of Greene's, on solid geometry, published in 1712, in which
he gives a quadrature.[282] He gives the same or another, I do
not know which, in the present work, in which the circle is 3-1/5
diameters. This volume is of 981 good folio pages, and treats of all
things, mental and material. The author is not at all mad, only wrong on
many points. It is the weakness of the
orthodox follower of any received system to impute insanity to the
solitary dissentient: which is voted (in due time) a very wrong opinion
about Copernicus, Columbus, or Galileo, but quite right about Robert
Greene. If misconceptions, acted on by too much self-opinion, be
sufficient evidence of madness, it would be a curious inquiry what is the
least per-centage of the reigning school which has been insane at any one
time. Greene is one of the sources for Newton being led to think of
gravitation by the fall of an apple: his authority is the gossip of
Martin Folkes.[283]
Probably Folkes had it from Newton's niece, Mrs. Conduitt, whom Voltaire
acknowledges as his authority.[284] It is in the draft found among
Conduitt's papers of memoranda to be sent to Fontenelle. But Fontenelle,
though a great retailer of anecdote, does not mention it in his
éloge of Newton; whence it may be suspected that it was left out
in the copy forwarded to France. D'Israeli has got an improvement on the
story: the apple "struck him a smart blow on the head": no doubt taking
him just on the organ of causality. He was "surprised at the force of the
stroke" from so small an apple: but then the apple had a mission; Homer
would have said it was Minerva in the form of an apple.
"This led him to consider the accelerating motion of falling bodies,"
which Galileo had settled long before: "from whence he deduced the
principle of gravity," which many had considered before him, but no one
had deduced anything from it. I cannot imagine whence D'Israeli
got the rap on the head, I mean got it for Newton: this is very unlike
his usual accounts of things. The story is pleasant and possible: its
only defect is that various writings, well known to Newton, a very
learned mathematician, had given more suggestion than a whole sack
of apples could have done, if they had tumbled on that mighty head all at
once. And Pemberton, speaking from Newton himself, says nothing more than
that the idea of the moon being retained by the same force which causes
the fall of bodies struck him for the first time while meditating in a
garden. One particular tree at Woolsthorpe has been selected as the
gallows of the appleshaped goddess: it died in 1820, and Mr. Turnor[285] kept the wood; but Sir
D. Brewster[286] brought
away a bit of root in 1814, and must have had it on his conscience for 43
years that he may have killed the tree. Kepler's suggestion of
gravitation with the inverse distance, and Bouillaud's proposed
substitution of the inverse square of the distance, are things which
Newton knew better than his modern readers. I discovered two anagrams on
his name, which are quite conclusive; the notion of gravitation was
not new; but Newton went on. Some wandering spirit,
probably whose business it was to resent any liberty taken with Newton's
name, put into the head of a friend of mine eighty-one anagrams on
my own pair, some of which hit harder than any apple.
DE MORGAN ANAGRAMS.
This friend, whom I must not name, has since made it up to about 800
anagrams on my name, of which I have seen about 650. Two of them I have
joined in the title-page: the reader may find the sense. A few of the
others are personal remarks.
"Great gun! do us a sum!"
is a sneer at my pursuits: but,
"Go! great sum! ∫a un du"
is more dignified.
"Sunt agro! gaudemus,"[287]
is happy as applied to one of whom it may be said:
"Ne'er out of town; 'tis such a horrid life;
But duly sends his family and wife."
"Adsum, nugator, suge!"[288]
is addressed to a student who continues talking after the lecture has
commenced: oh! the rascal!
"Graduatus sum! nego"[289]
applies to one who declined to subscribe for an M.A. degree.
symbolizes a person of very fixed habits.
"Gus! Gus! a mature don!
August man! sure, god!
And Gus must argue, O!
Snug as mud to argue,
Must argue on gauds.
A mad rogue stung us.
Gag a numerous stud
Go! turn us! damage us!
Tug us! O drag us! Amen.
Grudge us! moan at us!
Daunt us! gag us more!
Dog-ear us, man! gut us!
D—— us! a rogue tugs!"
are addressed to me by the circle-squarers; and,
"O! Gus! tug a mean surd!"
is smart upon my preference of an incommensurable value of π to 3-1/5, or some such simple substitute.
While,
"Gus! Gus! at 'em a' round!"
ought to be the backing of the scientific world to the author of the
Budget of Paradoxes.
The whole collection commenced existence in the head of a powerful
mathematician during some sleepless nights. Seeing how large a number was
practicable, he amused himself by inventing a digested plan of finding
more.
Is there any one whose name cannot be twisted into either praise or
satire? I have had given to me,
"Thomas Babington Macaulay
Mouths big: a Cantab anomaly."
NEWTON'S DE MUNDI SYSTEMATE LIBER.
A treatise of the system of the world. By Sir Isaac Newton. Translated
into English. London, 1728, 8vo.
I think I have a right to one little paradox of my own: I greatly
doubt that Newton wrote this book. Castiglione,[290] in his Newtoni Opuscula,[291] gives it in the Latin
which appeared in 1731,[292] not for the first time; he says
Angli omnes Newtono tribuunt.[293] It appeared just after Newton's
death, without the name of any editor, or any allusion to Newton's recent departure, purporting to be that
popular treatise which Newton, at the beginning of the third book of the
Principia, says he wrote, intending it to be the third book. It is
very possible that some observant turnpenny might construct such a
treatise as this from the third book, that it might be ready for
publication the moment Newton could not disown it. It has been treated
with singular silence: the name of the editor has never been given.
Rigaud[294] mentions it
without a word: I cannot find it in Brewster's Newton, nor in the
Biographia Britannica. There is no copy in the Catalogue of the
Royal Society's Library, either in English or Latin, except in
Castiglione. I am open to correction; but I think nothing from Newton's
acknowledged works will prove—as laid down in the suspected
work—that he took Numa's temple of Vesta, with a central fire, to
be intended to symbolize the sun as the center of our system, in the
Copernican sense.[295]
Mr. Edleston[296]
gives an account of the lectures "de motu corporum," and gives the
corresponding pages of the Latin "De Systemate Mundi" of 1731. But
no one mentions the English of 1728. This English seems to agree
with the Latin; but there is a mystery about it. The preface says, "That
this work as here published is genuine will so clearly appear by the
intrinsic marks it bears, that it will be but losing words and the
reader's time to take pains in giving him any other satisfaction." Surely
fewer words would have been lost if the prefator had said at once that
the work was from the manuscript preserved at Cambridge. Perhaps it was a
mangled copy clandestinely taken and interpreted.
A BACONIAN CONTROVERSY.
Lord Bacon not the author of "The Christian Paradoxes," being a
reprint of "Memorials of Godliness and Christianity," by Herbert Palmer,
B.D.[297] With
Introduction, Memoir, and Notes, by the Rev. Alexander B. Grosart,[298] Kenross. (Private
circulation, 1864).
I insert the above in this place on account of a slight connection
with the last. Bacon's Paradoxes,—so attributed—were first
published as his in some asserted "Remains," 1648.[299] They were admitted into his works in
1730, and remain there to this day. The title is "The Character of a
believing Christian, set forth in paradoxes and seeming contradictions."
The following is a specimen:
"He believes three to be one and one to be three; a father not to be
older than his son; a son to be equal with his father; and one proceeding
from both to be equal with both: he believes three persons in one nature,
and two natures in one person.... He believes the God of all grace to
have been angry with one that never offended Him; and that God that hates
sin to be reconciled to himself though sinning continually, and never
making or being able to make Him any satisfaction. He believes a most
just God to have punished a most just person, and to have justified
himself, though a most ungodly sinner. He believes himself freely
pardoned, and yet a sufficient satisfaction was made for him."
Who can doubt that if Bacon had written this it must have been wrong?
Many writers, especially on the Continent, have taken him as sneering at
(Athanasian) Christianity right and left. Many Englishmen have taken him
to be quite in earnest, and to have produced a body of edifying doctrine.
More than a century ago the Paradoxes were published as a penny tract;
and, again, at the same price, in the Penny Sunday Reader, vol.
vi, No. 148, a few passages were omitted, as too strong. But all
did not agree: in my copy of Peter Shaw's [300] edition (vol. ii, p. 283) the
Paradoxes have been cut out by the binder, who has left the backs of the
leaves. I never had the curiosity to see whether other copies of the
edition have been served in the same way. The Religious Tract Society
republished them recently in Selections from the Writings of Lord
Bacon, (no date; bad plan; about 1863, I suppose). No omissions were
made, so far as I find.
I never believed that Bacon wrote this paper; it has neither his
sparkle nor his idiom. I stated my doubts even before I heard that
Mr. Spedding, one of Bacon's editors, was of the same mind.
(Athenæum, July 16, 1864). I was little moved by the wide consent
of orthodox men: for I knew how Bacon, Milton, Newton, Locke, etc., were
always claimed as orthodox until almost the present day. Of this there is
a remarkable instance.
LOCKE AND SOCINIANISM.
Among the books which in my younger day were in some orthodox
publication lists—I think in the list of the Christian Knowledge
Society, but I am not sure—was Locke's [301] "Reasonableness of Christianity." It
seems to have come down from the eighteenth century, when the battle was
belief in Christ against unbelief, simpliciter, as the logicians
say. Now, if ever there was a Socinian[302] book in the world, it is this work of
Locke. "These two," says Locke, "faith and repentance, i.e., believing
Jesus to be the Messiah, and a good life, are the indispensable
conditions of the new covenant, to be performed by all those who would
obtain eternal life." All the book is amplification of this doctrine.
Locke, in this and many other things, followed Hobbes, whose doctrine, in
the Leviathan, is fidem, quanta ad salutem necessaria est, contineri
in hoc articulo, Jesus est Christus.[303] For this Hobbes was called an
atheist, which many still believe him to have been: some
of his contemporaries called him, rightly, a Socinian. Locke was known
for a Socinian as soon as his work appeared: Dr. John Edwards,[304] his assailant, says he
is "Socinianized all over." Locke, in his reply, says "there is not one
word of Socinianism in it:" and he was right: the positive Socinian
doctrine has not one word of Socinianism in it; Socinianism
consists in omissions. Locke and Hobbes did not dare deny the
Trinity: for such a thing Hobbes might have been roasted, and Locke might
have been strangled. Accordingly, the well-known way of teaching
Unitarian doctrine was the collection of the asserted essentials of
Christianity, without naming the Trinity, etc. This is the plan Newton
followed, in the papers which have at last been published.[305]
So I, for one, thought little about the general tendency of orthodox
writers to claim Bacon by means of the Paradoxes. I knew that, in his
"Confession of Faith"[306] he is a Trinitarian of a heterodox
stamp. His second Person takes human nature before he took flesh, not for
redemption, but as a condition precedent of creation. "God is so holy,
pure, and jealous, that it is impossible for him to be pleased in any
creature, though the work of his own hands.... [Gen. i. 10, 12, 18, 21,
25, 31, freely rendered]. But—purposing to become a Creator, and to
communicate to his creatures, he ordained in his eternal counsel that one
person of the Godhead should be united to one nature, and to one
particular of his creatures; that so, in the person of the Mediator, the
true ladder might be fixed, whereby God might descend to his
creatures and his creatures might ascend to God...."
This is republished by the Religious Tract Society, and seems to suit
their theology, for they confess to having omitted some things of which
they disapprove.
In 1864, Mr. Grosart published his discovery that the Paradoxes are by
Herbert Palmer; that they were first published surreptitiously, and
immediately afterwards by himself, both in 1645; that the "Remains" of
Bacon did not appear until 1648; that from 1645 to 1708, thirteen
editions of the "Memorials" were published, all containing the Paradoxes.
In spite of this, the Paradoxes were introduced into Bacon's works in
1730, where they have remained.
Herbert Palmer was of good descent, and educated as a Puritan. He was
an accomplished man, one of the few of his day who could speak French as
well as English. He went into the Church, and was beneficed by Laud,[307] in spite of his
puritanism; he sat in the Assembly of Divines, and was finally President
of Queens' College, Cambridge, in which post he died, August 13, 1647, in
the 46th year of his age.
Mr. Grosart says, speaking of Bacon's "Remains," "All who have had
occasion to examine our early literature are aware that it was a common
trick to issue imperfect, false, and unauthorized writings under any
recently deceased name that might be expected to take. The Puritans, down
to John Bunyan, were perpetually expostulating and protesting against
such procedure." I have met with instances of all this; but I did not
know that there was so much of it: a good collection would be very
useful. The work of 1728, attributed to Newton, is likely enough to be
one of the class.
Demonstration de l'immobilitez de la Terre.... Par M. de la
Jonchere,[308] Ingénieur
Français. Londres, 1728, 8vo.
A synopsis which is of a line of argument belonging to the beginning
of the preceding century.
TWO FORGOTTEN CIRCLE SQUARERS.
The Circle squared; together with the Ellipsis and several reflections
on it. The finding two geometrical mean proportionals, or doubling the
cube geometrically. By Richard Locke[309].... London, no date, probably about
1730, 8vo.
According to Mr. Locke, the circumference is three diameters,
three-fourths the difference of the diameter and the side of the
inscribed equilateral triangle, and three-fourths the difference between
seven-eighths of the diameter and the side of the same triangle. This
gives, he says, 3.18897. There is an addition to this tract, being an
appendix to a book on the longitude.
The Circle squar'd. By Thos. Baxter, Crathorn, Cleaveland, Yorkshire.
London, 1732, 8vo.
Here π = 3.0625. No proof is offered.[310]
The longitude discovered by the Eclipses, Occultations, and
Conjunctions of Jupiter's planets. By William Whiston. London, 1738.
This tract has, in some copies, the celebrated preface containing the
account of Newton's appearance before the Parliamentary Committee on the
longitude question, in 1714 (Brewster, ii. 257-266). This "historical
preface," is an insertion and is dated April 28, 1741, with four
additional pages dated August 10, 1741. The short "preface" is by the
publisher, John Whiston,[311] the author's son.
THE STEAMSHIP SUGGESTED.
A description and draught of a new-invented machine for carrying
vessels or ships out of, or into any harbour, port, or river, against
wind and tide, or in a calm. For which, His Majesty has granted letters
patent, for the sole benefit of the author, for the space of fourteen
years. By Jonathan Hulls.[312] London: printed for the author, 1737.
Price sixpence (folding plate and pp. 48, beginning from title).
(I ought to have entered this tract in its place. It is so rare that
its existence was once doubted. It is the earliest description of
steam-power applied to navigation. The plate shows a barge, with smoking
funnel, and paddles at the stem, towing a ship of war. The engine, as
described, is Newcomen's.[313]
In 1855, John Sheepshanks,[314] so well known as a friend of Art and
a public donor, reprinted this tract, in fac-simile, from his own copy;
twenty-seven copies of the original 12mo size, and twelve on old paper,
small 4to. I have an original copy, wanting the plate, and with "Price
sixpence" carefully erased, to the honor of the book.[315]
It is not known whether Hulls actually constructed a boat.[316] In all probability his
tract suggested to Symington, as Symington[317] did to Fulton.)
THE NEWTONIANS ATTACKED.
Le vrai système de physique générale de M. Isaac Newton exposé et
analysé en parallèle avec celui de Descartes. By Louis Castel[318] [Jesuit and F.R.S.]
Paris, 1743, 4to.
This is an elaborate correction of Newton's followers, and of Newton
himself, who it seems did not give his own views with perfect fidelity.
Father Castel, for instance, assures us that Newton placed the sun at
rest in the center of the system. Newton left the sun to arrange that
matter with the planets and the rest of the universe. In this volume of
500 pages there is right and wrong, both clever.
A dissertation on the Æther of Sir Isaac Newton. By Bryan Robinson,[319] M.D. Dublin, 1743,
8vo.[320]
A mathematical work professing to prove that the assumed ether causes
gravitation.
MATHEMATICAL THEOLOGY.
Mathematical principles of theology, or the existence of God
geometrically demonstrated. By Richard Jack, teacher of Mathematics.
London, 1747, 8vo.[321]
Propositions arranged after the manner of Euclid, with beings
represented by circles and squares. But these circles and squares are
logical symbols, not geometrical ones. I brought this book forward to the
Royal Commission on the British Museum as an instance of the absurdity of
attempting a classed catalogue from the titles of books.
The title of this book sends it either to theology or geometry: when, in
fact, it is a logical vagary. Some of the houses which Jack built were
destroyed by the fortune of war in 1745, at Edinburgh: who will say the
rebels did no good whatever? I suspect that Jack copied the ideas of J.B.
Morinus, "Quod Deus sit," Paris, 1636,[322] 4to, containing an attempt of the
same kind, but not stultified with diagrams.
TWO MODEL INDORSEMENTS.
Dissertation, découverte, et démonstrations de la quadrature
mathématique du cercle. Par M. de Fauré, géomètre. [s. l.,
probably Geneva] 1747, 8vo.
Analyse de la Quadrature du Cercle. Par M. de Fauré, Gentilhomme
Suisse. Hague, 1749,[323]
4to.
According to this octavo geometer and quarto gentleman, a diameter of
81 gives a circumference of 256. There is an amusing circumstance about
the quarto which has been overlooked, if indeed the book has ever been
examined. John Bernoulli (the one of the
day)[324] and Koenig[325] have both given an
attestation: my mathematical readers may stare as they please, such is
the fact. But, on examination, there will be reason to think the two sly
Swiss played their countryman the same trick as the medical man played
Miss Pickle, in the novel of that name. The lady only wanted to get his
authority against sousing her little nephew, and said, "Pray, doctor, is
it not both dangerous and cruel to be the means of letting a poor tender
infant perish by sousing it in water as cold as ice?"—"Downright
murder, I affirm," said the doctor; and certified accordingly. De Fauré
had built a tremendous scaffolding of equations, quite out of place, and
feeling cock-sure that his solutions, if correct, would square the
circle, applied to Bernoulli and Koenig—who after his tract of two
years before, must have known what he was at—for their approbation
of the solutions. And he got it, as follows, well guarded:
"Suivant les suppositions posées dans ce Mémoire, il est si évident
que t doit être = 34, y = 1, et z = 1, que cela n'a
besoin ni de preuve ni d'autorité pour être reconnu par tout le monde.[326]
"à Basle le 7e Mai 1749. Jean Bernoulli."
"Je souscris au jugement de Mr. Bernoulli, en conséquence de ces
suppositions.[327]
"à la Haye le 21 Juin 1749. S. Koenig."
On which de Fauré remarks with triumph—as I have no doubt it was
intended he should do—"il conste clairement par ma présente Analyse
et Démonstration, qu'ils y ont déja reconnu et approuvé
parfaitement que la quadrature du cercle est mathématiquement
démontrée."[328] It
should seem that it is easier to square the circle than to get round a
mathematician.
An attempt to demonstrate that all the Phenomena in Nature may be
explained by two simple active principles, Attraction and Repulsion,
wherein the attraction of Cohesion, Gravity and Magnetism are shown to be
one the same. By Gowin Knight. London, 1748, 4to.
Dr. Knight[329] was
Mr. Panizzi's[330]
archetype, the first Principal Librarian of the British Museum. He was
celebrated for his magnetical experiments. This work was long neglected;
but is now recognized as of remarkable resemblance to modern
speculations.
THOMAS WRIGHT OF DURHAM.
An original theory or Hypothesis of the Universe. By Thomas Wright[331] of Durham. London,
4to, 1750.
Wright is a speculator whose thoughts are now part of our current
astronomy. He took that view—or most of it—of the milky way
which afterwards suggested itself to William Herschel. I have given an
account of him and his work in the Philosophical Magazine for
April, 1848.
Wright was mathematical instrument maker to the King, and kept a
shop in Fleet Street. Is the celebrated business of Troughton &
Simms, also in Fleet Street, a lineal descendant of that of Wright? It is
likely enough, more likely that that—as I find him reported to have
affirmed—Prester John was the descendant of Solomon and the Queen
of Sheba. Having settled it thus, it struck me that I might apply to Mr.
Simms, and he informs me that it is as I thought, the line of descent
being Wright, Cole, John Troughton, Edward Troughton,[332] Troughton & Simms.[333]
BISHOP HORNE ON NEWTON.
The theology and philosophy in Cicero's Somnium Scipionis
explained. Or, a brief attempt to demonstrate, that the Newtonian system
is perfectly agreeable to the notions of the wisest ancients: and that
mathematical principles are the only sure ones. [By Bishop Horne,[334] at the age of
nineteen.] London, 1751, 8vo.
This tract, which was not printed in the collected works, and is now
excessively rare, is mentioned in Notes and Queries, 1st S., v,
490, 573; 2d S., ix, 15. The boyish satire on Newton is amusing. Speaking
of old Benjamin Martin,[335] he goes on as follows:
"But the most elegant account of the matter [attraction] is by that
hominiform animal, Mr. Benjamin Martin, who having attended Dr.
Desaguliers'[336] fine,
raree, gallanty shew for some years [Desaguliers was one of the first who
gave public experimental lectures, before the saucy boy was born] in the
capacity of a turnspit, has, it seems, taken it into his head to set up
for a philosopher."
Thus is preserved the fact, unknown to his biographers, that Benj.
Martin was an assistant to Desaguliers in his lectures. Hutton[337] says of him, that "he
was well skilled in the whole circle of the mathematical and
philosophical sciences, and wrote useful books on every one of them":
this is quite true; and even at this day he is read by twenty where Horne
is read by one; see the stalls, passim. All that I say of him,
indeed my knowledge of the tract, is due to this contemptuous mention of
a more durable man than himself. My assistant secretary at the
Astronomical Society, the late Mr. Epps,[338] bought the copy at a stall because
his eye was caught by the notice of "Old Ben Martin," of whom he was a
great reader. Old Ben could not be a Fellow of the Royal Society, because
he kept a shop: even though the shop sold nothing but philosophical
instruments. Thomas Wright, similarly situated as to shop and goods,
never was a Fellow. The Society of our day has greatly degenerated: those
of the old time would be pleased, no doubt, that the glories of their day
should be commemorated. In the early days
of the Society, there was a similar difficulty about Graunt, the author
of the celebrated work on mortality. But their royal patron, "who never
said a foolish thing," sent them a sharp message, and charged them if
they found any more such tradesmen, they should "elect them without more
ado."
Horne's first pamphlet was published when he was but twenty-one years
old. Two years afterwards, being then a Fellow of his college, and having
seen more of the world, he seems to have felt that his manner was a
little too pert. He endeavored, it is said, to suppress his first tract:
and copies are certainly of extreme rarity. He published the following as
his maturer view:
A fair, candid, and impartial state of the case between Sir Isaac
Newton and Mr. Hutchinson.[339] In which is shown how far a system of
physics is capable of mathematical demonstration; how far Sir Isaac's, as
such a system, has that demonstration; and consequently, what regard Mr.
Hutchinson's claim may deserve to have paid to it. By George Horne, M.A.
Oxford, 1753, 8vo.
It must be remembered that the successors of Newton were very apt to
declare that Newton had demonstrated attraction as a physical
cause: he had taken reasonable pains to show that he did not pretend to
this. If any one had said to Newton, I hold that every particle of matter
is a responsible being of vast intellect, ordered by the Creator to move
as it would do if every other particle attracted it, and gifted with
power to make its way in true accordance with that law, as easily as a
lady picks her way across the street; what have you to say against
it?—Newton must have replied, Sir! if you really undertake to
maintain this as demonstrable, your soul had better borrow a
little power from the particles of which your body is
made: if you merely ask me to refute it, I tell you that I neither can
nor need do it; for whether attraction comes in this way or in any other,
it comes, and that is all I have to do with it.
The reader should remember that the word attraction, as used by Newton
and the best of his followers, only meant a drawing towards,
without any implication as to the cause. Thus whether they said that
matter attracts matter, or that young lady attracts young gentleman, they
were using one word in one sense. Newton found that the law of the first
is the inverse square of the distance: I am not aware that the law of the
second has been discovered; if there be any chance, we shall see it at
the year 1856 in this list.
In this point young Horne made a hit. He justly censures those who
fixed upon Newton a more positive knowledge of what attraction is than he
pretended to have. "He has owned over and over he did not know what he
meant by it—it might be this, or it might be that, or it might be
anything, or it might be nothing." With the exception of the
nothing clause, this is true, though Newton might have answered
Horne by "Thou hast said it."
(I thought everybody knew the meaning of "Thou hast said it": but I
was mistaken. In three of the evangelists Σὺ λέγεις is
the answer to "Art thou a king?" The force of this answer, as always
understood, is "That is your way of putting it." The Puritans, who lived
in Bible phrases, so understood it: and Walter Scott, who caught all
peculiarities of language with great effect, makes a marked instance,
"Were you armed?—I was not—I went in my calling, as a
preacher of God's word, to encourage them that drew the sword in His
cause. In other words, to aid and abet the rebels, said the Duke. Thou
hast spoken it, replied the prisoner.")
Again, Horne quotes Rowning[340] as follows:
"Mr. Rowning, pt. 2, p. 5 in a note, has a very pretty conceit upon
this same subject of attraction, about every particle of a fluid being
intrenched in three spheres of attraction and repulsion, one within
another, 'the innermost of which (he says) is a sphere of repulsion,
which keeps them from approaching into contact; the next, a sphere of
attraction, diffused around this of repulsion, by which the particles are
disposed to run together into drops; and the outermost of all, a sphere
of repulsion, whereby they repel each other, when removed out of the
attraction.' So that between the urgings, and
solicitations, of one and t'other, a poor unhappy particle must
ever be at his wit's end, not knowing which way to turn, or whom to obey
first."
Rowning has here started the notion which Boscovich[341] afterwards developed.
I may add to what precedes that it cannot be settled that, as
Granger[342] says,
Desaguliers was the first who gave experimental lectures in London.
William Whiston gave some, and Francis Hauksbee[343] made the experiments. The prospectus,
as we should now call it, is extant, a quarto tract of plates and
descriptions, without date. Whiston, in his life, gives 1714 as the first
date of publication, and therefore, no doubt, of the lectures.
Desaguliers removed to London soon after 1712, and commenced his lectures
soon after that. It will be rather a nice point to settle which lectured
first; probabilities seem to go in favor of Whiston.
FALLACIES IN A THEORY OF ANNUITIES.
An Essay to ascertain the value of leases, and annuities for years and
lives. By W[eyman] L[ee]. London, 1737, 8vo.
A valuation of Annuities and Leases certain, for a single life. By
Weyman Lee, Esq. of the Inner Temple. London, 1751, 8vo. Third edition,
1773.
Every branch of exact science has its paradoxer. The world at large
cannot tell with certainty who is right in such questions as squaring the
circle, etc. Mr. Weyman Lee[344] was the assailant of what all who had
studied called demonstration in the question of annuities. He can be
exposed to the world: for his error arose out of his not being able to
see that the whole is the sum of all its parts.
By an annuity, say of £100, now bought, is meant that the buyer is to
have for his money £100 in a year, if he be then alive, £100 at the end
of two years, if then alive, and so on. It is clear that he would buy a
life annuity if he should buy the first £100 in one office, the second in
another, and so on. All the difference between buying the whole from one
office and buying all the separate contingent payments at different
offices, is immaterial to calculation. Mr. Lee would have agreed with the
rest of the world about the payments to be made to the several different
offices, in consideration of their several contracts: but he differed
from every one else about the sum to be paid to one office. He
contended that the way to value an annuity is to find out the term of
years which the individual has an even chance of surviving, and to charge
for the life annuity the value of an annuity certain for that term.
It is very common to say that Lee took the average life, or
expectation, as it is wrongly called, for his term: and this I have done
myself, taking the common story. Having exposed the absurdity of this
second supposition, taking it for Lee's, in my Formal Logic,[345] I will now do the same
with the first.
A mathematical truth is true in its extreme cases. Lee's principle is
that an annuity on a life is the annuity made certain for the term within
which it is an even chance the life drops. If, then, of a thousand
persons, 500 be sure to die within a year, and the other 500 be immortal,
Lee's price of an annuity to any one of these persons is the present
value of one payment: for one year is the term which each one has an even
chance of surviving and not surviving. But the true value is obviously
half that of a perpetual annuity: so that at 5 percent Lee's rule would
give less than the tenth of the true value. It must be said for the poor
circle-squarers, that they never err so much as this.
Lee would have said, if alive, that I have put an extreme case:
but any universal truth is true in its extreme cases. It is not
fair to bring forward an extreme case against a person who is speaking as
of usual occurrences: but it is quite fair when, as frequently happens,
the proposer insists upon a perfectly general acceptance of his
assertion. And yet many who go the whole hog protest against being
tickled with the tail. Counsel in court are good instances: they are
paradoxers by trade. June 13, 1849, at Hertford, there was an action
about a ship, insured against a total loss: some planks were
saved, and the underwriters refused to pay. Mr. Z. (for deft.) "There can
be no degrees of totality; and some timbers were saved."—L. C. B.
"Then if the vessel were burned to the water's edge, and some rope saved
in the boat, there would be no total loss."—Mr. Z. "This is putting
a very extreme case."—L. C. B. "The argument would go that length."
What would Judge Z.—as he now is—say to the extreme
case beginning somewhere between six planks and a bit of rope?
MONTUCLA'S WORK ON THE QUADRATURE.
Histoire des recherches sur la quadrature du cercle ... avec une
addition concernant les problèmes de la duplication du cube et de la
trisection de l'angle. Paris, 1754, 12mo. [By Montucla.]
This is the history of the subject.[346] It was a little episode to the great
history of mathematics by Montucla, of which the first edition appeared
in 1758. There was much addition at the end of the fourth volume of the
second edition; this is clearly by Montucla, though the bulk of the
volume is put together, with help from Montucla's papers, by Lalande.[347] There is also a second
edition of the history of the quadrature, Paris, 1831, 8vo, edited, I
think, by Lacroix; of which it is the great fault that it makes hardly
any use of the additional matter just mentioned.
Montucla is an admirable historian when he is writing from his own
direct knowledge: it is a sad pity that he did not tell us when he was
depending on others. We are not to trust a quarter of his book, and we
must read many other books to know which quarter. The fault is common
enough, but Montucla's good three-quarters is so good that the fault is
greater in him than in most others: I mean the fault of not
acknowledging; for an historian cannot read everything. But it must be
said that mankind give little encouragement to candor on this point.
Hallam, in his History of Literature, states with
his own usual instinct of honesty every case in which he depends upon
others: Montucla does not. And what is the consequence?—Montucla is
trusted, and believed in, and cried up in the bulk; while the smallest
talker can lament that Hallam should be so unequal and apt to depend on
others, without remembering to mention that Hallam himself gives the
information. As to a universal history of any great subject being written
entirely upon primary knowledge, it is a thing of which the possibility
is not yet proved by an example. Delambre attempted it with astronomy,
and was removed by death before it was finished,[348] to say nothing of the gaps he
left.
Montucla was nothing of a bibliographer, and his descriptions of books
in the first edition were insufficient. The Abbé Rive[349] fell foul of him, and as the phrase
is, gave it him. Montucla took it with great good humor, tried to mend,
and, in his second edition, wished his critic had lived to see the
vernis de bibliographe which he had given himself.
I have seen Montucla set down as an esprit fort, more than
once: wrongly, I think. When he mentions Barrow's[350] address to the Almighty, he adds, "On
voit, au reste, par là, que Barrow étoit un pauvre philosophe; car il
croyait en l'immortalité de l'âme, et en une Divinité autre que la nature
universelle."[351] This is irony, not an expression of
opinion. In the book of mathematical recreations which Montucla
constructed upon that of Ozanam,[352] and Ozanam upon that of Van Etten,[353] now best known in
England by Hutton's similar treatment of Montucla, there is an amusing
chapter on the quadrators. Montucla refers to his own anonymous book of
1754 as a curious book published by Jombert.[354] He seems to have been a little
ashamed of writing about circle-squarers: what a slap on the face for an
unborn Budgeteer!
Montucla says, speaking of France, that he finds three notions
prevalent among the cyclometers: (1) that there is a large reward offered
for success; (2) that the longitude problem depends on that success; (3)
that the solution is the great end and object of geometry. The same three
notions are equally prevalent among the
same class in England. No reward has ever been offered by the government
of either country. The longitude problem in no way depends upon perfect
solution; existing approximations are sufficient to a point of accuracy
far beyond what can be wanted.[355] And geometry, content with what
exists, has long passed on to other matters. Sometimes a cyclometer
persuades a skipper who has made land in the wrong place that the
astronomers are in fault, for using a wrong measure of the circle; and
the skipper thinks it a very comfortable solution! And this is the utmost
that the problem ever has to do with longitude.
ANTINEWTONIANISMUS.
Antinewtonianismus.[356] By Cælestino Cominale,[357] M.D. Naples, 1754 and
1756, 2 vols. 4to.
The first volume upsets the theory of light; the second vacuum, vis
inertiæ, gravitation, and attraction. I confess I never attempted these
big Latin volumes, numbering 450 closely-printed quarto pages. The man
who slays Newton in a pamphlet is the man for me. But I will lend them to
anybody who will give security, himself in £500, and two sureties in £250
each, that he will read them through, and give a full abstract; and I
will not exact security for their return. I have never seen any mention
of this book: it has a printer, but not a publisher, as happens with so
many unrecorded books.
OFFICIAL BLOW TO CIRCLE SQUARERS.
1755. The French Academy of Sciences came to the determination not to
examine any more quadratures or kindred problems. This was the
consequence, no doubt, of the publication of Montucla's book: the time
was well chosen; for that book was a full justification of the
resolution. The Royal Society followed the same course, I believe, a few
years afterwards. When our Board of Longitude was in existence, most of
its time was consumed in listening to schemes, many of which included the
quadrature of the circle. It is certain that many quadrators have
imagined the longitude problem to be connected with theirs: and no doubt
the notion of a reward offered by Government for a true quadrature is a
result of the reward offered for the longitude. Let it also be noted that
this longitude reward was not a premium upon excogitation of a mysterious
difficulty. The legislature was made to know that the rational hopes of
the problem were centered in the improvement of the lunar tables and the
improvement of chronometers. To these objects alone, and by name, the
offer was directed: several persons gained rewards for both; and the
offer was finally repealed.
AN INTERESTING HOAX.
Fundamentalis Figura Geometrica, primas tantum lineas circuli
quadraturæ possibilitatis ostendens. By Niels Erichsen (Nicolaus
Ericius), shipbuilder, of Copenhagen. Copenhagen, 1755, 12mo.
This was a gift from my oldest friend who was not a relative, Dr.
Samuel Maitland of the "Dark Ages."[358] He found it among his books, and
could not imagine how he came by it: I could have told him. He once
collected interpretations of the Apocalypse: and auction lots of such
books often contain quadratures. The
wonder is he never found more than one.
The quadrature is not worth notice. Erichsen is the only squarer I
have met with who has distinctly asserted the particulars of that reward
which has been so frequently thought to have been offered in England. He
says that in 1747 the Royal Society on the 2d of June, offered to give a
large reward for the quadrature of the circle and a true explanation of
magnetism, in addition to £30,000 previously promised for the same. I
need hardly say that the Royal Society had not £30,000 at that time, and
would not, if it had had such a sum, have spent it on the circle, nor on
magnetic theory; nor would it have coupled the two things. On this book,
see Notes and Queries, 1st S., xii, 306. Perhaps Erichsen meant
that the £30,000 had been promised by the Government, and the addition by
the Royal Society.
October 8, 1866. I receive a letter from a cyclometer who understands
that a reward is offered to any one who will square the circle, and that
all competitors are to send their plans to me. The hoaxers have not yet
failed out of the land.
TWO JESUIT CONTRIBUTIONS.
Theoria Philosophiæ Naturalis redacta ad unicam legem virium in natura
existentium. Editio Veneta prima. By Roger Joseph Boscovich.
Venice, 1763, 4to.
The first edition is said to be of Vienna, 1758.[359] This is a celebrated work on the
molecular theory of matter, grounded on the hypothesis of spheres of
alternate attraction and repulsion. Boscovich was a Jesuit of varied
pursuit. During his measurement of a degree of the meridian, while on
horseback or waiting for his observations, he composed a Latin poem of
about five thousand verses on eclipses, with notes, which he
dedicated to the Royal Society: De Solis et Lunæ defectibus,[360] London, Millar and
Dodsley, 1760, 4to.
Traité de paix entre Des Cartes et Newton, précédé des vies
littéraires de ces deux chefs de la physique moderne.... By Aimé Henri
Paulian.[361] Avignon,
1763, 12mo.
I have had these books for many years without feeling the least desire
to see how a lettered Jesuit would atone Descartes and Newton. On looking
at my two volumes, I find that one contains nothing but the literary life
of Descartes; the other nothing but the literary life of Newton. The
preface indicates more: and Watt mentions three volumes.[362] I dare say the first
two contain all that is valuable. On looking more attentively at the two
volumes, I find them both readable and instructive; the account of Newton
is far above that of Voltaire, but not so popular. But he should not have
said that Newton's family came from Newton in Ireland. Sir Rowland Hill
gives fourteen Newtons in Ireland;[363] twice the number of the cities that
contended for the birth of Homer may now contend for the origin of
Newton, on the word of Father Paulian.
Philosophical Essays, in three parts. By R. Lovett, Lay Clerk of the
Cathedral Church of Worcester. Worcester, 1766, 8vo.
The Electrical Philosopher: containing a new system of physics founded upon the principle of an universal
Plenum of elementary fire.... By R. Lovett, Worcester, 1774, 8vo.
Mr. Lovett[364] was
one of those ether philosophers who bring in elastic fluid as an
explanation by imposition of words, without deducing any one phenomenon
from what we know of it. And yet he says that attraction has received no
support from geometry; though geometry, applied to a particular law of
attraction, had shown how to predict the motions of the bodies of the
solar system. He, and many of his stamp, have not the least idea of the
confirmation of a theory by accordance of deduced results with
observation posterior to the theory.
BAILLY'S EXAGGERATED VIEW OF ASTRONOMY.
Lettres sur l'Atlantide de Platon, et sur l'ancien Histoire de l'Asie,
pour servir de suite aux lettres sur l'origine des Sciences, adressées à
M. de Voltaire, par M. Bailly.[365] London and Paris, 1779, 8vo.
I might enter here all Bailly's histories of astronomy.[366] The paradox which runs
through them all more or less, is the doctrine that astronomy is of
immense antiquity, coming from some forgotten source, probably the
drowned island of Plato, peopled by a race whom Bailly makes, as has been
said, to teach us everything except their existence and their name. These
books, the first scientific histories which belong to readable
literature, made a great impression by power of style: Delambre created a
strong reaction, of injurious amount, in favor of history founded on
contemporary documents, which early astronomy cannot furnish. These
letters are addressed to Voltaire, and continue the discussion. There is
one letter of Voltaire, being the fourth, dated Feb. 27, 1777, and signed
"le vieux malade de Ferney, V. puer centum annorum."[367] Then begin Bailly's letters, from
January 16 to May 12, 1778. From some ambiguous expressions in the
Preface, it would seem that these are fictitious letters, supposed to be
addressed to Voltaire at their dates. Voltaire went to Paris February 10,
1778, and died there May 30. Nearly all this interval was his closing
scene, and it is very unlikely that Bailly would have troubled him with
these letters.[368]
An inquiry into the cause of motion, or a general theory of physics.
By S. Miller. London, 1781, 4to
Newton all wrong: matter consists of two kinds of particles, one
inert, the other elastic and capable of expanding themselves ad
infinitum.
SAINT-MARTIN ON ERRORS AND TRUTH.
Des Erreurs et de la Vérité, ou les hommes rappelés au principe
universel de la science; ouvrage dans lequel, en faisant remarquer aux
observateurs l'incertitude de leurs recherches, et leurs méprises
continuelles, on leur indique la route qu'ils auroient dû suivre, pour
acquérir l'évidence physique sur l'origine du bien et du mal, sur
l'homme, sur la nature matérielle, et la nature sacrée; sur la base des
gouvernements politiques, sur l'autorité des souverains,
sur la justice civile et criminelle, sur les sciences, les langues, et
les arts. Par un Ph.... Inc.... A Edimbourg. 1782.[369] Two vols. 8vo.
This is the famous work of Louis Claude de Saint-Martin[370] (1743-1803), for whose
other works, vagaries included, the reader must look elsewhere: among
other things, he was a translator of Jacob Behmen.[371] The title promises much, and the
writer has smart thoughts now and then; but the whole is the wearisome
omniscience of the author's day and country, which no reader of our time
can tolerate. Not that we dislike omniscience; but we have it of our own
country, both home-made and imported; and fashions vary. But surely there
can be but one omniscience? Must a man have but one wife? Nay, may not a
man have a new wife while the old one is living? There was a famous
instrumental professor forty years ago, who presented a friend to Madame
——. The friend started, and looked surprised; for, not many
weeks before, he had been presented to another lady, with the same title,
at Paris. The musician observed his surprise, and quietly said, "Celle-ci
est Madame —— de Londres." In like manner we have a London
omniscience now current, which would make any one start who only knew the
old French article.
The book was printed at Lyons, but it was a trick of French authors to
pretend to be afraid of prosecution: it made a book look
wicked-like to have a feigned place of printing, and stimulated readers.
A Government which had undergone Voltaire would never have drawn its
sword upon quiet Saint-Martin. To make himself look still worse, he was
only ph[ilosophe] Inc...., which is generally read Inconnu[372] but sometimes
Incrédule; [373]
most likely the ambiguity was intended. There is an awful paradox about
the book, which explains, in part, its leaden sameness. It is all about
l'homme, l'homme, l'homme,[374] except as much as treats of les
hommes, les hommes, les hommes;[375] but not one single man is mentioned
by name in its 500 pages. It reminds one of
"Water, water everywhere,
And not a drop to drink."
Not one opinion of any other man is referred to, in the way of
agreement or of opposition. Not even a town is mentioned: there is
nothing which brings a capital letter into the middle of a sentence,
except, by the rarest accident, such a personification as Justice.
A likely book to want an Edimbourg godfather!
Saint-Martin is great in mathematics. The number four
essentially belongs to straight lines, and nine to curves. The
object of a straight line is to perpetuate ad infinitum the
production of a point from which it emanates. A circle 
bounds the production of all its
radii, tends to destroy them, and is in some sort their enemy. How is it
possible that things so distinct should not be distinguished in their
number as well as in their action? If this important observation
had been made earlier, immense trouble would have been saved to the
mathematicians, who would have been prevented from searching for a common
measure to lines which have nothing in common. But, though all straight
lines have the number four, it must not be supposed that they are
all equal, for a line is the result of its law and its number; but though
both are the same for all lines of a sort, they act differently, as to
force, energy, and duration, in different individuals; which explains all
differences of length, etc. I congratulate the reader who understands
this; and I do not pity the one who does not.
Saint-Martin and his works are now as completely forgotten as if they
had never been born, except so far as this, that some one may take up one
of the works as of heretical character, and lay it down in
disappointment, with the reflection that it is as dull as orthodoxy. For
a person who was once in some vogue, it would be difficult to pick out a
more fossil writer, from Aa to Zypœus, except,—though it is
unusual for (,—) to represent an interval of more than a
year—his unknown opponent. This opponent, in the very year of the
Des Erreurs ... published a book in two parts with the same
fictitious place of printing;
Tableau Naturel des Rapports qui existent entre Dieu, l'Homme, et
l'Univers. A Edimbourg, 1782, 8vo.[376]
There is a motto from the Des Erreurs itself, "Expliquer les
choses par l'homme, et non l'homme par les choses. Des Erreurs et de
la Vérité, par un PH.... INC...., p. 9."[377] This work is set down in various
catalogues and biographies as written by the PH.... INC.... himself. But
it is not usual for a writer to publish two works in the same year, one
of which takes a motto from the other. And the second work is profuse in
capitals and italics, and uses Hebrew learning: its style differs much
from the first work. The first work sets out from man, and has nothing to
do with God: the second is religious and raps the knuckles of the first
as follows: "Si nous voulons nous préserver de toutes les illusions,
et surtout des amorces de l'orgueil par lesquelles l'homme est si souvent
séduit, ne prenons jamais les hommes, mais toujours Dieu pour
notre terme de comparaison."[378] The first uses four and
nine in various ways, of which I have quoted one: the second says,
"Et ici se trouve déjà une explication des nombres quatre et
neuf, qui ont peu embarrassé dans l'ouvrage déjà cité. L'homme
s'est égaré en allant de quatre à neuf...."[379] The work cited is the
Erreurs, etc., and the citation is in the motto, which is the text
of the opposition sermon.
A FORERUNNER OF THE METRIC SYSTEM.
Method to discover the difference of the earth's diameters; proving
its true ratio to be not less variable than as 45 is to 46, and shortest
in its pole's axis 174 miles.... likewise a method for fixing an
universal standard for weights and measures. By Thomas Williams.[380] London, 1788, 8vo.
Mr. Williams was a paradoxer in his day, and proposed what was, no
doubt, laughed at by some. He proposed the sort of plan which the
French—independently of course—carried into effect a few
years after. He would have the 52d degree of latitude divided into
100,000 parts and each part a geographical yard. The geographical ton was
to be the cube of a geographical yard filled with sea-water taken some
leagues from land. All multiples and sub-divisions were to be
decimal.
I was beginning to look up those who had made similar proposals, when
a learned article on the proposal of a metrical system came
under my eye in the Times of Sept. 15, 1863. The author cites
Mouton,[381] who would
have the minute of a degree divided into 10,000 virgulæ; James
Cassini,[382] whose foot
was to be six thousandths of a minute; and Paucton,[383] whose foot was the 400,000th of a
degree. I have verified the first and third statements; surely the second
ought to be the six-thousandth.
An inquiry into the Copernican system ... wherein it is proved, in the
clearest manner, that the earth has only her diurnal motion ... with an
attempt to point out the only true way whereby mankind can receive any
real benefit from the study of the heavenly bodies. By John Cunningham.[384] London, 1789, 8vo.
The "true way" appears to be the treatment of heaven and earth as
emblematical of the Trinity.
Cosmology. An inquiry into the cause of what is called gravitation or
attraction, in which the motions of the heavenly bodies, and the
preservation and operations of all nature, are deduced from an universal
principle of efflux and reflux. By T. Vivian,[385] vicar of Cornwood, Devon. Bath, 1792,
12mo.
Attraction, an influx of matter to the sun; centrifugal force, the
solar rays; cohesion, the pressure of the atmosphere. The confusion about
centrifugal force, so called, as demanding an external agent, is
very common.
THOMAS PAINE'S RIGHTS OF MAN.
The rights of Man, being an answer to Mr.
Burke's attack on the French Revolution.[386] By Thomas Paine.[387] In two parts. 1791-1792. 8vo.
(Various editions.)[388]
A vindication of the rights of Woman, with
strictures on political and moral subjects. By Mary Wollstonecraft.[389] 1792. 8vo.
A sketch of the rights of Boys and Girls. By Launcelot Light, of Westminster School; and
Lætitia Lookabout, of Queen's Square, Bloomsbury. [By the Rev. Samuel
Parr,[390] LL.D.] 1792.
8vo. (pp.64).
When did we three meet before? The first work has sunk into oblivion:
had it merited its title, it might have lived. It is what the
French call a pièce de circonstance; it belongs in time to the
French Revolution, and in matter to Burke's opinion of that movement.
Those who only know its name think it was really an attempt to write a
philosophical treatise on what we now call socialism. Silly government
prosecutions gave it what it never could have got for itself.
Mary Wollstonecraft seldom has her name spelled right. I suppose the
O! O! character she got made her Woolstonecraft. Watt gives double
insinuation, for his cross-reference sends us to Goodwin.[391] No doubt the title of
the book was an act of discipleship to Paine's Rights of Man; but
this title is very badly chosen. The book was marred by it, especially
when the authoress and her husband assumed the right of dispensing with
legal sanction until the approach of offspring brought them to a sense of
their child's interest.[392] Not a hint of such a claim is found
in the book, which is mostly about female education. The right claimed
for woman is to have the education of a rational human being, and not to
be considered as nothing but woman throughout youthful training. The
maxims of Mary Wollstonecraft are now, though not derived from her,
largely followed in the education of girls, especially in home education:
just as many of the political principles of Tom Paine, again not derived
from him, are the guides of our actual legislation. I remember, forty
years ago, an old lady used to declare that she disliked girls from the
age of sixteen to five-and-twenty. "They are full," said she, "of
femalities." She spoke of their behavior to women as well as to
men. She would have been shocked to know that she
was a follower of Mary Wollstonecraft, and had packed half her book into
one sentence.
The third work is a satirical attack on Mary Wollstonecraft and Tom
Paine. The details of the attack would convince any one that neither has
anything which would now excite reprobation. It is utterly unworthy of
Dr. Parr, and has quite disappeared from lists of his works, if it were
ever there. That it was written by him I take to be evident, as follows.
Nichols,[393] who could
not fail to know, says (Anecd., vol. ix, p. 120): "This is a
playful essay by a first-rate scholar, who is elsewhere noticed in this
volume, but whose name I shall not bring forward on so trifling an
occasion." Who the scholar was is made obvious by Master Launcelot being
made to talk of Bellendenus.[394] Further, the same boy is made to say,
"Let Dr. Parr lay his hand upon his heart, if his conscience will let
him, and ask himself how many thousands of wagon-loads of this article
[birch] he has cruelly misapplied." How could this apply to Parr, with
his handful of private pupils,[395] and no reputation for severity? Any
one except himself would have called on the head-master of Westminster or
Eton. I doubt whether the name of Parr could be connected with the rod by
anything in print, except the above and an anecdote of his pupil, Tom
Sheridan.[396] The Doctor
had dressed for a dinner visit, and was ready a quarter of
an hour too soon to set off. "Tom," said he, "I think I had better whip
you now; you are sure to do something while I am out."—"I wish you
would, sir!" said the boy; "it would be a letter of licence for the whole
evening." The Doctor saw the force of the retort: my two tutelaries will
see it by this time. They paid in advance; and I have given liberal
interpretation to the order.
The following story of Dr. Parr was told me and others, about 1829, by
the late Leonard Horner,[397] who knew him intimately. Parr was
staying in a house full of company, I think in the north of England. Some
gentlemen from America were among the guests, and after dinner they
disputed some of Parr's assertions or arguments. So the Doctor broke out
with "Do you know what country you come from? You come from the place to
which we used to send our thieves!" This made the host angry, and he gave
Parr such a severe rebuke as sent him from the room in ill-humor. The
rest walked on the lawn, amusing the Americans with sketches of the
Doctor. There was a dark cloud overhead, and from that cloud presently
came a voice which called Tham (Parr-lisp for Sam). The
company were astonished for a moment, but thought the Doctor was calling
his servant in the house, and that the apparent direction was an illusion
arising out of inattention. But presently the sound was repeated,
certainly from the cloud,
"And nearer, clearer, deadlier than before."
There was now a little alarm: where could the Doctor have got to? They
ran to his bedroom, and there they discovered a sufficient rather than
satisfactory explanation. The Doctor had taken his pipe into his bedroom,
and had seated himself, in sulky mood, upon the higher bar of a large and
deep old-fashioned grate with a high mantelshelf. Here he had tumbled
backwards, and doubled himself up between the bars and the back of the
grate. He was fixed tight, and when he called for help, he could only
throw his voice up the chimney. The echo from the cloud was the warning
which brought his friends to the rescue.
ATTACKS ON RELIGIOUS CUSTOMS.
Days of political paradox were coming, at which we now stare.
Cobbett[398] said, about
1830, in earnest, that in the country every man who did not take off his
hat to the clergyman was suspected, and ran a fair chance of having
something brought against him. I heard this assertion canvassed, when it
was made, in a party of elderly persons. The Radicals backed it, the old
Tories rather denied it, but in a way which satisfied me they ought to
have denied it less if they could not deny it more. But it must be said
that the Governments stopped far short of what their partisans would have
had them do. All who know Robert Robinson's[399] very quiet assault on church-made
festivals in his History and Mystery of Good Friday (1777)[400] will hear or remember
with surprise that the British Critic pronounced it a direct,
unprovoked, and malicious libel on the most sacred institutions of
the national Church. It was reprinted again and again: in 1811 it was in
a cheap form at 6s. 6d. a hundred. When the Jacobin day came, the State
was really in a fright: people thought twice before they published what
would now be quite disregarded. I examined a quantity of letters
addressed to George Dyer[401] (Charles Lamb's G.D.) and what
between the autographs of Thelwall, Hardy, Horne Tooke, and all the
rebels,[402] put together
a packet which produced five guineas, or thereabouts, for the widow.
Among them were the following verses, sent by the author—who would
not put his name, even in a private letter, for fear of
accidents—for consultation whether they could safely be sent to an
editor: and they were not sent. The occasion was the public
thanksgiving at St. Paul's for the naval victories, December 19,
1797.
"God bless me! what a thing!
Have you heard that the King
Goes to St. Paul's?
Good Lord! and when he's there,
He'll roll his eyes in prayer,
To make poor Johnny stare
At this fine thing.
"No doubt the plan is wise
To blind poor Johnny's eyes
By this grand show;
For should he once suppose
That he's led by the nose,
Down the whole fabric goes,
Church, lords, and king.
"As he shouts Duncan's[403] praise,
Mind how supplies they'll raise
In wondrous haste.
For while upon the sea
We gain one victory,
John still a dupe will be
And taxes pay.
"Till from his little store
Three-fourths or even more
Goes to the Crown.
Ah, John! you little think
How fast we downward sink
And touch the fatal brink
At which we're slaves."
I would have indicted the author for not making his thirds and
sevenths rhyme. As to the rhythm, it is not much better than what the
French sang in the Calais theater when the Duke of Clarence[404] took over Louis XVIII
in 1814.
"God save noble Clarence,
Who brings our king to France;
God save Clarence!
He maintains the glory
Of the British navy,
etc., etc."
Perhaps had this been published, the Government would have assailed it
as a libel on the church service. They got into the way of defending
themselves by making libels on the Church, of what were libels, if on
anything, on the rulers of the State; until the celebrated trials of Hone
settled the point for ever, and established that juries will not convict
for one offence, even though it have been committed, when they know the
prosecution is directed at another offence and another intent.
HONE'S FAMOUS TRIALS.
The results of Hone's trials (William Hone, 1779-1842) are among the
important constitutional victories of our century. He published parodies
on the Creeds, the Lord's Prayer, the Catechism, etc., with intent to
bring the Ministry into contempt: everybody knew that was his
purpose. The Government indicted him for impious, profane,
blasphemous intent, but not for seditious intent. They hoped to wear him
out by proceeding day by day. December 18, 1817, they hid themselves
under the Lord's Prayer, the Creed, and the Commandments; December 19,
under the Litany; December 20, under the Athanasian Creed, an odd place
for shelter when they could not find it in the previous places. Hone
defended himself for six, seven, and eight hours on the several days: and
the jury acquitted him in 15, 105, and 20 minutes. In the second trial
the offense was laid both as profanity and as sedition, which seems to
have made the jury hesitate. And they probably came to think that the
second count was false pretence: but the length of their deliberation is
a satisfactory addition to the value of the whole. In the first trial the
Attorney-General (Shepherd) had the impudence to say that the libel had
nothing of a political tendency about it, but was avowedly set off
against the religion and worship of the Church of England. The whole is
political in every sentence; neither more nor less political than the
following, which is part of the parody on the Catechism: "What is thy
duty towards the Minister? My duty towards the Minister is, to trust him
as much as I can; to honor him with all my words, with all my bows, with
all my scrapes, and with all my cringes; to flatter him; to give him
thanks; to give up my whole soul to him; to idolize his name, and obey
his word, and serve him blindly all the days of his political life." And
the parody on the Creed begins, "I believe in George, the Regent
almighty, maker of new streets and Knights of the Bath." This is what the
Attorney-General said had nothing of a political tendency about it. But
this was on the first trial: Hone was not known. The first day's
trial was under Justice Abbott (afterwards C. J. Tenterden).[405] It was perfectly
understood, when Chief Justice Ellenborough[406] appeared in Court on the second day,
that he was very angry at the first result, and put his junior aside to
try his own rougher dealing. But Hone tamed the lion. An eye-witness told
me that when he implored of Hone not to detail his own father Bishop
Law's[407] views on the
Athanasian Creed, which humble petition Hone kindly granted, he held by
the desk for support. And the same when—which is not
reported—the Attorney-General appealed to the Court for protection
against a stinging attack which Hone made on the
Bar: he held on, and said, "Mr. Attorney, what can I do!" I
was a boy of twelve years old, but so strong was the feeling of
exultation at the verdicts that boys at school were not prohibited from
seeing the parodies, which would have been held at any other time quite
unfit to meet their eyes. I was not able to comprehend all about the Lord
Chief Justice until I read and heard again in after years. In the
meantime, Joe Miller had given me the story of the leopard which was sent
home on board a ship of war, and was in two days made as docile as a cat
by the sailors.[408] "You
have got that fellow well under," said an officer. "Lord bless your
Honor!" said Jack, "if the Emperor of Marocky would send us a cock
rhinoceros, we'd bring him to his bearings in no time!" When I came to
the subject again, it pleased me to entertain the question whether, if
the Emperor had sent a cock rhinoceros to preside on the third day in the
King's Bench, Hone would have mastered him: I forget how I settled
it. There grew up a story that Hone caused Lord Ellenborough's death, but
this could not have been true. Lord Ellenborough resigned his seat in a
few months, and died just a year after the trials; but sixty-eight years
may have had more to do with it than his defeat.
A large subscription was raised for Hone, headed by the Duke of
Bedford[409] for £105.
Many of the leading anti-ministerialists joined: but there were many of
the other side who avowed their disapprobation of the false pretense.
Many could not venture their names. In the list I find: A member of
the House of Lords, an enemy to persecution, and especially to religious
persecution employed for political purposes—No parodist, but an
enemy to persecution—A juryman on the third day's trial—Ellen
Borough—My name would ruin me—Oh! minions of Pitt—Oil
for the Hone—The Ghosts of Jeffries[410] and Sir William Roy [Ghosts of
Jeffries in abundance]—A conscientious Jury and a conscientious
Attorney, £1 6s. 8d.—To Mr. Hone, for defending in his own person
the freedom of the press, attacked for a political object, under the old
pretense of supporting Religion—A cut at corruption—An
Earldom for myself and a translation for my brother—One who
disapproves of parodies, but abhors persecution—From a schoolboy
who wishes Mr. Hone to have a very grand subscription—"For
delicacy's sake forbear," and "Felix trembled"—"I will go myself
to-morrow"—Judge Jeffries' works rebound in calf by Law—Keep
us from Law, and from the Shepherd's paw—I must not give you my
name, but God bless you!—As much like Judge Jeffries as the present
times will permit—May Jeffries' fame and Jeffries' fate on every
modern Jeffries wait—No parodist, but an admirer of the man who has
proved the fallacy of the Lawyer's Law, that when a man is his own
advocate he has a fool for his client—A Mussulman who thinks it
would not be an impious libel to parody the Koran—May the
suspenders of the Habeas Corpus Act be speedily suspended—Three
times twelve for thrice-tried Hone, who cleared the cases himself alone,
and won three heats by twelve to one, £1 16s.—A conscientious
attorney, £1 6s. 8d.—Rev. T. B. Morris, rector of Shelfanger, who
disapproves of the parodies, but abhors the making an affected zeal for
religion the pretext for political persecution—A Lawyer opposed in
principle to Law—For the Hone that set the razor
that shaved the rats—Rev. Dr. Samuel Parr, who most seriously
disapproves of all parodies upon the hallowed language of Scripture and
the contents of the Prayer-book, but acquits Mr. Hone of intentional
impiety, admires his talents and fortitude, and applauds the good sense
and integrity of his juries—Religion without hypocrisy, and Law
without impartiality—O Law! O Law! O Law!
These are specimens of a great many allusive mottoes. The subscription
was very large, and would have bought a handsome annuity, but Hone
employed it in the bookselling trade, and did not thrive. His Everyday
Book[411] and his
Apocryphal New Testament,[412] are useful books. On an annuity he
would have thriven as an antiquarian writer and collector. It is well
that the attack upon the right to ridicule Ministers roused a dormant
power which was equal to the occasion. Hone declared, on his honor, that
he had never addressed a meeting in his life, nor spoken a word before
more than twelve persons. Had he—which however could not then be
done—employed counsel and had a guilty defense made for him,
he would very likely have been convicted, and the work would have been
left to be done by another. No question that the parodies disgusted all
who reverenced Christianity, and who could not separate the serious and
the ludicrous, and prevent their existence in combination.
My extracts, etc., are from the nineteenth, seventeenth, and sixteenth
editions of the three trials, which seem to have been contemporaneous
(all in 1818) as they are made up into one book, with additional title
over all, and the motto "Thrice the brindled cat hath mew'd." They are
published by Hone himself, who I should have said was a publisher as
well as was to be. And though the trials only ended Dec. 20, 1817, the
preface attached to this common title is dated Jan. 23, 1818.[413]
The spirit which was roused against the false dealing of the
Government, i.e., the pretense of prosecuting for impiety when all the
world knew the real offense was, if anything, sedition—was not got
up at the moment: there had been previous exhibitions of it. For example,
in the spring of 1818 Mr. Russell, a little printer in Birmingham, was
indicted for publishing the Political Litany[414] on which Hone was afterwards tried.
He took his witnesses to the summer Warwick assizes, and was told that
the indictment had been removed by certiorari into the King's Bench. He
had notice of trial for the spring assizes at Warwick: he took his
witnesses there, and the trial was postponed by the Crown. He then had
notice for the summer assizes at Warwick; and so on. The policy seems to
have been to wear out the obnoxious parties, either by delays or by
heaping on trials. The Government was odious, and knew it could
not get verdicts against ridicule, and could get verdicts
against impiety. No difficulty was found in convicting the sellers of
Paine's works, and the like. When Hone was held to bail it was seen that
a crisis was at hand. All parties in politics furnished him with parodies
in proof of religious persons having made instruments of them. The
parodies by Addison and Luther were contributed by a Tory lawyer, who was
afterwards a judge.
Hone had published, in 1817, tracts of purely political ridicule:
Official Account of the Noble Lord's Bite,[415] Trial of the Dog for Biting the
Noble Lord, etc. These were not touched. After the trials, it is
manifest that Hone was to be unassailed, do what he might. The
Political House that Jack built, in 1819; The Man in the Moon,
1820; The Queen's Matrimonial Ladder, Non mi ricordo,
The R—l Fowls, 1820; The Political Showman at Home,
with plates by G. Cruickshank,[416] 1821 [he did all the plates]; The
Spirit of Despotism, 1821—would have been legitimate marks for
prosecution in previous years. The biting caricature of several of these
works are remembered to this day. The Spirit of Despotism was a
tract of 1795, of which a few copies had been privately circulated with
great secrecy. Hone reprinted it, and prefixed the following address to
"Robert Stewart, alias Lord Castlereagh"[417]: "It appears to me that if,
unhappily, your counsels are allowed much longer to prevail in the
Brunswick Cabinet, they will bring on a crisis, in which the king may be
dethroned or the people enslaved. Experience has shown that the people
will not be enslaved—the alternative is the affair of your
employers." Hone might say this without notice.
In 1819 Mr. Murray[418] published Lord Byron's Don
Juan,[419] and Hone
followed it with Don John, or Don Juan Unmasked, a little account
of what the publisher to the Admiralty was allowed to issue without
prosecution. The parody on the Commandments was a case very much in
point: and Hone makes a stinging allusion to the use of the
"unutterable Name, with a profane levity unsurpassed by any other
two lines in the English language." The lines are
"'Tis strange—the Hebrew noun which means 'I am,'
The English always use to govern d——n."
Hone ends with: "Lord Byron's dedication of 'Don Juan' to Lord
Castlereagh was suppressed by Mr. Murray from delicacy to Ministers. Q.
Why did not Mr. Murray suppress Lord Byron's parody on the Ten
Commandments? A. Because it contains nothing in ridicule of
Ministers, and therefore nothing that they could suppose would
lead to the displeasure of Almighty God."
The little matters on which I have dwelt will never appear in history
from their political importance, except in a few words of result. As a
mode of thought, silly evasions of all kinds belong to such a work as the
present. Ignorance, which seats itself in the chair of knowledge, is a
mother of revolutions in politics, and of unread pamphlets in
circle-squaring. From 1815 to 1830 the question of revolution or no
revolution lurked in all our English discussions. The high classes must
govern; the high classes shall not govern; and thereupon issue was to be
joined. In 1828-33 the question came to issue; and it was, Revolution
with or without civil war; choose. The choice was wisely made; and the
Reform Bill started a new system so well dovetailed into the old that the
joinings are hardly visible. And now, in 1867, the thing is repeated with
a marked subsidence of symptoms; and the party which has taken the place
of the extinct Tories is carrying through Parliament a wider extension of
the franchise than their opponents would have ventured. Napoleon used to
say that a decided nose was a sign of power: on which it has been
remarked that he had good reason to say so before the play was done. And
so had our country; it was saved from a religious war, and from a civil
war, by the power of that nose over its colleagues.
THOMAS TAYLOR, THE PLATONIST.
The Commentaries of Proclus.[420] Translated by Thomas Taylor.[421] London, 1792, 2 vols.
4to.[422]
The reputation of "the Platonist" begins to grow, and will continue to
grow. The most authentic account is in the Penny Cyclopædia,
written by one of the few persons who knew him well, and one of the fewer
who possess all his works. At page lvi of the Introduction is Taylor's
notion of the way to find the circumference. It is not geometrical, for
it proceeds on the motion of a point: the words "on account of the
simplicity of the impulsive motion, such a line must be either straight
or circular" will suffice to show how Platonic it is. Taylor certainly
professed a kind of heathenism. D'lsraeli said, "Mr. T. Taylor, the
Platonic philosopher and the modern Plethon,[423] consonant to that philosophy,
professes polytheism." Taylor printed this in large type, in a page by
itself after the dedication, without any disavowal. I have seen the
following, Greek and translation both, in his handwriting: "Πᾶς ἀγαθὸς
ᾗ ἀγαθὸς
ἐθνικός·
καὶ πᾶς
χριστιανὸς ᾗ
χριστιανὸς
κακός. Every good man, so far as
he is a good man, is a heathen; and every Christian, so far as he is a
Christian, is a bad man." Whether Taylor had in his head the Christian of
the New Testament, or whether he drew from those members of the
"religious world" who make manifest the religious flesh and the religious
devil, cannot be decided by us, and perhaps was
not known to himself. If a heathen, he was a virtuous one.
A NEW ERA IN FICTION.
(1795.) This is the date of a very remarkable paradox. The religious
world—to use a name claimed by a doctrinal sect—had long set
its face against amusing literature, and all works of imagination.
Bunyan, Milton, and a few others were irresistible; but a long face was
pulled at every attempt to produce something readable for poor people and
poor children. In 1795, a benevolent association began to
circulate the works of a lady who had been herself a dramatist, and had
nourished a pleasant vein of satire in the society of Garrick and his
friends; all which is carefully suppressed in some biographies. Hannah
More's[424] Cheap
Repository Tracts,[425] which were bought by millions of
copies, destroyed the vicious publications with which the hawkers deluged
the country, by the simple process of furnishing the hawkers with
something more saleable.
Dramatic fiction, in which the characters are drawn by
themselves, was, at the middle of the last century, the monopoly of
writers who required indecorum, such as Fielding and Smollett. All, or
nearly all, which could be permitted to the young, was dry narrative,
written by people who could not make their personages talk
character; they all spoke alike. The author of the Rambler[426] is ridiculed, because
his young ladies talk Johnsonese; but the satirists forget that all the
presentable novel-writers were equally incompetent; even the author of
Zeluco (1789)[427]
is the strongest possible case in point.
Dr. Moore,[428] the
father of the hero of Corunna,[429] with good narrative power, some sly
humor, and much observation of character, would have been, in our day, a
writer of the Peacock[430] family. Nevertheless, to one who is
accustomed to our style of things, it is comic to read the dialogue of a
jealous husband, a suspected wife, a faithless maid-servant, a tool of a
nurse, a wrong-headed pomposity of a priest, and a sensible physician,
all talking Dr. Moore through their masks. Certainly an Irish soldier
does say "by Jasus," and a cockney footman "this here" and "that there";
and this and the like is all the painting of characters which is effected
out of the mouths of the bearers by a narrator of great power. I suspect
that some novelists repressed their power under a rule that a narrative
should narrate, and that the dramatic should be confined to the
drama.
I make no exception in favor of Miss Burney;[431] though she was the forerunner of a
new era. Suppose a country in which dress is always of one color;
suppose an importer who brings in cargoes of blue stuff, red stuff, green
stuff, etc., and exhibits dresses of these several colors, that person is
the similitude of Miss Burney. It would be a delightful change from a
universal dull brown, to see one person all red, another all blue, etc.;
but the real inventor of pleasant dress would be the one who could mix
his colors and keep down the bright and gaudy. Miss Burney's introduction
was so charming, by contrast, that she nailed such men as Johnson, Burke,
Garrick, etc., to her books. But when a person who has read them with
keen pleasure in boyhood, as I did, comes back to them after a long
period, during which he has made acquaintance with the great novelists of
our century, three-quarters of the pleasure is replaced by wonder that he
had not seen he was at a puppet-show, not at a drama. Take some
labeled characters out of our humorists, let them be put together
into one piece, to speak only as labeled: let there be a Dominie with
nothing but "Prodigious!" a Dick Swiveller with nothing but adapted
quotations; a Dr. Folliott with nothing but sneers at Lord Brougham;[432] and the whole will
pack up into one of Miss Burney's novels.
Maria Edgeworth,[433]
Sydney Owenson (Lady Morgan),[434] Jane Austen,[435] Walter Scott,[436] etc., are all of our century; as are,
I believe, all the Minerva Press novels, as they were called, which show
some of the power in question. Perhaps dramatic talent found its best
encouragement in the drama itself. But I cannot ascertain that any such
power was directed at the multitude, whether educated or uneducated, with
natural mixture of character, under the restraints of decorum, until the
use of it by two religious writers of the school called "evangelical,"
Hannah More and Rowland Hill.[437] The Village Dialogues, though
not equal to the Repository Tracts, are in many parts an approach,
and perhaps a copy; there is frequently humorous satire, in that most
effective form, self-display. They were published in 1800, and, partly at
least, by the Religious Tract Society, the lineal successor of
the Repository association, though knowing nothing about its
predecessor. I think it right to add that Rowland Hill here mentioned is
not the regenerator of the Post Office.[438] Some do not distinguish accurately; I
have heard of more than one who took me to have had a logical controversy
with a diplomatist who died some years before I was born.
THE RELIGIOUS TRACT SOCIETY.
A few years ago, an attempt was made by myself and others to collect
some information about the Cheap Repository (see Notes and
Queries, 3d Series, vi. 241, 290, 353; Christian Observer,
Dec. 1864, pp. 944-49). It appeared that after the Religious Tract
Society had existed more than fifty years, a friend presented it with a
copy of the original prospectus of the Repository, a thing the
existence of which was not known. In this prospectus it is announced that
from the plan "will be carefully excluded whatever is enthusiastic,
absurd, or superstitious." The "evangelical" party had, from the
foundation of the Religious Tract Society, regretted that the
Repository Tracts "did not contain a fuller statement of the great
evangelical principles"; while in the prospectus it is also stated that
"no cause of any particular party is intended to be served by it, but
general Christianity will be promoted upon practical principles." This
explains what has often been noticed, that the tracts contain a mild form
of "evangelical" doctrine, free from that more fervid dogmatism which
appears in the Village Dialogues; and such as H. More's friend,
Bishop Porteus[439]—a great promoter of the
scheme—might approve. The Religious Tract Society (in 1863)
republished some of H. More's tracts, with alterations, additions, and
omissions ad libitum. This is an improper way of dealing with the
works of the dead; especially when the reprints are of popular works. A
small type addition to the preface contains: "Some alterations and
abridgements have been made to adapt them to the present times and the
aim of the Religious Tract Society." I think every publicity ought to be
given to the existence of such a practice; and I reprint what I said on
the subject in Notes and Queries.
Alterations in works which the Society republishes are a necessary
part of their plan, though such notes as they should judge to be
corrective would be the best way of proceeding. But the fact of
alteration should be very distinctly announced on the title of the work
itself, not left to a little bit of small type at the end of the preface,
in the place where trade advertisements, or directions to the binder, are
often found. And the places in which alteration has been made should be
pointed out, either by marks of omission, when omission is the
alteration, or by putting the altered sentences in brackets, when change
has been made. May any one alter the works of the dead at his own
discretion? We all know that readers in general will
take each sentence to be that of the author whose name is on the title;
so that a correcting republisher makes use of his author's name to
teach his own variation. The tortuous logic of "the trade," which is
content when "the world" is satisfied, is not easily answered, any more
than an eel is easily caught; but the Religious Tract Society may be
convinced [in the old sense] in a sentence. On which course would
they feel most safe in giving their account to the God of truth? "In your
own conscience, now?"
I have tracked out a good many of the variations made by the Religious
Tract Society in the recently published volume of Repository
Tracts. Most of them are doctrinal insertions or amplifications, to
the matter of which Hannah More would not have objected—all that
can be brought against them is the want of notice. But I have found two
which the respect I have for the Religious Tract Society, in spite of
much difference on various points, must not prevent my designating as
paltry. In the story of Mary Wood, a kind-hearted clergyman converses
with the poor girl who has ruined herself by lying. In the original, he
"assisted her in the great work of repentance;" in the reprint it is to
be shown in some detail how he did this. He is to begin by pointing out
that "the heart is deceitful above all things and desperately wicked."
Now the clergyman's name is Heartwell: so to prevent his name from
contradicting his doctrine, he is actually cut down to Harwell.
Hannah Moore meant this good man for one of those described in Acts xv.
8, 9, and his name was appropriate.
Again, Mr. Flatterwell, in persuasion of Parley the porter to let him
into the castle, declares that the worst he will do is to "play an
innocent game of cards just to keep you awake, or sing a cheerful song
with the maids." Oh fie! Miss Hannah More! and you a single lady too, and
a contemporary of the virtuous Bowdler![440] Though Flatterwell be an allegory
of the devil, this is really too indecorous, even for him. Out with the
three last words! and out it is.
The Society cuts a poor figure before a literary tribunal. Nothing was
wanted except an admission that the remarks made by me were unanswerable,
and this was immediately furnished by the Secretary (N. and Q., 3d
S., vi. 290). In a reply of which six parts out of seven are a very
amplified statement that the Society did not intend to reprint all
Hannah More's tracts, the remaining seventh is as follows:
"I am not careful [perhaps this should be careful not] to
notice Professor De Morgan's objections to the changes in 'Mary Wood' or
'Parley the Porter,' but would merely reiterate that the tracts were
neither designed nor announced to be 'reprints' of the originals [design
is only known to the designers; as to announcement, the title is ''Tis
all for the best, The Shepherd of Salisbury Plain, and other narratives
by Hannah More']; and much less [this must be careful not; further
removed from answer than not careful] can I occupy your space by a
treatise on the Professor's question: 'May any one alter the works of the
dead at his own discretion?'"
To which I say: Thanks for help!
I predict that Hannah More's Cheap Repository Tracts will
somewhat resemble the Pilgrim's Progress in their fate. Written
for the cottage, and long remaining in their original position, they will
become classical works of their kind. Most assuredly this will happen if
my assertion cannot be upset, namely, that they contain the first
specimens of fiction addressed to the world at large, and widely
circulated, in which dramatic—as distinguished from
puppet—power is shown, and without indecorum.
According to some statements I have seen, but which I have not
verified, other publishing bodies, such as the Christian Knowledge
Society, have taken the same liberty with the names of the dead as the
Religious Tract Society. If it be so, the impropriety is the work of the
smaller spirits who have not been sufficiently overlooked. There must be
an overwhelming majority in the higher councils to feel that, whenever
altered works are published, the fact of alteration should be
made as prominent as the name of the author. Everything short of this
is suppression of truth, and will ultimately destroy the credit of the
Society. Equally necessary is it that the alterations should be noted.
When it comes to be known that the author before him is altered, he knows
not where nor how nor by whom, the lowest reader will lose his
interest.
A TRIBUTE TO WILLIAM FREND.
The principles of Algebra. By William Frend.[441] London, 1796, 8vo. Second Part,
1799.
This Algebra, says Dr. Peacock,[442] shows "great distrust of the results
of algebraical science which were in existence at the time when it was
written." Truly it does; for, as Dr. Peacock had shown by full citation,
it makes war of extermination upon all that distinguishes algebra from
arithmetic. Robert Simson[443] and Baron Maseres[444] were Mr. Frend's predecessors in this
opinion.
The genuine respect which I entertained for my father-in-law did not
prevent my canvassing with perfect freedom his anti-algebraical and
anti-Newtonian opinions, in a long obituary memoir read at the
Astronomical Society in February 1842, which was written by me. It was
copied into the Athenæum of March 19. It must be said that if the
manner in which algebra was presented to the learner had been true
algebra, he would have been right: and if he had confined himself to
protesting against the imposition of attraction as a fundamental part of
the existence of matter, he would have been in unity with a great many,
including Newton himself. I wish he had preferred amendment to rejection
when he was a college tutor: he wrote and spoke English with a clearness
which is seldom equaled.
His anti-Newtonian discussions are confined to the preliminary
chapters of his Evening Amusements,[445] a series of astronomical lessons in
nineteen volumes, following the moon through a period of the golden
numbers.
There is a mistake about him which can never be destroyed. It is
constantly said that, at his celebrated trial in 1792, for sedition and
opposition to the Liturgy, etc., he was expelled from the
University. He was banished. People cannot see the difference; but
it made all the difference to Mr. Frend. He held his fellowship and its
profits till his marriage in 1808, and was a member of the University and
of its Senate till his death in 1841, as any Cambridge Calendar up to
1841 will show. That they would have expelled him if they could, is
perfectly true; and there is a funny story—also perfectly
true—about their first proceedings being under a statute which
would have given the power, had it not been discovered during the
proceedings that the statute did not exist. It had come so near to
existence as to be entered into the Vice-Chancellor's book for his
signature, which it wanted, as was not seen till Mr. Frend exposed it: in
fact, the statute had never actually passed.
There is an absurd mistake in Gunning's[446] Reminiscences of Cambridge. In
quoting a passage of Mr. Frend's pamphlet, which was very obnoxious to
the existing Government, it is printed that the poor market-women
complained that they were to be scotched a quarter of their wages
by taxation; and attention is called to the word by its being three times
printed in italics. In the pamphlet it is "sconced"; that very common old
word for fined or mulcted.
Lord Lyndhurst,[447]
who has [1863] just passed away under a load of years and honors, was Mr.
Frend's private pupil at Cambridge. At the time of the celebrated trial,
he and two others amused themselves, and vented the feeling which was
very strong among the undergraduates, by chalking the walls of Cambridge
with "Frend for ever!" While thus engaged in what, using the term
legally, we are probably to call his first publication, he and his
friends were surprised by the proctors. Flight and chase followed of
course: Copley and one of the others, Serjeant Rough,[448] escaped: the third, whose name I
forget, but who afterwards, I have been told was a bishop,[449] being lame, was
captured and impositioned. Looking at the Cambridge Calendar to verify
the fact that Copley was an undergraduate at the time, I find that there
are but two other men in the list of honors of his year whose names are
now widely remembered. And they were both celebrated schoolmasters;
Butler[450] of Harrow,
and Tate[451] of
Richmond.
But Mr. Frend had another noted pupil. I once had a conversation with
a very remarkable man, who was generally called "Place,[452] the tailor," but who was politician,
political economist, etc., etc. He sat in the room above his
shop—he was then a thriving master tailor at Charing
Cross—surrounded by books enough for nine, to shame a proverb. The
blue books alone, cut up into strips, would have measured Great Britain
for oh-no-we-never-mention-'ems, the Highlands included. I cannot find a
biography of this worthy and able man. I happened to mention William
Frend, and he said, "Ah! my old master, as I always call him. Many and
many a time, and year after year, did he come in every now and then
to give me instruction, while I was sitting on the board, working for my
living, you know."
Place, who really was a sound economist, is joined with Cobbett,
because they were together at one time, and because he was, in 1800,
etc., a great Radical. But for Cobbett he had a great contempt. He told
me the following story. He and others were advising with Cobbett about
the defense he was to make on a trial for seditious libel which was
coming on. Said Place, "You must put in the letters you have received
from Ministers, members of the Commons from the Speaker downwards, etc.,
about your Register, and their wish to have subjects noted. You must then
ask the jury whether a person so addressed must be considered as a common
sower of sedition, etc. You will be acquitted; nay, if your intention
should get about, very likely they will manage to stop proceedings."
Cobbett was too much disturbed to listen; he walked about the room
ejaculating "D—— the prison!" and the like. He had not the
sense to follow the advice, and was convicted.
Cobbett, to go on with the chain, was a political acrobat, ready for
any kind of posture. A friend of mine gave me several times an account of
a mission to him. A Tory member—those who know the old Tory world
may look for his initials in initials of two consecutive words of "Pay
his money with interest"—who was, of course, a political opponent,
thought Cobbett had been hardly used, and determined to subscribe
handsomely towards the expenses he was incurring as a candidate. My
friend was commissioned to hand over the money—a bag of sovereigns,
that notes might not be traced. He went into Cobbett's committee-room,
told the patriot his errand, and put the money on the table. "And to
whom, sir, am I indebted?" said Cobbett. "The donor," was the answer, "is
Mr. Andrew Theophilus Smith," or some such unlikely pair of baptismals.
"Ah!" said Cobbett, "I have known Mr. A. T. S. a long time! he was always
a true friend of his country!"
To return to Place. He is a noted instance of the advantage of our
jury system, which never asks a man's politics, etc. The late King of
Hanover, when Duke of Cumberland, being unpopular, was brought under
unjust suspicions by the suicide of his valet: he must have seduced the
wife and murdered the husband. The charges were as absurd as those
brought against the Englishman in the Frenchman's attempt at satirical
verses upon him:
"The Englishman is a very bad man;
He drink the beer and he steal the can:
He kiss the wife and he beat the man;
And the Englishman is a very G—— d——."
The charges were revived in a much later day, and the defense might
have given some trouble. But Place, who had been the foreman at the
inquest, came forward, and settled the question in a few lines. Every one
knew that the old Radical was quite free of all disposition to suppress
truth from wish to curry favor with royalty.
John Speed,[453] the
author of the English History,[454] (1632) which Bishop Nicolson[455] calls the best
chronicle extant, was a man, like Place, of no education, but what he
gave himself. The bishop says he would have done better if he had a
better training: but what, he adds, could have been expected from a
tailor! This Speed was, as well as Place. But he was released from
manual labor by Sir Fulk Grevil,[456] who enabled him to study.
A STORY ON SIMSON.
I have elsewhere noticed that those who oppose the mysteries of
algebra do not ridicule them; this I want the cyclometers to do. Of the
three who wrote against the great point, the negative quantity, and the
uses of 0 which are connected with it, only one could fire a squib. That
Robert Simson[457] should
do such a thing will be judged impossible by all who admit tradition. I
do not vouch for the following; I give it as a proof of the impression
which prevailed about him:
He used to sit at his open window on the ground floor, as deep in
geometry as a Robert Simson ought to be. Here he would be accosted by
beggars, to whom he generally gave a trifle, he roused himself to hear a
few words of the story, made his donation, and instantly dropped down
into his depths. Some wags one day stopped a mendicant who was on his way
to the window with "Now, my man, do as we tell you, and you will get
something from that gentleman, and a shilling from us besides. You will
go and say you are in distress, he will ask you who you are, and you will
say you are Robert Simson, son of John Simson of Kirktonhill." The man
did as he was told; Simson quietly gave him a coin, and dropped off. The
wags watched a little, and saw him rouse himself again, and exclaim
"Robert Simson, son of John Simson of Kirktonhill! why, that is myself.
That man must be an impostor." Lord Brougham tells the same story, with
some difference of details.
BARON MASERES.
Baron Maseres[458]
was, as a writer, dry; those who knew his writings will feel that he
seldom could have taken in a joke or issued a pun. Maseres was the fourth
wrangler of 1752, and first Chancellor's medallist (or highest in
classics); his second was Porteus[459] (afterward Bishop of London).
Waring[460] came five
years after him: he could not get Maseres through the second page of his
first book on algebra; a negative quantity stood like a lion in the way.
In 1758 he published his Dissertation on the Use of the Negative
Sign,[461] 4to. There
are some who care little about + and -, who would give it house-room for
the sake of the four words "Printed by Samuel Richardson."
Maseres speaks as follows: "A single quantity can never be marked with
either of those signs, or considered as either affirmative or negative;
for if any single quantity, as b, is marked either with the sign +
or with the sign - without assigning some other quantity, as a, to
which it is to be added, or from which it is to be subtracted, the mark
will have no meaning or signification: thus if it be said that the square
of -5, or the product of -5 into -5, is equal to +25, such an assertion
must either signify no more than that 5 times 5 is equal to 25 without
any regard to the signs, or it must be mere nonsense and unintelligible
jargon. I speak according to the foregoing definition, by which the
affirmativeness or negativeness of any quantity implies a relation to
another quantity of the same kind to which it is added, or from which
it is subtracted; for it may perhaps be very clear and intelligible to
those who have formed to themselves some other idea of affirmative and
negative quantities different from that above defined."
Nothing can be more correct, or more identically logical: +5 and -5,
standing alone, are jargon if +5 and -5 are to be understood as without
reference to another quantity. But those who have "formed to themselves
some other idea" see meaning enough. The great difficulty of the
opponents of algebra lay in want of power or will to see extension of
terms. Maseres is right when he implies that extension, accompanied by
its refusal, makes jargon. One of my paradoxers was present at a meeting
of the Royal Society (in 1864, I think) and asked permission to make some
remarks upon a paper. He rambled into other things, and, naming me, said
that I had written a book in which two sides of a triangle are pronounced
equal to the third.[462] So they are, in the sense in which
the word is used in complete algebra; in which A + B = C makes A, B, C,
three sides of a triangle, and declares that going over A and B, one
after the other, is equivalent, in change of place, to going over C at
once. My critic, who might, if he pleased, have objected to extension,
insisted upon reading me in unextended meaning.
On the other hand, it must be said that those who wrote on the other
idea wrote very obscurely about it and justified Des Cartes (De
Methodo)[463] when he
said: "Algebram vero, ut solet doceri, animadverti certis regulis et
numerandi formulis ita esse contentam, ut videatur potius ars quædam
confusa, cujus usu ingenium quodam modo turbatur et obscuratur, quam
scientia qua excolatur et perspicacius reddatur."[464] Maseres wrote this
sentence on the title of his own work, now before me; he would have made
it his motto if he had found it earlier.
There is, I believe, in Cobbett's Annual Register,[465] an account of an
interview between Maseres and Cobbett when in prison.
The conversation of Maseres was lively, and full of serious anecdote:
but only one attempt at humorous satire is recorded of him; it is an
instructive one. He was born in 1731 (Dec. 15), and his father was a
refugee. French was the language of the house, with the pronunciation of
the time of Louis XIV. He lived until 1824 (May 19), and saw the race of
refugees who were driven out by the first Revolution. Their pronunciation
differed greatly from his own; and he used to amuse himself by mimicking
them. Those who heard him and them had the two schools of pronunciation
before them at once; a thing which seldom happens. It might even yet be
worth while to examine the Canadian pronunciation.
Maseres went as Attorney-General to Quebec; and was appointed Cursitor
Baron of our Exchequer in 1773. There is a curious story about his
mission to Canada, which I have heard as good tradition, but have never
seen in print. The reader shall have it as cheap as I; and I confess I
rather believe it. Maseres was inveterately honest; he could not, at the
bar, bear to see his own client victorious, when he knew his cause was a
bad one. On a certain occasion he was in a cause which he knew would go
against him if a certain case were quoted. Neither the judge nor the
opposite counsel seemed to remember this case, and Maseres could not help
dropping an allusion which brought it out. His business as a
barrister fell off, of course. Some time after, Mr. Pitt (Chatham) wanted
a lawyer to send to Canada on a private mission, and wanted a very
honest man. Some one mentioned Maseres, and told the above story:
Pitt saw that he had got the man he wanted. The mission was
satisfactorily performed, and Maseres remained as Attorney-General.
The Doctrine of Life Annuities[466] (4to, 726 pages, 1783) is a strange
paradox. Its size, the heavy dissertations on the national debt, and the
depth of algebra supposed known, put it out of the question as an
elementary work, and it is unfitted for the higher student by its
elaborate attempt at elementary character, shown in its rejection of
forms derived from chances in favor of the average, and its
exhibition of the separate values of the years of an annuity, as
arithmetical illustrations. It is a climax of unsaleability,
unreadability, and inutility. For intrinsic nullity of interest, and
dilution of little matter with much ink, I can compare this book to
nothing but that of Claude de St. Martin, elsewhere mentioned, or the
lectures On the Nature and Properties of Logarithms, by James
Little,[467] Dublin,
1830, 8vo. (254 heavy pages of many words and few symbols), a wonderful
weight of weariness.
The stock of this work on annuities, very little diminished, was given
by the author to William Frend, who paid warehouse room for it until
about 1835, when he consulted me as to its disposal. As no publisher
could be found who would take it as a gift, for any purpose of sale, it
was consigned, all but a few copies, to a buyer of waste paper.
Baron Maseres's republications are well known: the Scriptores
Logarithmici[468] is
a set of valuable reprints, mixed with much which might
better have entered into another collection. It is not so well known that
there is a volume of optical reprints, Scriptores Optici, London,
1823, 4to, edited for the veteran of ninety-two by Mr. Babbage[469] at twenty-nine. This
excellent volume contains James Gregory, Des Cartes, Halley, Barrow, and
the optical writings of Huyghens, the Principia of the undulatory
theory. It also contains, by the sort of whim in which such men as
Maseres, myself, and some others are apt to indulge, a reprint of "The
great new Art of weighing Vanity,"[470] by M. Patrick Mathers, Arch-Bedel to
the University of St. Andrews, Glasgow, 1672. Professor Sinclair,[471] of Glasgow, a good man
at clearing mines of the water which they did not want, and furnishing
cities with water which they did want, seems to have written absurdly
about hydrostatics, and to have attacked a certain Sanders,[472] M.A. So Sanders,
assisted by James Gregory, published a heavy bit of jocosity about him.
This story of the authorship rested on a note made in his copy by Robert
Gray, M.D.; but it has since been fully confirmed by a letter of James
Gregory to Collins, in the Macclesfield Correspondence. "There is one
Master Sinclair, who did write the Ars Magna et Nova,[473] a pitiful ignorant
fellow, who hath lately written horrid nonsense in the hydrostatics, and
hath abused a master in the University, one Mr. Sanders, in print. This
Mr. Sanders ... is resolved to cause the Bedel of the University to write
against him.... We resolve to make excellent sport with him."
On this I make two remarks: First, I have learned from experience that
old notes, made in books by their possessors, are statements of high
authority: they are almost always confirmed. I do not receive them
without hesitation; but I believe that of all the statements about books
which rest on one authority, there is a larger percentage of truth in the
written word than in the printed word. Secondly, I mourn to think that
when the New Zealander picks up his old copy of this book, and reads it
by the associations of his own day, he may, in spite of the many
assurances I have received that my Athenæum Budget was amusing,
feel me to be as heavy as I feel James Gregory and Sanders. But he will
see that I knew what was coming, which Gregory did not.
MR. FREND'S BURLESQUE.
It was left for Mr. Frend to prove that an impugner of algebra could
attempt ridicule. He was, in 1803, editor of a periodical The
Gentleman's Monthly Miscellany, which lasted a few months.[474] To this, among other
things, he contributed the following, in burlesque of the use made of 0,
to which he objected.[475] The imitation of Rabelais, a writer
in whom he delighted, is good: to those
who have never dipped, it may give such a notion as they would not easily
get elsewhere. The point of the satire is not so good. But in truth it is
not easy to make pungent scoffs upon what is common sense to all mankind.
Who can laugh with effect at six times nothing is nothing, as false or
unintelligible? In an article intended for that undistinguishing know-0
the "general reader," there would have been no force of satire, if
division by 0 had been separated from multiplication by the
same.
I have followed the above by another squib, by the same author, on the
English language. The satire is covertly aimed at theological
phraseology; and any one who watches this subject will see that it is a
very just observation that the Greek words are not boiled enough.
Pantagruel's Decision of the Question about Nothing.
"Pantagruel determined to have a snug afternoon with Epistemon and
Panurge. Dinner was ordered to be set in a small parlor, and a particular
batch of Hermitage with some choice Burgundy to be drawn from a remote
corner of the cellar upon the occasion. By way of lunch, about an hour
before dinner, Pantagruel was composing his stomach with German sausages,
reindeer's tongues, oysters, brawn, and half a dozen different sorts of
English beer just come into fashion, when a most thundering knocking was
heard at the great gate, and from the noise they expected it to announce
the arrival at least of the First Consul, or king Gargantua. Panurge was
sent to reconnoiter, and after a quarter of an hour's absence, returned
with the news that the University of Pontemaca was waiting his highness's
leisure in the great hall, to propound a question which had turned the
brains of thirty-nine students, and had flung twenty-seven more into a
high fever. With all my heart, says Pantagruel, and swallowed down three
quarts of Burton ale; but remember, it wants but an hour of dinner time,
and the question must be asked in as few words as possible; for I cannot
deprive myself of the pleasure I expected to enjoy in the company of my
good friends for a set of mad-headed masters. I wish brother John was
here to settle these matters with the black gentry.
"Having said or rather growled this, he proceeded to the hall of
ceremony, and mounted his throne; Epistemon and Panurge standing on each
side, but two steps below him. Then advanced to the throne the three
beadles of the University of Pontemaca with their silver staves on their
shoulders, and velvet caps on their heads, and they were followed by
three times three doctors, and thrice three times three masters of art;
for everything was done in Pontemaca by the number three, and on this
account the address was written on parchment, one foot in breadth, and
thrice three times thrice three feet in length. The beadles struck the
ground with their heads and their staves three times in approaching the
throne; the doctors struck the ground with their heads thrice three
times, and the masters did the same thrice each time, beating the ground
with their heads thrice three times. This was the accustomed form of
approaching the throne, time out of mind, and it was said to be
emblematic of the usual prostration of science to the throne of
greatness.
"The mathematical professor, after having spit, and hawked, and
cleared his throat, and blown his nose on a handkerchief lent to him, for
he had forgotten to bring his own, began to read the address. In this he
was assisted by three masters of arts, one of whom, with a silver pen,
pointed out the stops; the second with a small stick rapped his knuckles
when he was to raise or lower his voice; and a third pulled his hair
behind when he was to look Pantagruel in the face. Pantagruel began to
chafe like a lion: he turned first on one side, then on the
other: he listened and groaned, and groaned and listened, and was in the
utmost cogitabundity of cogitation. His countenance began to brighten,
when, at the end of an hour, the reader stammered out these words:
"'It has therefore been most clearly proved that as all matter may be
divided into parts infinitely smaller than the infinitely smallest part
of the infinitesimal of nothing, so nothing has all the properties of
something, and may become, by just and lawful right, susceptible of
addition, subtraction, multiplication, division, squaring, and cubing:
that it is to all intents and purposes as good as anything that has been,
is, or can be taught in the nine universities of the land, and to deprive
it of its rights is a most cruel innovation and usurpation, tending to
destroy all just subordination in the world, making all universities
superfluous, leveling vice-chancellors, doctors, and proctors, masters,
bachelors, and scholars, to the mean and contemptible state of butchers
and tallow-chandlers, bricklayers and chimney-sweepers, who, if it were
not for these learned mysteries, might think that they knew as much as
their betters. Every one then, who has the good of science at heart, must
pray for the interference of his highness to put a stop to all the
disputes about nothing, and by his decision to convince all gainsayers
that the science of nothing is taught in the best manner in the
universities, to the great edification and improvement of all the youth
in the land.'
"Here Pantagruel whispered in the ear of Panurge, who nodded to
Epistemon, and they two left the assembly, and did not return for an
hour, till the orator had finished his task. The three beadles had thrice
struck the ground with their heads and staves, the doctors had
finished their compliments, and the masters were making their
twenty-seven prostrations. Epistemon and Panurge went up to Pantagruel,
whom they found fast asleep and snoring; nor could he be roused but by as
many tugs as there had been bowings from the corps of learning. At
last he opened his eyes, gave a good stretch, made half a dozen yawns,
and called for a stoup of wine. I thank you, my masters, says he; so
sound a nap I have not had since I came from the island of Priestfolly.
Have you dined, my masters? They answered the question by as many bows as
at entrance; but his highness left them to the care of Panurge, and
retired to the little parlor with Epistemon, where they burst into a fit
of laughter, declaring that this learned Baragouin about nothing was just
as intelligible as the lawyer's Galimathias. Panurge conducted the
learned body into a large saloon, and each in his way hearing a
clattering of plates and glasses, congratulated himself on his
approaching good cheer. There they were left by Panurge, who took his
chair by Pantagruel just as the soup was removed, but he made up for the
want of that part of his dinner by a pint of champagne. The learning of
the university had whetted their appetites; what they each ate it is
needless to recite; good wine, good stories, and hearty laughs went
round, and three hours elapsed before one soul of them recollected the
hungry students of Pontemaca.
"Epistemon reminded them of the business in hand, and orders were
given for a fresh dozen of hermitage to be put upon table, and the royal
attendants to get ready. As soon as the dozen bottles were emptied,
Pantagruel rose from table, the royal trumpets sounded, and he was
accompanied by the great officers of his court into the large dining
hall, where was a table with forty-two covers. Pantagruel sat at the
head, Epistemon at the bottom, and Panurge in the middle, opposite an
immense silver tureen, which would hold fifty gallons of soup. The wise
men of Pontemaca then took their seats according to seniority. Every
countenance glistened with delight; the music struck up; the dishes were
uncovered. Panurge had enough to do to handle the immense silver ladle:
Pantagruel and Epistemon had no time for eating, they were fully employed
in carving. The bill of fare announced the names of a hundred
different dishes. From Panurge's ladle came into the soup plate as much
as he took every time out of the tureen; and as it was the rule of the
court that every one should appear to eat, as long as he sat at table,
there was the clattering of nine and thirty spoons against the silver
soup-plates for a quarter of an hour. They were then removed, and knives
and forks were in motion for half an hour. Glasses were continually
handed round in the mean time, and then everything was removed, except
the great tureen of soup. The second course was now served up, in
dispatching which half an hour was consumed; and at the conclusion the
wise men of Pontemaca had just as much in their stomachs as Pantagruel in
his head from their address: for nothing was cooked up for them in every
possible shape that Panurge could devise.
"Wine-glasses, large decanters, fruit dishes, and plates were now set
on. Pantagruel and Epistemon alternately gave bumper toasts: the
University of Pontemaca, the eye of the world, the mother of taste and
good sense and universal learning, the patroness of utility, and the
second only to Pantagruel in wisdom and virtue (for these were her
titles), was drank standing with thrice three times three, and huzzas and
clattering of glasses; but to such wine the wise men of Pontemaca had not
been accustomed; and though Pantagruel did not suffer one to rise from
table till the eighty-first glass had been emptied, not even the weakest
headed master of arts felt his head in the least indisposed. The
decanters indeed were often removed, but they were brought back
replenished, filled always with nothing.
"Silence was now proclaimed, and in a trice Panurge leaped into the
large silver tureen. Thence he made his bows to Pantagruel and the whole
company, and commenced an oration of signs, which lasted an hour and a
half, and in which he went over all the matter contained in the Pontemaca
address; and though the wise men looked very serious during the whole
time, Pantagruel himself and his whole court could not help
indulging in repeated bursts of laughter. It was universally acknowledged
that he excelled himself, and that the arguments by which he beat the
English masters of arts at Paris were nothing to the exquisite selection
of attitudes which he this day assumed. The greatest shouts of applause
were excited when he was running thrice round the tureen on its rim, with
his left hand holding his nose, and the other exercising itself nine and
thirty times on his back. In this attitude he concluded with his back to
the professor of mathematics; and at the instant he gave his last flap,
by a sudden jump, and turning heels over head in the air, he presented
himself face to face to the professor, and standing on his left leg, with
his left hand holding his nose, he presented to him, in a white satin
bag, Pantagruel's royal decree. Then advancing his right leg, he fixed it
on the professor's head, and after three turns, in which he clapped his
sides with both hands thrice three times, down he leaped, and Pantagruel,
Epistemon, and himself took their leaves of the wise men of
Pontemaca.
"The wise men now retired, and by royal orders were accompanied by a
guard, and according to the etiquette of the court, no one having a royal
order could stop at any public house till it was delivered. The
procession arrived at Pontemaca at nine o'clock the next morning, and the
sound of bells from every church and college announced their arrival. The
congregation was assembled; the royal decree was saluted in the same
manner as if his highness had been there in person; and after the proper
ceremonies had been performed, the satin bag was opened exactly at twelve
o'clock. A finely emblazoned roll was drawn forth, and the public orator
read to the gaping assembly the following words:
"'They who can make something out of nothing shall have nothing to eat
at the court of—Pantagruel.'"
Origin of the English Language, related by a Swede.
"Some months ago in a party in Holland, consisting of natives of
various countries, the merit of their respective languages became a topic
of conversation. A Swede, who had been a great traveler, and could
converse in most of the modern languages of Europe, laughed very heartily
at an Englishman, who had ventured to speak in praise of the tongue of
his dear country. I never had any trouble, says he, in learning English.
To my very great surprise, the moment I sat foot on shore at Gravesend, I
found out, that I could understand, with very little trouble, every word
that was said. It was a mere jargon, made up of German, French, and
Italian, with now and then a word from the Spanish, Latin or Greek. I had
only to bring my mouth to their mode of speaking, which was done with
ease in less than a week, and I was everywhere taken for a true-born
Englishman; a privilege by the way of no small importance in a country,
where each man, God knows why, thinks his foggy island superior to any
other part of the world: and though his door is never free from some dun
or other coming for a tax, and if he steps out of it he is sure to be
knocked down or to have his pocket picked, yet he has the insolence to
think every foreigner a miserable slave, and his country the seat of
everything wretched. They may talk of liberty as they please, but Spain
or Turkey for my money: barring the bowstring and the inquisition, they
are the most comfortable countries under heaven, and you need not be
afraid of either, if you do not talk of religion and politics. I do not
see much difference too in this respect in England, for when I was there,
one of their most eminent men for learning was put in prison for a couple
of years, and got his death for translating one of Æsop's fables into
English, which every child in Spain and Turkey is taught, as soon as he
comes out of his leading strings. Here all the company unanimously cried
out against the Swede, that it was impossible: for in
England, the land of liberty, the only thing its worst enemies could say
against it, was, that they paid for their liberty a much greater price
than it was worth.—Every man there had a fair trial according to
laws, which everybody could understand; and the judges were cool,
patient, discerning men, who never took the part of the crown against the
prisoner, but gave him every assistance possible for his defense.
"The Swede was borne down, but not convinced; and he seemed determined
to spit out all his venom. Well, says he, at any rate you will not deny
that the English have not got a language of their own, and that they came
by it in a very odd way. Of this at least I am certain, for the whole
history was related to me by a witch in Lapland, whilst I was bargaining
for a wind. Here the company were all in unison again for the story.
"In ancient times, said the old hag, the English occupied a spot in
Tartary, where they lived sulkily by themselves, unknowing and unknown.
By a great convulsion that took place in China, the inhabitants of that
and the adjoining parts of Tartary were driven from their seats, and
after various wanderings took up their abode in Germany. During this time
nobody could understand the English, for they did not talk, but hissed
like so many snakes. The poor people felt uneasy under this circumstance,
and in one of their parliaments, or rather hissing meetings, it was
determined to seek a remedy: and an embassy was sent to some of our
sisterhood then living on Mount Hecla. They were put to a nonplus, and
summoned the Devil to their relief. To him the English presented their
petitions, and explained their sad case; and he, upon certain conditions,
promised to befriend them, and to give them a language. The poor Devil
was little aware of what he had promised; but he is, as all the world
knows, a man of too much honor to break his word. Up and down the world
then he went in quest of this new language: visited all the universities,
and all the schools, and all the courts of law,
and all the play-houses, and all the prisons; never was poor devil so
fagged. It would have made your heart bleed to see him. Thrice did he go
round the earth in every parallel of latitude; and at last, wearied and
jaded out, back came he to Hecla in despair, and would have thrown
himself into the volcano, if he had been made of combustible materials.
Luckily at that time our sisters were engaged in settling the balance of
Europe; and whilst they were looking over projects, and counter-projects,
and ultimatums, and post ultimatums, the poor Devil, unable to assist
them was groaning in a corner and ruminating over his sad condition.
"On a sudden, a hellish joy overspread his countenance; up he jumped,
and, like Archimedes of old, ran like a madman amongst the throng,
turning over tables, and papers, and witches, roaring out for a full hour
together nothing else but 'tis found, 'tis found! Away were sent the
sisterhood in every direction, some to traverse all the corners of the
earth, and others to prepare a larger caldron than had ever yet been set
upon Hecla. The affairs of Europe were at a stand: its balance was thrown
aside; prime ministers and ambassadors were everywhere in the utmost
confusion; and, by the way, they have never been able to find the balance
since that time, and all the fine speeches upon the subject, with which
your newspapers are every now and then filled, are all mere hocus-pocus
and rhodomontade. However, the caldron was soon set on, and the air was
darkened by witches riding on broomsticks, bringing a couple of folios
under each arm, and across each shoulder. I remember the time exactly: it
was just as the council of Nice had broken up, so that they got books and
papers there dog cheap; but it was a bad thing for the poor English, as
these were the worst materials that entered into the caldron. Besides, as
the Devil wanted some amusement, and had not seen an account of the
transactions of this famous council, he had all the books brought from it
laid before him, and split his sides almost with laughing, whilst
he was reading the speeches and decrees of so many of his old friends and
acquaintances. All this while the witches were depositing their loads in
the great caldron. There were books from the Dalai Lama, and from China:
there were books from the Hindoos, and tallies from the Caffres: there
were paintings from Mexico, and rocks of hieroglyphics from Egypt: the
last country supplied besides the swathings of two thousand mummies, and
four-fifths of the famed library of Alexandria. Bubble! bubble! toil and
trouble! never was a day of more labor and anxiety; and if our good
master had but flung in the Greek books at the proper time, they would
have made a complete job of it. He was a little too impatient: as the
caldron frothed up, he skimmed it off with a great ladle, and filled some
thousands of our wind-bags with the froth, which the English with great
joy carried back to their own country. These bags were sent to every
district: the chiefs first took their fill, and then the common people;
hence they now speak a language which no foreigner can understand, unless
he has learned half a dozen other languages; and the poor people, not one
in ten, understand a third part of what is said to them. The hissing,
however, they have not entirely got rid of, and every seven years, when
the Devil, according to agreement, pays them a visit, they entertain him
at their common halls and county meetings with their original
language.
"The good-natured old hag told me several other circumstances,
relative to this curious transaction, which, as there is an Englishman in
company, it will be prudent to pass over in silence: but I cannot help
mentioning one thing which she told me as a very great secret. You know,
says she to me, that the English have more religions among them than any
other nation in Europe, and that there is more teaching and sermonizing
with them than in any other country. The fact is this; it matters not who
gets up to teach them, the hard words of the Greek were not sufficiently
boiled, and whenever they get into a
sentence, the poor people's brains are turned, and they know no more what
the preacher is talking about, than if he harangued them in Arabic. Take
my word for it if you please; but if not, when you get to England, desire
the bettermost sort of people that you are acquainted with to read to you
an act of parliament, which of course is written in the clearest and
plainest style in which anything can be written, and you will find that
not one in ten will be able to make tolerable sense of it. The language
would have been an excellent language, if it had not been for the council
of Nice, and the words had been well boiled.
"Here the company burst out into a fit of laughter. The Englishman got
up and shook hands with the Swede: si non è vero, said he, è
ben trovato.[476]
But, however I may laugh at it here, I would not advise you to tell this
story on the other side of the water. So here's a bumper to Old England
for ever, and God save the king."
ON YOUTHFUL PRODIGIES.
The accounts given of extraordinary children and adolescents
frequently defy credence.[477] I will give two well-attested
instances.
The celebrated mathematician Alexis Claude Clairault (now Clairaut)[478] was certainly born in
May, 1713. His treatise on curves of double curvature (printed in 1731)[479] received the
approbation of the Academy of Sciences, August 23, 1729. Fontenelle, in
his certificate of this, calls the author sixteen years of age, and does
not strive to exaggerate the wonder, as he might have done, by reminding
his readers that this work, of original and sustained mathematical
investigation, must have been coming from the pen at the ages of fourteen
and fifteen. The truth was, as attested by De Molières,[480] Clairaut had given public proofs of
his power at twelve years old. His age being thus publicly certified, all
doubt is removed: say he had been—though great wonder would still
have been left—twenty-one instead of sixteen, his appearance, and
the remembrances of his friends, schoolfellows, etc., would have made it
utterly hopeless to knock off five years of that age while he was on view
in Paris as a young lion. De Molières, who examined the work officially
for the Garde des Sceaux, is transported beyond the bounds of
official gravity, and says that it "ne mérite pas seulement d'être
imprimé, mais d'être admiré comme un prodige d'imagination, de
conception, et de capacité."[481]
That Blaise Pascal was born in June, 1623, is perfectly well
established and uncontested.[482] That he wrote his conic sections at
the age of sixteen might be difficult to establish, though tolerably well
attested, if it were not for one circumstance, for the book was not
published. The celebrated theorem, "Pascal's hexagram,"[483] makes all the rest come very easy.
Now Curabelle,[484] in a
work published in 1644, sneers at Desargues,[485] whom he quotes, for having, in 1642,
deferred a discussion until "cette grande proposition nommée le Pascale
verra le jour."[486] That
is, by the time Pascal was nineteen, the hexagram was circulating
under a name derived from the author. The common story about Pascal,
given by his sister,[487]
is an absurdity which no doubt has prejudiced many against tales of early
proficiency. He is made, when quite a boy, to invent geometry in the
order of Euclid's propositions: as if that order were natural
sequence of investigation. The hexagram at ten years old would be a
hundred times less unlikely.
The instances named are painfully astonishing: I give one which has
fallen out of sight, because it will preserve an imperfect biography.
John Wilson[488] is
Wilson of that Ilk, that is, of "Wilson's Theorem." It is
this: if p be a prime number, the product of all the numbers up to
p-1, increased by 1, is divisible without remainder by p.
All mathematicians know this as Wilson's theorem, but few know who Wilson
was. He was born August 6, 1741, at the Howe in Applethwaite, and he was
heir to a small estate at Troutbeck in Westmoreland. He was sent to
Peterhouse, at Cambridge, and while an undergraduate was considered
stronger in algebra than any one in the University, except Professor
Waring, one of the most powerful algebraists of the century.[489] He was the senior
wrangler of 1761, and was then for some time a private tutor. When
Paley,[490] then in his
third year, determined to make a push for the senior wranglership, which
he got, Wilson was recommended to him as a tutor. Both were ardent in
their work, except that sometimes Paley, when he came for his lesson,
would find "Gone a fishing" written on his tutor's outer door: which was
insult added to injury, for Paley was very fond of fishing. Wilson soon
left Cambridge, and went to the bar. He practised on the northern circuit
with great success; and, one day, while passing his vacation on his
little property at Troutbeck, he received information, to his great
surprise, that Lord Thurlow,[491] with whom he had no
acquaintance, had recommended him to be a Judge of the Court of Common
Pleas. He died, Oct. 18, 1793, with a very high reputation as a lawyer
and a Judge. These facts are partly from Meadley's Life of
Paley,[492] no doubt
from Paley himself, partly from the Gentleman's Magazine, and from
an epitaph written by Bishop Watson.[493] Wilson did not publish anything: the
theorem by which he has cut his name in the theory of numbers was
communicated to Waring, by whom it was published. He married, in 1788, a
daughter of Serjeant Adair,[494] and left issue. Had a family,
many will say: but a man and his wife are a family, even without
children. An actuary may be allowed to be accurate in this matter, of
which I was reminded by what an actuary wrote of another actuary. William
Morgan,[495] in the life
of his uncle Dr. Richard Price,[496] says that the Doctor and his wife
were "never blessed with an addition to their family." I never met with
such accuracy elsewhere. Of William Morgan I add that my surname and
pursuits have sometimes, to my credit be it said, made a confusion
between him and me. Dates are nothing to the mistaken; the last three
years of Morgan's life were the first three years of my actuary-life
(1830-33). The mistake was to my advantage as well as to my credit. I owe
to it the acquaintance of one of the noblest of the human race, I mean
Elizabeth Fry,[497] who
came to me for advice about a philanthropic design, which involved life
questions, under a general impression that some Morgan had attended to
such things.[498]
NEWTON AGAIN OVERTHROWN.
A treatise on the sublime science of heliography, satisfactorily
demonstrating our great orb of light, the sun, to be absolutely no other
than a body of ice! Overturning all the received systems of the universe
hitherto extant; proving the celebrated and indefatigable Sir Isaac
Newton, in his theory of the solar system, to be as far distant from the
truth, as many of the heathen authors of Greece and Rome. By Charles
Palmer,[499] Gent.
London, 1798, 8vo.
Mr. Palmer burned some tobacco with a burning glass, saw that a lens
of ice would do as well, and then says:
"If we admit that the sun could be removed, and a terrestrial body of
ice placed in its stead, it would produce the same effect. The sun is a
crystaline body receiving the radiance of God, and operates on this earth
in a similar manner as the light of the sun does when applied to a convex
mirror or glass."
Nov. 10, 1801. The Rev. Thomas Cormouls,[500] minister of Tettenhall, addressed a
letter to Sir Wm. Herschel, from which I extract the following:
"Here it may be asked, then, how came the doctrines of Newton to solve
all astronomic Phenomina, and all problems concerning the same, both a
parte ante and a parte post.[501] It is answered that he certainly
wrought the principles he made use of into strickt analogy with the real
Phenomina of the heavens, and that the rules and results arizing from
them agree with them and resolve accurately all
questions concerning them. Though they are not fact and true, or nature,
but analogous to it, in the manner of the artificial numbers of
logarithms, sines, &c. A very important question arises here, Did
Newton mean to impose upon the world? By no means: he received and used
the doctrines reddy formed; he did a little extend and contract his
principles when wanted, and commit a few oversights of consequences. But
when he was very much advanced in life, he suspected the fundamental
nullity of them: but I have from a certain anecdote strong ground to
believe that he knew it before his decease and intended to have retracted
his error. But, however, somebody did deceive, if not wilfully,
negligently at least. That was a man to whom the world has great
obligations too. It was no less a philosopher than Galileo."
That Newton wanted to retract before his death, is a notion not
uncommon among paradoxers. Nevertheless, there is no retraction in the
third edition of the Principia, published when Newton was
eighty-four years old! The moral of the above is, that a gentleman who
prefers instructing William Herschel to learning how to spell, may find a
proper niche in a proper place, for warning to others. It seems that
gravitation is not truth, but only the logarithm of it.
BISHOPS AS PARADOXERS.
The mathematical and philosophical works of the Right Rev. John
Wilkins[502].... In two
volumes. London, 1802, 8vo.
This work, or at least part of the edition—all for aught I
know—is printed on wood; that is, on paper made from wood-pulp. It
has a rough surface; and when held before a candle is of very unequal
transparency. There is in it a reprint of the works on the earth and
moon. The discourse on the possibility of going to the moon, in this and
the edition of 1640, is incorporated: but from the account in the life
prefixed, and a mention by D'Israeli, I should suppose that it had
originally a separate title-page, and some circulation as a separate
tract. Wilkins treats this subject half seriously, half jocosely; he has
evidently not quite made up his mind. He is clear that "arts are not yet
come to their solstice," and that posterity will bring hidden things to
light. As to the difficulty of carrying food, he thinks, scoffing Puritan
that he is, the Papists may be trained to fast the voyage, or may find
the bread of their Eucharist "serve well enough for their
viaticum."[503] He
also puts the case that the story of Domingo Gonsales may be realized,
namely, that wild geese find their way to the moon. It will be
remembered—to use the usual substitute for, It has been
forgotten—that the posthumous work of Bishop Francis Godwin[504] of Llandaff was
published in 1638, the very year of Wilkins's first edition, in time for
him to mention it at the end. Godwin makes Domingo Gonsales get to the
moon in a chariot drawn by wild geese, and, as old books would say,
discourses fully on that head. It is not a little amusing that Wilkins
should have been seriously accused of plagiarizing Godwin, Wilkins
writing in earnest, or nearly so, and Godwin writing fiction. It may
serve to show philosophers how very near pure speculation comes to fable.
From the sublime to the ridiculous is but a step: which is the sublime,
and which the ridiculous, every one must settle for himself. With me,
good fiction is the sublime, and bad speculation the ridiculous. The
number of bishops in my list is small. I might, had I possessed the book,
have opened the list of quadrators with an Archbishop of Canterbury, or
at least with a divine who was not wholly not archbishop. Thomas
Bradwardine[505]
(Bragvardinus, Bragadinus) was elected in 1348; the Pope put in
another, who died unconsecrated; and Bradwardine was again elected in
1349, and lived five weeks longer, dying, I suppose, unconfirmed and
unconsecrated.[506]
Leland says he held the see a year, unus tantum annulus,[507] which seems to be a
confusion: the whole business, from the first election, took about a
year. He squared the circle, and his performance was printed at Paris in
1494. I have never seen it, nor any work of the author, except a tract on
proportion.
As Bradwardine's works are very scarce indeed, I give two titles from
one of the Libri catalogues.
"Arithmetic. Brauardini (Thomæ) Arithmetica
speculativa revisa et correcta a Petro Sanchez Ciruelo Aragonesi, black
letter, elegant woodcut title-page, VERY
RARE, folio. Parisiis, per Thomam Anguelast (pro Olivier
Senant), s. a. circa 1510.[508]
"This book, by Thomas Bradwardine, Archbishop of Canterbury must be
exceedingly scarce as it has escaped the notice of Professor De Morgan,
who, in his Arithmetical Books, speaks of a treatise of the same
author on proportions,[509] printed at Vienna in 1515, but does
not mention the present work.
"Bradwardine (Archbp. T.). Brauardini (Thomæ) Geometria speculativa,
com Tractato de Quadratura Circuli bene revisa a Petro Sanchez Ciruelo,
SCARCE, folio. Parisiis, J. Petit,
1511.[510]
"In this work we find the polygones étoilés,[511] see Chasles (Aperçu, pp. 480,
487, 521, 523, &c.) on the merit of the discoveries of this English
mathematician, who was Archbishop of Canterbury in the XIVth Century (tempore Edward III. A.D. 1349); and who applied geometry to theology. M.
Chasles says that the present work of Bradwardine contains 'Une théorie
nouvelle qui doit faire honneur au XIVe
Siècle.'"[512]
The titles do not make it quite sure that Bradwardine is the
quadrator; it may be Peter Sanchez after all.[513]
THE QUESTION OF PARALLELS.
Nouvelle théorie des parallèles. Par Adolphe Kircher[514] [so signed at the end of the
appendix]. Paris, 1803, 8vo.
An alleged emendation of Legendre.[515] The author refers to attempts by
Hoffman,[516] 1801, by
Hauff,[517] 1799, and to
a work of Karsten,[518]
or at least a theory of Karsten, contained in "Tentamen novæ parallelarum
theoriæ notione situs fundatæ; auctore G. C. Schwal,[519] Stuttgardæ, 1801, en 8 volumes."
Surely this is a misprint; eight volumes on the theory of
parallels? If there be such a work, I trust I and it may never meet,
though ever so far produced.
Soluzione ... della quadratura del Circolo. By Gaetano Rossi.[520] London, 1804, 8vo.
The three remarkable points of this book are, that the household of
the Prince of Wales took ten copies, Signora Grassini[521] sixteen, and that the circumference
is 3-1/5 diameters. That is, the appetite of Grassini for quadrature
exceeded that of the whole household (loggia) of the Prince of
Wales in the ratio in which the semi-circumference exceeds the diameter.
And these are the first two in the list of subscribers. Did the author
see this theorem?
A PATRIOTIC PARADOX.
Britain independent of commerce; or proofs, deduced from an
investigation into the true cause of the wealth of nations, that our
riches, prosperity, and power are derived from sources inherent in
ourselves, and would not be affected, even though our commerce were
annihilated. By Wm. Spence.[522] 4th edition, 1808, 8vo.
A patriotic paradox, being in alleviation of the Commerce panic which
the measures of Napoleon I.—who felt our Commerce, while Mr.
Spence only saw it—had awakened. In this very month (August,
1866), the Pres. Brit. Assoc. has applied a similar salve to the coal
panic; it is fit that science, which rubbed the sore, should find a
plaster. We ought to have an iron panic and a timber panic; and a solemn
embassy to the Americans, to beg them not to whittle, would be desirable.
There was a gold panic beginning, before the new fields were discovered.
For myself, I am the unknown and unpitied victim of a chronic
gutta-percha panic: I never could get on without it; to me, gutta percha
and Rowland Hill are the great discoveries of our day; and not
unconnected either, gutta percha being to the submarine post what Rowland
Hill is to the superterrene. I should be sorry to lose cow-choke—I
gave up trying to spell it many years ago—but if gutta percha go, I
go too. I think, that perhaps when, five hundred years hence, the people
say to the Brit. Assoc. (if it then exist) "Pray gentlemen, is it not
time for the coal to be exhausted?" they will be answered out of Molière
(who will certainly then exist): "Cela était autrefois ainsi, mais
nous avons changé tout cela."[523] A great many people think that if the
coal be used up, it will be announced some unexpected morning by all the
yards being shut up and written notice outside, "Coal all gone!" just
like the "Please, ma'am, there ain't no more sugar," with which the maid
servant damps her mistress just at breakfast-time. But these persons
should be informed that there is every reason to think that there will be
time, as the city gentleman said, to venienti the occurrite
morbo.[524]
SOME SCIENTIFIC PARADOXES.
An appeal to the republic of letters in behalf of injured science,
from the opinions and proceedings of some modern authors of elements of
geometry. By George Douglas.[525] Edinburgh, 1810, 8vo.
Mr. Douglas was the author of a very good set of mathematical
tables, and of other works. He criticizes Simson,[526] Playfair,[527] and others,—sometimes, I think,
very justly. There is a curious phrase which occurs more than once. When
he wants to say that something or other was done before Simson or another
was born, he says "before he existed, at least as an author." He seems to
reserve the possibility of Simson's pre-existence, but at the same
time to assume that he never wrote anything in his previous state. Tell
me that Simson pre-existed in any other way than as editor of some
pre-existent Euclid? Tell Apella![528]
1810. In this year Jean Wood, Professor of Mathematics in the
University of Virginia (Richmond),[529] addressed a printed circular to "Dr.
Herschel, Astronomer, Greenwich Observatory." No mistake was more common
than the natural one of imagining that the Private Astronomer of
the king was the Astronomer Royal. The letter was on the difference
of velocities of the two sides of the earth, arising from the composition
of the rotation and the orbital motion. The paradox is a fair one,
and deserving of investigation; but, perhaps it would not be easy to
deduce from it tides, trade-winds, aerolithes, &c., as Mr. Wood
thought he had done in a work from which he gives an extract, and which
he describes as published. The composition of rotations, &c., is not
for the world at large: the paradox of the non-rotation of the moon about
her axis is an instance. How many persons know that when a wheel rolls on
the ground, the lowest point is moving upwards, the highest point
forwards, and the intermediate points in all degrees of betwixt and
between? This is too short an explanation, with some good
difficulties.
The Elements of Geometry. In 2 vols. [By the Rev. J. Dobson,[530] B.D.] Cambridge, 1815.
4to.
Of this unpunctuating paradoxer I shall give an account in his own
way: he would not stop for any one; why should I stop for him? It is
worth while to try how unpunctuated sentences will read.
The reverend J Dobson BD late fellow of saint Johns college Cambridge
was rector of Brandesburton in Yorkshire he was seventh wrangler in 1798
and died in 1847 he was of that sort of eccentricity which permits
account of his private life if we may not rather say that in such cases
private life becomes public there is a tradition that he was called Death
Dobson on account of his head and aspect of countenance being not very
unlike the ordinary pictures of a human skull his mode of life is
reported to have been very singular whenever he visited Cambridge he was
never known to go twice to the same inn he never would sleep at the
rectory with another person in the house some ancient charwoman used to
attend to the house but never slept in it he has been known in the time
of coach travelling to have deferred his return to Yorkshire on
account of his disinclination to travel with a lady in the coach he
continued his mathematical studies until his death and till his executors
sold the type all his tracts to the number of five were kept in type at
the university press none of these tracts had any stops except full stops
at the end of paragraphs only neither had they capitals except one at the
beginning of a paragraph so that a full stop was generally followed by
some white as there is not a single proper name in the whole of the book
I have I am not able to say whether he would have used capitals before
proper names I have inserted them as usual for which I hope his spirit
will forgive me if I be wrong he also published the elements of geometry
in two volumes quarto Cambridge 1815 this book had also no stops except
when a comma was wanted between letters as in the straight lines AB, BC I
should also say that though the title is unpunctuated in the author's
part it seems the publishers would not stand it in their imprint this
imprint is punctuated as usual and Deighton and Sons to prove the
completeness of their allegiance have managed that comma semicolon and
period shall all appear in it why could they not have contrived
interrogation and exclamation this is a good precedent to establish the
separate right of the publisher over the imprint it is said that only
twenty of the tracts were printed and very few indeed of the book on
geometry it is doubtful whether any were sold there is a copy of the
geometry in the university library at Cambridge and I have one myself the
matter of the geometry differs entirely from Euclid and is so fearfully
prolix that I am sure no mortal except the author ever read it the man
went on without stops and without stop save for a period at the end of a
paragraph this is the unpunctuated account of the unpunctuating geometer
suum cuique tribuito[531] Mrs Thrale[532] would have been amused at a Dobson
who managed to come to a full stop without either of the three
warnings.
I do not find any difficulty in reading Dobson's geometry; and I have
read more of it to try reading without stops than I should have done had
it been printed in the usual way. Those who dip into the middle of my
paragraph may be surprised for a moment to see "on account of his
disinclination to travel with a lady in the coach he continued his
mathematical studies until his death and [further, of course] until his
executors sold the type." But a person reading straight through would
hardly take it so. I should add that, in order to give a fair trial, I
did not compose as I wrote, but copied the words of the correspondent who
gave me the facts, so far as they went.
A RELIGIOUS PARADOX.
Philosophia Sacra, or the principles of natural Philosophy.
Extracted from Divine Revelation. By the Rev. Samuel Pike.[533] Edited by the Rev.
Samuel Kittle.[534]
Edinburgh, 1815, 8vo.
This is a work of modified Hutchinsonianism, which I have seen cited
by several. Though rather dark on the subject, it seems not to contradict
the motion of the earth, or the doctrine of gravitation. Mr. Kittle gives
a list of some Hutchinsonians,—as Bishop Horne;[535] Dr. Stukeley;[536] the Rev. W. Jones,[537] author of
Physiological Disquisitions; Mr. Spearman,[538] author of Letters on the
Septuagint and editor of Hutchinson; Mr. Barker,[539] author of Reflexions on
Learning; Dr. Catcott,[540] author of a work on the creation,
&c.; Dr. Robertson,[541] author of a Treatise on the Hebrew
Language; Dr. Holloway,[542] author of Originals, Physical and
Theological; Dr. Walter Hodges,[543] author of a work on Elohim;
Lord President Forbes (ob. 1747).[544]
The Rev. William Jones, above mentioned (1726-1800), the friend and
biographer of Bishop Horne and his stout defender, is best known
as William Jones of Nayland, who (1757)[545] published the Catholic Doctrine of
the Trinity; he was also strong for the Hutchinsonian physical
trinity of fire, light, and spirit. This well-known work was generally
recommended, as the defence of the orthodox system, to those who could
not go into the learning of the subject. There is now a work more suited
to our time: The Rock of Ages, by the Rev. E. H. Bickersteth,[546] now published by the
Religious Tract Society, without date, answered by the Rev. Dr. Sadler,[547] in a work (1859)
entitled Gloria Patri, in which, says Mr. Bickersteth, "the author
has not even attempted to grapple with my main propositions." I have read
largely on the controversy, and I think I know what this means. Moreover,
when I see the note "There are two other passages to which Unitarians
sometimes refer, but the deduction they draw from them is, in each case,
refuted by the context"—I think I see why the two texts are not
named. Nevertheless, the author is a little more disposed to yield to
criticism than his foregoers; he does not insist on texts and readings
which the greatest editors have rejected. And he writes with courtesy,
both direct and oblique, towards his antagonists; which, on his side of
this subject, is like letting in fresh air. So that I suspect the two
books will together make a tolerably good introduction to the subject for
those who cannot go deep. Mr. Bickersteth's book is well arranged and
indexed, which is a point of superiority to Jones of Nayland. There is a
point which I should gravely recommend to writers on the orthodox side.
The Unitarians in England have frequently contended that the
method of proving the divinity of Jesus Christ from the New Testament
would equally prove the divinity of Moses. I have not fallen in the way
of any orthodox answers specially directed at the repeated tracts written
by Unitarians in proof of their assertion. If there be any, they should
be more known; if there be none, some should be written. Which ever side
may be right, the treatment of this point would be indeed coming to close
quarters. The heterodox assertion was first supported, it is said, by
John Bidle or Biddle (1615-1662) of Magdalen College, Oxford, the
earliest of the English Unitarian writers, previously known by a
translation of part of Virgil and part of Juvenal.[548] But I cannot find that he wrote on
it.[549] It is the
subject of "αἱρεσεων
ἀναστασις, or a
new way of deciding old controversies. By Basanistes. Third edition,
enlarged," London, 1815, 8vo.[550] It is the appendix to the amusing,
"Six more letters to Granville Sharp, Esq., ... By Gregory Blunt, Esq."
London, 8vo., 1803.[551]
This much I can confidently say, that the study of these tracts would
prevent orthodox writers from some curious slips, which are slips obvious
to all sides of opinion. The lower defenders of orthodoxy frequently vex
the spirits of the higher ones.
Since writing the above I have procured Dr. Sadler's answer. I thought
I knew what the challenger meant when he said the respondent had not
grappled with his main propositions. I should say that he is
clung on to from beginning to end. But perhaps Mr. B. has his own meaning
of logical terms, such as "proposition": he certainly has his own meaning
of "cumulative." He says his evidence is cumulative; not a catena, the
strength of which is in its weakest part, but distinct and independent
lines, each of which corroborates the other. This is the very opposite of
cumulative: it is distributive. When different arguments
are each necessary to a conclusion, the evidence is cumulative;
when any one will do, even though they strengthen each other, it is
distributive. The word "cumulative" is a synonym of the law word
"constructive"; a whole which will do made out of parts which separately
will not. Lord Strafford [552] opens his defence with the use of
both words: "They have invented a kind of accumulated or
constructive evidence; by which many actions, either totally
innocent in themselves, or criminal in a much inferior degree, shall,
when united, amount to treason." The conclusion is, that Mr. B. is
a Cambridge man; the Oxford men do not confuse the elementary terms of
logic. O dear old Cambridge! when the New Zealander comes let him find
among the relics of your later sons some proof of attention to the
elementary laws of thought. A little-go of logic, please!
Mr. B., though apparently not a Hutchinsonian, has a nibble at a
physical Trinity. "If, as we gaze on the sun shining in the firmament, we
see any faint adumbration of the doctrine of the Trinity in the fontal
orb, the light ever generated, and the heat proceeding from the sun and
its beams—threefold and yet one, the sun, its light, and its heat,—that luminous globe, and the
radiance ever flowing from it, are both evident to the eye; but the vital
warmth is felt, not seen, and is only manifested in the life it
transfuses through creation. The proof of its real existence is
self-demonstrating."
We shall see how Revilo[553] illustrates orthodoxy by mathematics.
It was my duty to have found one of the many illustrations from physics;
but perhaps I should have forgotten it if this instance had not come in
my way. It is very bad physics. The sun, apart from its light, evident to
the eye! Heat more self-demonstrating than light, because felt!
Heat only manifested by the life it diffuses! Light implied not necessary
to life! But the theology is worse than Sabellianism[554]. To adumbrate—i.e., make a
picture of—the orthodox doctrine, the sun must be heavenly body,
the light heavenly body, the heat heavenly body; and yet, not three
heavenly bodies, but one heavenly body. The truth is, that this
illustration and many others most strikingly illustrate the Trinity of
fundamental doctrine held by the Unitarians, in all its differences from
the Trinity of persons held by the Orthodox. Be right which may, the
right or wrong of the Unitarians shines out in the comparison. Dr. Sadler
confirms me—by which I mean that I wrote the above before I saw
what he says—in the following words: "The sun is one object with
two properties, and these properties have a parallel not in the
second and third persons of the Trinity, but in the attributes of
Deity."
The letting light alone, as self-evident, and making heat
self-demonstrating, because felt—i.e., perceptible now and
then—has the character of the Irishman's astronomy:
"Long life to the moon, for a dear noble cratur,
Which serves us for lamplight all night in the dark,
While the sun only shines in the day, which by natur,
Wants no light at all, as ye all may remark."
SIR RICHARD PHILLIPS.
Sir Richard Phillips[555] (born 1768) was conspicuous in 1793,
when he was sentenced to a year's imprisonment[556] for selling Paine's Rights of
Man; and again when, in 1807[557], he was knighted as Sheriff of
London. As a bookseller, he was able to enforce his opinions in more ways
than others. For instance, in James Mitchell's[558] Dictionary of the Mathematical and
Physical Sciences, 1823, 12mo, which, though he was not technically a
publisher, was printed for him—a book I should recommend to the
collector of works of reference—there is a temperate description of
his doctrines, which one may almost swear was one of his conditions
previous to undertaking the work. Phillips himself was not only an
anti-Newtonian, but carried to a fearful excess the notion that statesmen
and Newtonians were in league to deceive the world. He saw this plot in
Mrs. Airy's[559] pension,
and in Mrs. Somerville's[560]. In 1836, he did me the honor to
attempt my conversion. In his first letter he says:
"Sir Richard Phillips has an inveterate abhorrence of all the
pretended wisdom of philosophy derived from the monks and doctors of the
middle ages, and not less of those of higher name who merely sought to
make the monkish philosophy more plausible, or so to disguise it as to
mystify the mob of small thinkers."
So little did his writings show any knowledge of antiquity, that I
strongly suspect, if required to name one of the monkish doctors, he
would have answered—Aristotle. These schoolmen, and the
"philosophical trinity of gravitating force, projectile force, and void
space," were the bogies of his life.
I think he began to publish speculations in the Monthly
Magazine (of which he was editor) in July 1817: these he republished
separately in 1818. In the Preface, perhaps judging the feelings of
others by his own, he says that he "fully expects to be vilified,
reviled, and anathematized, for many years to come." Poor man! he was let
alone. He appeals with confidence to the "impartial decision of
posterity"; but posterity does not appoint a hearing for one per cent. of
the appeals which are made; and it is much to be feared that an article
in such a work of reference as this will furnish nearly all her materials
fifty years hence. The following, addressed to M. Arago,[561] in 1835, will give posterity as good
a notion as she will probably need:
"Even the present year has afforded EVER-MEMORABLE examples, paralleled only by that of
the Romish Conclave which persecuted Galileo. Policy has adopted that
maxim of Machiavel which teaches that it is more prudent to
reward partisans than to persecute
opponents. Hence, a bigotted party had influence enough with the late
short-lived administration [I think he is wrong as to the administration]
of Wellington, Peel, &c., to confer munificent royal pensions on
three writers whose sole distinction was their advocacy of the Newtonian
philosophy. A Cambridge professor last year published an elaborate volume
in illustration of Gravitation, and on him has been conferred a
pension of 300l. per annum. A lady has written a light popular
view of the Newtonian Dogmas, and she has been complimented by a pension
of 200l. per annum. And another writer, who has recently published
a volume to prove that the only true philosophy is that of Moses, has
been endowed with a pension of 200l. per annum. Neither of them
were needy persons, and the political and ecclesiastical bearing of the
whole was indicated by another pension of 300l. bestowed on a
political writer, the advocate of all abuses and prejudices. Whether the
conduct of the Romish Conclave was more base for visiting with legal
penalties the promulgation of the doctrines that the Earth turns on its
axis and revolves around the Sun; or that of the British Court, for its
craft in conferring pensions on the opponents of the plain corollary,
that all the motions of the Earth are 'part and parcel' of these great
motions, and those again and all like them consecutive displays of still
greater motions in equality of action and reaction, is A QUESTION which must be reserved for the casuists of
other generations.... I cannot expect that on a sudden you and your
friends will come to my conclusion, that the present philosophy of the
Schools and Universities of Europe, based on faith in witchcraft, magic,
&c., is a system of execrable nonsense, by which quacks live on
the faith of fools; but I desire a free and fair examination of my
Aphorisms, and if a few are admitted to be true, merely as courteous
concessions to arithmetic, my purpose will be effected, for men will thus
be led to think; and if they think, then the fabric of false
assumptions, and degrading superstitions will soon tumble in ruins."
This for posterity. For the present time I ground the fame of Sir R.
Phillips on his having squared the circle without knowing it, or
intending to do it. In the Protest presently noted he discovered
that "the force taken as 1 is equal to the sum of all its fractions ...
thus 1 = 1/4 + 1/9 + 1/16 + 1/25, &c., carried to infinity." This the
mathematician instantly sees is equivalent to the theorem that the
circumference of any circle is double of the diagonal of the cube on its
diameter.[562]
I have examined the following works of Sir R. Phillips, and heard of
many others:
Essays on the proximate mechanical causes of the general phenomena of
the Universe, 1818, 12mo.[563]
Protest against the prevailing principles of natural philosophy, with
the development of a common sense system (no date, 8vo, pp. 16).[564]
Four dialogues between an Oxford Tutor and a disciple of the
common-sense philosophy, relative to the proximate causes of material
phenomena. 8vo, 1824.
A century of original aphorisms on the proximate causes of the
phenomena of nature, 1835, 12mo.
Sir Richard Phillips had four valuable qualities; honesty, zeal,
ability, and courage. He applied them all to teaching matters about
which he knew nothing; and gained himself an uncomfortable life and a
ridiculous memory.
Astronomy made plain; or only way the true perpendicular distance of
the Sun, Moon, or Stars, from this earth, can be obtained. By Wm. Wood.[565] Chatham, 1819,
12mo.
If this theory be true, it will follow, of course, that this earth is
the only one God made, and that it does not whirl round the sun, but
vice versa, the sun round it.
WHATELY'S FAMOUS PARADOX.
Historic doubts relative to Napoleon Buonaparte. London, 1819,
8vo.
This tract has since been acknowledged by Archbishop Whately[566] and reprinted. It is
certainly a paradox: but differs from most of those in my list as being a
joke, and a satire upon the reasoning of those who cannot receive
narrative, no matter what the evidence, which is to them utterly
improbable a priori. But had it been serious earnest, it would not
have been so absurd as many of those which I have brought forward. The
next on the list is not a joke.
The idea of the satire is not new. Dr. King,[567] in the dispute on the genuineness of
Phalaris, proved with humor that Bentley did not write his own
dissertation. An attempt has lately been made, for the honor of Moses, to
prove, without humor, that Bishop Colenso did not
write his own book. This is intolerable: anybody who tries to use such a
weapon without banter, plenty and good, and of form suited to the
subject, should get the drubbing which the poor man got in the Oriental
tale for striking the dervishes with the wrong hand.
The excellent and distinguished author of this tract has ceased to
live. I call him the Paley of our day: with more learning and more
purpose than his predecessor; but perhaps they might have changed places
if they had changed centuries. The clever satire above named is not the
only work which he published without his name. The following was
attributed to him, I believe rightly: "Considerations on the Law of
Libel, as relating to Publications on the subject of Religion, by John
Search." London, 1833, 8vo. This tract excited little attention: for
those who should have answered, could not. Moreover, it wanted a
prosecution to call attention to it: the fear of calling such attention
may have prevented prosecutions. Those who have read it will have seen
why.
The theological review elsewhere mentioned attributes the pamphlet of
John Search on blasphemous libel to Lord Brougham. This is quite absurd:
the writer states points of law on credence where the judge must have
spoken with authority. Besides which, a hundred points of style are
decisive between the two. I think any one who knows Whately's writing
will soon arrive at my conclusion. Lord Brougham himself informs me that
he has no knowledge whatever of the pamphlet.
It is stated in Notes and Queries (3 S. xi. 511) that Search
was answered by the Bishop of Ferns[568] as S. N., with a rejoinder by Blanco
White.[569] These
circumstances increase the probability that Whately was written against
and for.
VOLTAIRE A CHRISTIAN.
Voltaire Chrétien; preuves tirées de ses ouvrages. Paris, 1820,
12mo.
If Voltaire have not succeeded in proving himself a strong theist and
a strong anti-revelationist, who is to succeed in proving himself one
thing or the other in any matter whatsoever? By occasional confusion
between theism and Christianity; by taking advantage of the formal
phrases of adhesion to the Roman Church, which very often occur, and are
often the happiest bits of irony in an ironical production; by citations
of his morality, which is decidedly Christian, though often attributed to
Brahmins; and so on—the author makes a fair case for his paradox,
in the eyes of those who know no more than he tells them. If he had said
that Voltaire was a better Christian than himself knew of, towards all
mankind except men of letters, I for one should have agreed with him.
Christian! the word has degenerated into a synonym of
man, in what are called Christian countries. So we have the parrot
who "swore for all the world like a Christian," and the two dogs who
"hated each other just like Christians." When the Irish duellist of the
last century, whose name may be spared in consideration of its historic
fame and the worthy people who bear it, was
(June 12, 1786) about to take the consequence of his last brutal murder,
the rope broke, and the criminal got up, and exclaimed, "By
—— Mr. Sheriff, you ought to be ashamed of yourself! this
rope is not strong enough to hang a dog, far less a Christian!" But such
things as this are far from the worst depravations. As to a word so
defiled by usage, it is well to know that there is a way of escape from
it, without renouncing the New Testament. I suppose any one may assume
for himself what I have sometimes heard contended for, that no New
Testament word is to be used in religion in any sense except that of the
New Testament. This granted, the question is settled. The word
Christian, which occurs three times, is never recognized as
anything but a term of contempt from those without the pale to those
within. Thus, Herod Agrippa, who was deep in Jewish literature, and a
correspondent of Josephus, says to Paul (Acts xxvi. 28), "Almost thou
persuadest me to be (what I and other followers of the state religion
despise under the name) a Christian." Again (Acts xi. 26), "The disciples
(as they called themselves) were called (by the surrounding
heathens) Christians first in Antioch." Thirdly (1 Peter iv. 16), "Let
none of you suffer as a murderer.... But if as a Christian
(as the heathen call it by whom the suffering comes), let him not be
ashamed." That is to say, no disciple ever called himself a
Christian, or applied the name, as from himself, to another disciple,
from one end of the New Testament to the other; and no disciple need
apply that name to himself in our day, if he dislike the associations
with which the conduct of Christians has clothed it.
WRONSKI ON THE LONGITUDE PROBLEM.
Address of M. Hoene Wronski to the British Board of Longitude, upon
the actual state of the mathematics, their reform, and upon the new
celestial mechanics, giving the definitive solution of the problem of
longitude.[570] London,
1820, 8vo.
M. Wronski[571] was
the author of seven quartos on mathematics, showing very great power of
generalization. He was also deep in the transcendental philosophy,[572] and had the Absolute
at his fingers' ends. All this knowledge was rendered useless by a
persuasion that he had greatly advanced beyond the whole world, with many
hints that the Absolute would not be forthcoming, unless prepaid. He was
a man of the widest extremes. At one time he desired people to see all
possible mathematics in
Fx = A0Ω0 + A1Ω1 + A2Ω2 + A3Ω3 + &c.
which he did not explain, though there is meaning to it in the
quartos. At another time he was proposing the general solution of the[573] fifth degree by help
of 625 independent equations of one form and 125 of another. The first
separate memoir from any Transactions that I ever possessed was given to
me when at Cambridge; the refutation (1819) of this asserted solution,
presented to the Academy of Lisbon by Evangelista Torriano. I cannot say
I read it. The tract above is an attack on modern mathematicians in
general, and on the Board of Longitude, and Dr. Young.[574]
DR. MILNER'S PARADOXES.
1820. In this year died Dr. Isaac Milner,[575] President of Queens' College,
Cambridge, one of the class of rational paradoxers. Under this name I
include all who, in private life, and in matters which concern
themselves, take their own course, and suit their own notions, no matter
what other people may think of them. These men will put things to uses
they were never intended for, to the great distress and disgust of their
gregarious friends. I am one of the class, and I could write a little
book of cases in which I have incurred absolute reproach for not "doing
as other people do." I will name two of my atrocities: I took one of
those butter-dishes which have for a top a dome with holes in it, which
is turned inward, out of reach of accident, when not in use. Turning the
dome inwards, I filled the dish with water, and put a sponge in the dome:
the holes let it fill with water, and I had a penwiper, always moist, and
worth its price five times over. "Why! what do you mean? It was made to
hold butter. You are always at some queer thing or other!" I bought a
leaden comb, intended to dye the hair, it being supposed that the
application of lead will have this effect. I did not try: but I divided
the comb into two, separated the part of closed prongs from the other;
and thus I had two ruling machines. The lead marks paper, and by drawing
the end of one of the machines along a ruler, I could rule twenty lines
at a time, quite fit to write on. I thought I should have killed a friend
to whom I explained it: he could not for the life of him understand how
leaden lines on paper would dye the hair.
But Dr. Milner went beyond me. He wanted a seat suited to his shape,
and he defied opinion to a fearful point. He spread a thick block
of putty over a wooden chair and sat in it until it had taken a ceroplast
copy of the proper seat. This he gave to a carpenter to be imitated in
wood. One of the few now living who knew him—my friend, General
Perronet Thompson[576]—answers for the wood, which was
shown him by Milner himself; but he does not vouch for the material being
putty, which was in the story told me at Cambridge; William Frend[577] also remembered it.
Perhaps the Doctor took off his great seal in green wax, like the Crown;
but some soft material he certainly adopted; and very comfortable he
found the wooden copy.
The same gentleman vouches for Milner's lamp: but this had visible
science in it; the vulgar see no science in the construction of
the chair. A hollow semi-cylinder, but not with a circular curve,
revolved on pivots. The curve was calculated on the law that, whatever
quantity of oil might be in the lamp, the position of equilibrium just
brought the oil up to the edge of the cylinder, at which a bit of wick
was placed. As the wick exhausted the oil, the cylinder slowly revolved
about the pivots so as to keep the oil always touching the wick.
Great discoveries are always laughed at; but it is very often not the
laugh of incredulity; it is a mode of distorting the sense of inferiority
into a sense of superiority, or a mimicry of superiority interposed
between the laugher and his feeling of inferiority. Two persons in
conversation agreed that it was often a nuisance not to
be able to lay hands on a bit of paper to mark the place in a book, every
bit of paper on the table was sure to contain something not to be spared.
I very quietly said that I always had a stock of bookmarkers ready cut,
with a proper place for them: my readers owe many of my anecdotes to this
absurd practice. My two colloquials burst into a fit of laughter; about
what? Incredulity was out of the question; and there could be nothing
foolish in my taking measures to avoid what they knew was an
inconvenience. I was in this matter obviously their superior, and so they
laughed at me. Much more candid was the Royal Duke of the last century,
who was noted for slow ideas. "The rain comes into my mouth," said he,
while riding. "Had not your Royal Highness better shut your mouth?" said
the equerry. The Prince did so, and ought, by rule, to have laughed
heartily at his adviser; instead of this, he said quietly, "It doesn't
come in now."
HERBART'S MATHEMATICAL PSYCHOLOGY.
De Attentionis mensura causisque primariis. By J. F. Herbart.[578] Kœnigsberg,
1822, 4to.
This celebrated philosopher maintained that mathematics ought to be
applied to psychology, in a separate tract, published also in 1822: the
one above seems, therefore, to be his challenge on the subject. It is on
attention, and I think it will hardly support Herbart's thesis. As
a specimen of his formula, let t be the time elapsed since the
consideration began, β the whole perceptive
intensity of the individual, φ the whole of
his mental force, and z the force given to a notion by attention
during the time t. Then,
z = φ (1 - ε-βt)
Now for a test. There is a jactura, v, the meaning of
which I do not comprehend. If there be anything in it, my mathematical
readers ought to interpret it from the formula
v = πφβ/(1 - β)ε-βt + Cε-t
and to this task I leave them, wishing them better luck than mine. The
time may come when other manifestations of mind, besides belief,
shall be submitted to calculation: at that time, should it arrive, a
final decision may be passed upon Herbart.
ON THE WHIZGIG.
The theory of the Whizgig considered; in as much as it mechanically
exemplifies the three working properties of nature; which are now set
forth under the guise of this toy, for children of all ages. London,
1822, 12mo (pp. 24, B. McMillan, Bow Street, Covent Garden).
The toy called the whizgig will be remembered by many. The
writer is a follower of Jacob Behmen,[579] William Law,[580] Richard Clarke,[581] and Eugenius
Philalethes.[582] Jacob
Behmen first announced the three working properties of nature, which
Newton stole, as described in the Gentleman's Magazine, July,
1782, p. 329. These laws are illustrated in the whizgig. There is the
harsh astringent, attractive compression; the bitter compunction,
repulsive expansion; and the stinging anguish, duplex motion. The author
hints that he has written other works, to which he gives no clue. I have
heard that Behmen was pillaged by Newton, and Swedenborg[583] by Laplace,[584] and Pythagoras by Copernicus,[585] and Epicurus by
Dalton,[586] &c. I do
not think this mention will revive Behmen; but it may the whizgig, a very
pretty toy, and philosophical withal, for few of those who used it could
explain it.
SOME MYTHOLOGICAL PARADOXES.
A Grammar of infinite forms; or the mathematical elements of ancient
philosophy and mythology. By Wm. Howison.[587] Edinburgh, 1823, 8vo.
A curius combination of geometry and mythology. Perseus, for instance,
is treated under the head, "the evolution of diminishing hyperbolic
branches."
The Mythological Astronomy of the Ancients; part the second: or the
key of Urania, the words of which will unlock all the mysteries of
antiquity. Norwich, 1823, 12mo.
A Companion to the Mythological Astronomy, &c., containing remarks
on recent publications.... Norwich, 1824, 12mo.
A new Theory of the Earth and of planetary motion; in which it is
demonstrated that the Sun is vicegerent of his own system. Norwich, 1825,
12mo.
The analyzation of the writings of the Jews, so far as they are found
to have any connection with the sublime science of astronomy. [This is
pp. 97-180 of some other work, being all I have seen.]
These works are all by Sampson Arnold Mackey,[588] for whom see Notes and
Queries, 1st S. viii. 468, 565, ix. 89, 179. Had it not been for
actual quotations given by one correspondent only (1st S. viii. 565),
that journal would have handed him down as a man of some real learning.
An extraordinary man he certainly was: it is not one illiterate shoemaker
in a thousand who could work upon such a singular mass of Sanskrit and
Greek words, without showing evidence of being able to read a line in
any language but his own, or to spell that correctly. He was an
uneducated Godfrey Higgins.[589] A few extracts will put this in a
strong light: one for history of science, one for astronomy, and one for
philology:
"Sir Isaac Newton was of opinion that 'the atmosphere of the earth was
the sensory of God; by which he was enabled to see quite round the
earth:' which proves that Sir Isaac had no idea that God could see
through the earth.
"Sir Richard [Phillips] has given the most rational explanation of the
cause of the earth's elliptical orbit that I have ever seen in print. It
is because the earth presents its watery hemisphere to the sun at one
time and that of solid land the other; but why has he made his Oxonian
astonished at the coincidence? It is what I taught in my attic twelve
years before.
"Again, admitting that the Eloim were powerful and intelligent beings
that managed these things, we would accuse them of being the
authors of all the sufferings of Chrisna. And as they and the
constellation of Leo were below the horizon, and consequently cut off
from the end of the zodiac, there were but eleven constellations of the
zodiac to be seen; the three at the end were wanted, but those three
would be accused of bringing Chrisna into the troubles which at last
ended in his death. All this would be expressed in the Eastern language
by saying that Chrisna was persecuted by those Judoth Ishcarioth!!!!!
[the five notes of exclamation are the author's]. But the astronomy of
those distant ages, when the sun was at the south pole in winter, would
leave five of those Decans cut off from our view, in the latitude of
twenty-eight degrees; hence Chrisna died of wounds from five
Decans, but the whole five may be included in Judoth Ishcarioth! for the
phrase means 'the men that are wanted at the extreme parts.' Ishcarioth
is a compound of ish, a man, and carat wanted or taken
away, and oth the plural termination, more ancient than
im...."
I might show at length how Michael is the sun, and the D'-ev-'l in
French Di-ob-al, also 'L-evi-ath-an—the evi being the radical part
both of devil and leviathan—is the Nile, which the
sun dried up for Moses to pass: a battle celebrated by Jude. Also how
Moses, the same name as Muses, is from mesha, drawn
out of the water, "and hence we called our land which is saved from the
water by the name of marsh." But it will be of more use to collect
the character of S. A. M. from such correspondents of Notes and
Queries as have written after superficial examination. Great
astronomical and philological attainments, much ability and learning; had
evidently read and studied deeply; remarkable for the originality of his
views upon the very abstruse subject of mythological astronomy, in which
he exhibited great sagacity. Certainly his views were original;
but their sagacity, if it be allowable to copy his own mode of
etymologizing, is of an ori-gin-ale cast, resembling that of a
person who puts to his mouth liquors both distilled and fermented.
A KANTESIAN JEWELER.
Principles of the Kantesian, or transcendental philosophy. By Thomas
Wirgman.[590] London,
1824, 8vo.
Mr. Wirgman's mind was somewhat attuned to psychology; but he was
cracky and vagarious. He had been a fashionable jeweler in St. James's
Street, no doubt the son or grandson of Wirgman at "the well-known
toy-shop in St. James's Street," where Sam Johnson
smartened himself with silver buckles. (Boswell, æt. 69). He would
not have the ridiculous large ones in fashion; and he would give no more
than a guinea a pair; such, says Boswell, in Italics, were the
principles of the business: and I think this may be the first
place in which the philosophical word was brought down from heaven to mix
with men. However this may be, my Wirgman sold snuff-boxes, among
other things, and fifty years ago a fashionable snuff-boxer would be
under inducement, if not positively obliged, to have a stock with very
objectionable pictures. So it happened that Wirgman—by reason of a
trifle too much candor—came under the notice of the
Suppression Society, and ran considerable risk. Mr. Brougham was
his counsel; and managed to get him acquitted. Years and years after
this, when Mr. Brougham was deep in the formation of the London
University (now University College), Mr. Wirgman called on him. "What
now?" said Mr. B. with his most sarcastic look—a very perfect thing
of its kind—"you're in a scrape again, I suppose!" "No! indeed!"
said W., "my present object is to ask your interest for the chair of
Moral Philosophy in the new University!" He had taken up Kant!
Mr. Wirgman, an itinerant paradoxer, called on me in 1831: he came to
convert me. "I assure you," said he, "I am nothing but an old brute of a
jeweler;" and his eye and manner were of the extreme of jocosity, as good
in their way, as the satire of his former counsel. I mention him as one
of that class who go away quite satisfied that they have wrought
conviction. "Now," said he, "I'll make it clear to you! Suppose a number
of gold-fishes in a glass bowl,—you understand? Well! I come with
my cigar and go puff, puff, puff, over the bowl, until there is a little
cloud of smoke: now, tell me, what will the gold-fishes say to that?" "I
should imagine," said I, "That they would not know what to make of it."
"By Jove! you're a Kantian;" said he, and with this and the like, he left
me, vowing that it was delightful to talk to so
intelligent a person. The greatest compliment Wirgman ever received was
from James Mill, who used to say he did not understand Kant. That
such a man as Mill should think this worth saying is a feather in the cap
of the jocose jeweler.
Some of my readers will stare at my supposing that Boswell may have
been the first down-bringer of the word principles into common
life; the best answer will be a prior instance of the word as true
vernacular; it has never happened to me to notice one. Many words have
very common uses which are not old. Take the following from Nichols
(Anecd. ix. 263): "Lord Thurlow presents his best respects to Mr.
and Mrs. Thicknesse, and assures them that he knows of no cause to
complain of any part of Mr. Thicknesse's carriage; least of all the
circumstance of sending the head to Ormond Street." Surely Mr. T. had
lent Lord T. a satisfactory carriage with a movable head, and the above
is a polite answer to inquiries. Not a bit of it! carriage is here
conduct, and the head is a bust. The vehicles of the
rich, at the time, were coaches, chariots, chaises, etc., never
carriages, which were rather carts. Gibbon has the word for
baggage-wagons. In Jane Austen's novels the word carriage is
established.
WALSH'S DELUSIONS.
John Walsh,[591] of Cork (1786-1847). This discoverer
has had the honor of a biography from Professor Boole, who, at my
request, collected information about him on the scene of his labors. It
is in the Philosophical Magazine for November, 1851, and will, I
hope, be transferred to some biographical collection where it may find a
larger class of readers. It is the best biography of a single hero of the
kind that I know. Mr. Walsh introduced himself to me, as he did to
many others, in the anterowlandian days of the Post-office; his unpaid
letters were double, treble, &c. They contained his pamphlets, and
cost their weight in silver: all have the name of the author, and all are
in octavo or in quarto letter-form: most are in four pages, and all dated
from Cork. I have the following by me:
The Geometric Base, 1825.—The theory of plane angles.
1827.—Three Letters to Dr. Francis Sadleir. 1838.—The
invention of polar geometry. By Irelandus. 1839.—The theory of
partial functions. Letter to Lord Brougham. 1839.—On the invention
of polar geometry. 1839.—Letter to the Editor of the Edinburgh
Review. 1840.—Irish Manufacture. A new method of tangents.
1841.—The normal diameter in curves. 1843.—Letter to Sir R.
Peel. 1845.—[Hints that Government should compel the introduction
of Walsh's Geometry into Universities.]—Solution of Equations of
the higher orders. 1845.
Besides these, there is a Metalogia, and I know not how many
others.
Mr. Boole,[592] who
has taken the moral and social features of Walsh's delusions from the
commiserating point of view, which makes ridicule out of place, has been
obliged to treat Walsh as Scott's Alan Fairford treated his client Peter
Peebles; namely, keep the scarecrow out of court while the case was
argued. My plan requires me to bring him in: and when he comes in at the
door, pity and sympathy fly out at the window. Let the reader remember
that he was not an ignoramus in mathematics: he might have won his spurs
if he could have first served as an esquire. Though so illiterate that
even in Ireland he never picked up anything more Latin than
Irelandus, he was a very pretty mathematician spoiled in the
making by intense self-opinion.
This is part of a private letter to me at the back of a page of print:
I had never addressed a word to him:
"There are no limits in mathematics, and those that assert there are,
are infinite ruffians, ignorant, lying blackguards. There is no
differential calculus, no Taylor's theorem, no calculus of variations,
&c. in mathematics. There is no quackery whatever in mathematics; no
% equal to anything. What sheer ignorant blackguardism that!
"In mechanics the parallelogram of forces is quackery, and is
dangerous; for nothing is at rest, or in uniform, or in rectilinear
motion, in the universe. Variable motion is an essential property of
matter. Laplace's demonstration of the parallelogram of forces is a
begging of the question; and the attempts of them all to show that the
difference of twenty minutes between the sidereal and actual revolution
of the earth round the sun arises from the tugging of the Sun and Moon at
the pot-belly of the earth, without being sure even that the earth has a
pot-belly at all, is perfect quackery. The said difference arising from
and demonstrating the revolution of the Sun itself round some distant
center."
In the letter to Lord Brougham we read as follows:
"I ask the Royal Society of London, I ask the Saxon crew of that crazy
hulk, where is the dogma of their philosophic god now?... When the Royal
Society of London, and the Academy of Sciences of Paris, shall have read
this memorandum, how will they appear? Like two cur dogs in the paws of
the noblest beast of the forest.... Just as this note was going to press,
a volume lately published by you was put into my hands, wherein you
attempt to defend the fluxions and Principia of Newton. Man! what
are you about? You come forward now with your special pleading, and
fraught with national prejudice, to defend, like the philosopher
Grassi,[593] the
persecutor of Galileo, principles and reasoning which,
unless you are actually insane, or an ignorant quack in mathematics, you
know are mathematically false. What a moral lesson this for the students
of the University of London from its head! Man! demonstrate corollary 3,
in this note, by the lying dogma of Newton, or turn your thoughts to
something you understand.
"Walsh Irelandus."
Mr. Walsh—honor to his memory—once had the consideration
to save me postage by addressing a pamphlet under cover to a Member of
Parliament, with an explanatory letter. In that letter he gives a candid
opinion of himself:
(1838.) "Mr. Walsh takes leave to send the enclosed corrected copy to
Mr. Hutton as one of the Council of the University of London, and to save
postage for the Professor of Mathematics there. He will find in it
geometry more deep and subtle, and at the same time more simple and
elegant, than it was ever contemplated human genius could invent."
He then proceeds to set forth that a certain "tomfoolery lemma," with
its "tomfoolery" superstructure, "never had existence outside the shallow
brains of its inventor," Euclid. He then proceeds thus:
"The same spirit that animated those philosophers who sent Galileo to
the Inquisition animates all the philosophers of the present day without
exception. If anything can free them from the yoke of error, it is the
[Walsh] problem of double tangence. But free them it will, how deeply
soever they may be sunk into mental slavery—and God knows that is
deeply enough; and they bear it with an admirable grace; for none bear
slavery with a better grace than tyrants. The lads must adopt my
theory.... It will be a sad reverse for all our great professors to be
compelled to become schoolboys in their gray years. But the sore scratch
is to be compelled, as they had before been compelled one thousand years
ago, to have recourse to Ireland for instruction."
The following "Impromptu" is no doubt by Walsh himself: he was more of
a poet than of an astronomer:
"Through ages unfriended,
With sophistry blended,
Deep science in Chaos had slept;
Its limits were fettered,
Its voters unlettered,
Its students in movements but crept.
Till, despite of great foes,
Great Walsh first arose,
And with logical might did unravel
Those mazes of knowledge,
Ne'er known in a college,
Though sought for with unceasing travail.
With cheers we now hail him,
May success never fail him,
In Polar Geometrical mining;
Till his foes be as tamed
As his works are far-famed
For true philosophic refining."
Walsh's system is, that all mathematics and physics are wrong: there
is hardly one proposition in Euclid which is demonstrated. His example
ought to warn all who rely on their own evidence to their own success. He
was not, properly speaking, insane; he only spoke his mind more freely
than many others of his class. The poor fellow died in the Cork union,
during the famine. He had lived a happy life, contemplating his own
perfections, like Brahma on the lotus-leaf.[594]
GROWTH OF FREEDOM OF OPINION.
The year 1825 brings me to about the middle of my Athenæum
list: that is, so far as mere number of names mentioned is concerned.
Freedom of opinion, beyond a doubt, is gaining ground, for good or for
evil, according to what the speaker happens to think: admission of
authority is no longer made in the old way. If we take soul-cure and
body-cure, divinity and medicine, it is manifest that a change has come
over us. Time was when it was enough that dose or dogma should be
certified by "Il a été ordonné, Monsieur, il a été ordonné,"[595] as the apothecary said
when he wanted to operate upon poor de Porceaugnac. Very much changed:
but whether for good or for evil does not now matter; the question is,
whether contempt of demonstration such as our paradoxers show has
augmented with the rejection of dogmatic authority. It ought to be
just the other way: for the worship of reason is the system on which, if
we trust them, the deniers of guidance ground their plan of life. The
following attempt at an experiment on this point is the best which I can
make; and, so far as I know, the first that ever was made.
Say that my list of paradoxers divides in 1825: this of itself proves
nothing, because so many of the earlier books are lost, or not likely to
be come at. It would be a fearful rate of increase which would make the
number of paradoxes since 1825 equal to the whole number before that
date. Let us turn now to another collection of mine, arithmetical books,
of which I have published a list. The two collections are similarly
circumstanced as to new and old books; the paradoxes had no care given to
the collection of either; the arithmetical books equal care to both. The
list of arithmetical books, published in 1847, divides at 1735; the
paradoxes, up to 1863, divide at 1825. If we take the process which is
most against the distinction, and allow every year from 1847 to 1863 to
add a year to 1735, we should say that the arithmetical writers divide at
1751. This rough process may serve, with sufficient certainty, to show
that the proportion of paradoxes to books of sober demonstration is on
the increase; and probably, quite as much as the proportion of
heterodoxes to books of orthodox adherence. So that divinity and medicine
may say to geometry, Don't you sneer: if rationalism,
homœopathy, and their congeners are on the rise among us, your
enemies are increasing quite as fast. But geometry replies—Dear
friends, content yourselves with the rational inference that the rise of
heterodoxy within your pales is not conclusive against you, taken alone;
for it rises at the same time within mine. Store within your garners the
precious argument that you are not proved wrong by increase of dissent;
because there is increase of dissent against exact science. But do not
therefore even yourselves to me: remember that you, Dame Divinity,
have inflicted every kind of penalty, from the stake to the stocks, in
aid of your reasoning; remember that you, Mother Medicine, have not many
years ago applied to Parliament for increase of forcible hindrance of
antipharmacopœal drenches, pills, and powders. Who ever heard of my
asking the legislature to fine blundering circle-squarers? Remember that
the D in dogma is the D in decay; but the D in demonstration is the D in
durability.
THE STATUS OF MEDICINE.
I have known a medical man—a young one—who was seriously
of the opinion that the country ought to be divided into medical
parishes, with a practitioner appointed to each, and a penalty for
calling in any but the incumbent curer. How should people know how to
choose? The hair-dressers once petitioned Parliament for an act to compel
people to wear wigs. My own opinion is of the opposite extreme, as in the
following letter (Examiner, April 5, 1856); which, to my surprise,
I saw reprinted in a medical journal, as a plan not absolutely to
be rejected. I am perfectly satisfied that it would greatly promote true
medical orthodoxy, the predominance of well educated thinkers, and the
development of their desirable differences.
"Sir. The Medical Bill and the medical
question generally is one on which experience would teach, if people
would be taught.
"The great soul question took three hundred years to settle: the
little body question might be settled in thirty years, if the decisions
in the former question were studied.
"Time was when the State believed, as honestly as ever it believed
anything, that it might, could, and should find out
the true doctrine for the poor ignorant community; to which, like a
worthy honest state, it added would. Accordingly, by the
assistance of the Church, which undertook the physic, the surgery, and
the pharmacy of sound doctrine all by itself, it sent forth its legally
qualified teachers into every parish, and woe to the man who called in
any other. They burnt that man, they whipped him, they imprisoned him,
they did everything but what was Christian to him, all for his soul's
health and the amendment of his excesses.
"But men would not submit. To the argument that the State was a father
to the ignorant, they replied that it was at best the ignorant father of
an ignorant son, and that a blind man could find his way into a ditch
without another blind man to help him. And when the State said—But
here we have the Church, which knows all about it, the ignorant community
declared that it had a right to judge that question, and that it would
judge it. It also said that the Church was never one thing long, and that
it progressed, on the whole, rather more slowly than the ignorant
community.
"The end of it was, in this country, that every one who chose taught
all who chose to let him teach, on condition only of an open and true
registration. The State was allowed to patronize one particular
Church, so that no one need trouble himself to choose a pastor from the
mere necessity of choosing. But every church is allowed its colleges, its
studies, its diplomas; and every man is allowed his choice. There is no
proof that our souls are worse off than in the sixteenth century; and,
judging by fruits, there is much reason to hope they are better off.
"Now the little body question is a perfect parallel to the great soul
question in all its circumstances. The only things in which the parallel
fails are the following: Every one who believes in a future state sees
that the soul question is incomparably more important than the body
question, and every one can try the body question by experiment to a
larger extent than the soul question. The proverb, which always has a
spark of truth at the bottom, says that every man of forty is either a
fool or a physician; but did even the proverb maker ever dare to say that
every man is at any age either a fool or a fit teacher of religion?
"Common sense points out the following settlement of the medical
question: and to this it will come sooner or later.
"Let every man who chooses—subject to one common law of
manslaughter for all the crass cases—doctor the bodies of
all who choose to trust him, and recover payment according to agreement
in the courts of law. Provided always that every person practising should
be registered at a moderate fee in a register to be republished every six
months.
"Let the register give the name, address, and asserted qualification
of each candidate—as licentiate, or doctor, or what not, of this or
that college, hall, university, &c., home or foreign. Let it be
competent to any man to describe himself as qualified by study in public
schools without a diploma, or by private study, or even by intuition or
divine inspiration, if he please. But whatever he holds his qualification
to be, that let him declare. Let all qualification which of its own nature
admits of proof be proved, as by the diploma or certificate, &c.,
leaving things which cannot be proved, as asserted private study,
intuition, inspiration, &c., to work their own way.
"Let it be highly penal to assert to the patient any qualification
which is not in the register, and let the register be sold very cheap.
Let the registrar give each registered practitioner a copy of the
register in his own case; let any patient have the power to demand a
sight of this copy; and let no money for attendance be recoverable in any
case in which there has been false representation.
"Let any party in any suit have a right to produce what medical
testimony he pleases. Let the medical witness produce his register, and
let his evidence be for the jury, as is that of an engineer or a
practitioner of any art which is not attested by diplomas.
"Let any man who practises without venturing to put his name on the
register be liable to fine and imprisonment.
"The consequence would be that, as now, anybody who pleases might
practise; for the medical world is well aware that there is no power of
preventing what they call quacks from practising. But very different from
what is now, every man who practises would be obliged to tell the whole
world what his claim is, and would run a great risk if he dared to tell
his patient in private anything different from what he had told the whole
world.
"The consequence would be that a real education in anatomy,
physiology, chemistry, surgery, and what is known of the thing called
medicine, would acquire more importance than it now has.
"It is curious to see how completely the medical man of the nineteenth
century squares with the priest of the sixteenth century. The clergy of
all sects are now better divines and better men than they ever were. They
have lost Bacon's reproach that they took a smaller measure of things
than any other educated men; and the physicians are now in this
particular the rearguard of the learned world; though it may be true that
the rear in our day is further on in the march than the van of Bacon's
day. Nor will they ever recover the lost position until medicine is as
free as religion.
"To this it must come. To this the public, which will decide for
itself, has determined it shall come. To this the public has, in fact,
brought it, but on a plan which it is not desirable to make permanent. We
will be as free to take care of our bodies as of our souls and of our
goods. This is the profession of all who sign as I do, and the practice
of most of those who would not like the name
"Heteropath."
The motion of the Sun in the Ecliptic, proved to be uniform in a
circular orbit ... with preliminary observations on the fallacy of the
Solar System. By Bartholomew Prescott,[596] 1825, 8vo.
The author had published, in 1803, a Defence of the Divine
System, which I never saw; also, On the inverted scheme of
Copernicus. The above work is clever in its satire.
THE CHRISTIAN EVIDENCE SOCIETY.
Manifesto of the Christian Evidence Society, established Nov. 12,
1824. Twenty-four plain questions to honest men.
These are two broadsides of August and November, 1826, signed by
Robert Taylor,[597] A.B.,
Orator of the Christian Evidence Society. This gentleman was a clergyman,
and was convicted of blasphemy in 1827,
for which he suffered imprisonment, and got the name of the Devil's
Chaplain. The following are quotations:
"For the book of Revelation, there was no original Greek at all, but
Erasmus wrote it himself in Switzerland, in the year 1516. Bishop
Marsh,[598] vol. i. p.
320."—"Is not God the author of your reason? Can he then be the
author of anything which is contrary to your reason? If reason be a
sufficient guide, why should God give you any other? if it be not a
sufficient guide, why has he given you that?"
I remember a votary of the Society being asked to substitute for
reason "the right leg," and for guide "support," and to
answer the two last questions: he said there must be a quibble, but he
did not see what. It is pleasant to reflect that the argumentum à
carcere[599] is
obsolete. One great defect of it was that it did not go far enough: there
should have been laws against subscriptions for blasphemers, against
dealing at their shops, and against rich widows marrying them.
Had I taken in theology, I must have entered books against
Christianity. I mention the above, and Paine's Age of Reason,
simply because they are the only English modern works that ever came in
my way without my asking for them. The three parts of the Age of
Reason were published in Paris 1793, Paris 1795, and New York 1807.
Carlile's[600] edition is
of London, 1818, 8vo. It must be republished when the time comes, to show
what stuff governments and clergy were afraid of at the beginning of this
century. I should never have seen the book, if it had not been
prohibited: a bookseller put it under my nose with a fearful look round
him; and I could do no less, in common curiosity, than buy a work which
had been so complimented by church and state. And when I had read it, I
said in my mind to church and state,—Confound you! you have taken
me in worse than any reviewer I ever met with. I forget what I gave for
the book, but I ought to have been able to claim compensation
somewhere.
THE CABBALA.
Cabbala Algebraica. Auctore Gul. Lud. Christmann.[601] Stuttgard, 1827, 4to.
Eighty closely printed pages of an attempt to solve equations of every
degree, which has a process called by the author cabbala. An
anonymous correspondent spells cabbala as follows, χαββαλλ, and makes 666
out of its letters. This gentleman has sent me since my Budget commenced,
a little heap of satirical communications, each having a 666 or two; for
instance, alluding to my remarks on the spelling of chemistry, he
finds the fated number in χιμεια. With these are challenges
to explain them, and hints about the end of the world. All these letters
have different fantastic seals; one of them with the legend "keep your
temper,"—another bearing "bank token five pence." The only
signature is a triangle with a little circle in it, which I interpret to
mean that the writer confesses himself to be the round man stuck in the
three-cornered hole, to be explained as in Sydney Smith's joke.
There is a kind of Cabbala Alphabetica which the investigators of the
numerals in words would do well to take up: it is the formation of
sentences which contain all the letters of the alphabet, and each only
once. No one has done it with v and j treated as
consonants; but you and I can do it. Dr. Whewell[602] and I amused ourselves, some years
ago, with attempts. He could not make sense, though he joined words: he
gave me
Phiz, styx, wrong, buck, flame, quid.
I gave him the following, which he agreed was "admirable sense": I
certainly think the words would never have come together except in this
way:
I, quartz pyx, who fling muck beds.
I long thought that no human being could say this under any
circumstances. At last I happened to be reading a religious
writer—as he thought himself—who threw aspersions on his
opponents thick and threefold. Heyday! came into my head, this fellow
flings muck beds; he must be a quartz pyx. And then I remembered that a
pyx is a sacred vessel, and quartz is a hard stone, as hard as the heart
of a religious foe-curser. So that the line is the motto of the ferocious
sectarian, who turns his religious vessels into mudholders, for the
benefit of those who will not see what he sees.
I can find no circumstances for the following, which I received from
another:
Fritz! quick! land! hew gypsum box.
From other quarters I have the following:
Dumpy quiz! whirl back fogs next.
This might be said in time of haze to the queer little figure in the
Dutch weather-toy, which comes out or goes in with the change in the
atmosphere. Again,
Export my fund! Quiz black whigs.
This Squire Western might have said, who was always afraid of the
whigs sending the sinking-fund over to Hanover. But the following is the
best: it is good advice to a young man, very well expressed under the
circumstances:
Get nymph; quiz sad brow; fix luck.
Which in more sober English would be, Marry; be cheerful; watch your
business. There is more edification, more religion in this than in all
the 666-interpretations put together.
Such things would make excellent writing copies, for they secure
attention to every letter; v and j might be placed at the
end.
ON GODFREY HIGGINS.
The Celtic Druids. By Godfrey Higgins,[603] Esq. of Skellow Grange, near
Doncaster. London, 1827, 4to.
Anacalypsis, or an attempt to draw aside the veil of the Saitic Isis:
or an inquiry into the origin of languages, nations, and religions. By
Godfrey Higgins, &c..., London, 1836, 2 vols. 4to.
The first work had an additional preface and a new index in 1829.
Possibly, in future time, will be found bound up with copies of the
second work two sheets which Mr. Higgins circulated among his friends in
1831: the first a "Recapitulation," the second "Book vi. ch. 1."
The system of these works is that—
"The Buddhists of Upper India (of whom the Phenician Canaanite,
Melchizedek, was a priest), who built the Pyramids, Stonehenge, Carnac,
&c. will be shown to have founded all the ancient mythologies of the
world, which, however varied and corrupted in recent times, were
originally one, and that one founded on principles sublime, beautiful,
and true."
These works contain an immense quantity of learning, very honestly put
together. I presume the enormous number of facts, and the goodness of the
index, to be the reasons why the Anacalypsis found a permanent
place in the old reading-room of the British Museum, even before
the change which greatly increased the number of books left free to the
reader in that room.
Mr. Higgins, whom I knew well in the last six years of his life, and
respected as a good, learned, and (in his own way) pious man, was
thoroughly and completely the man of a system. He had that sort of mental
connection with his theory that made his statements of his authorities
trustworthy: for, besides perfect integrity, he had no bias towards
alteration of facts: he saw his system in the way the fact was presented
to him by his authority, be that what it might.
He was very sure of a fact which he got from any of his authorities:
nothing could shake him. Imagine a conversation between him and an Indian
officer who had paid long attention to Hindoo antiquities and their
remains: a third person was present, ego qui scribo. G. H.
"You know that in the temples of I-forget-who the Ceres is always
sculptured precisely as in Greece." Col. ——, "I really
do not remember it, and I have seen most of these temples." G. H.
"It is so, I assure you, especially at I-forget-where." Col.
——, "Well, I am sure! I was encamped for six weeks at the
gate of that very temple, and, except a little shooting, had nothing to
do but to examine its details, which I did, day after day, and I found
nothing of the kind." It was of no use at all.
Godfrey Higgins began life by exposing and conquering, at the expense
of two years of his studies, some shocking abuses which existed in the
York Lunatic Asylum. This was a proceeding which called much attention to
the treatment of the insane, and produced much good effect. He was very
resolute and energetic. The magistracy of his time had such scruples
about using the severity of law to people of such station as well-to-do
farmers, &c.: they would allow a great deal of resistance, and
endeavor to mollify the rebels into obedience. A young farmer flatly
refused to pay under an order of affiliation made upon him by Godfrey
Higgins. He was duly warned; and persisted: he shortly found himself in
gaol. He went there sure to conquer the Justice, and the first thing he
did was to demand to see his lawyer. He was told, to his horror, that as
soon as he had been cropped and prison-dressed, he might see as many
lawyers as he pleased, to be looked at, laughed at, and advised that
there was but one way out of the scrape. Higgins was, in his
speculations, a regular counterpart of Bailly; but the celebrated Mayor
of Paris had not his nerve. It was impossible to say, if their characters
had been changed, whether the unfortunate crisis in which Bailly was not
equal to the occasion would have led to very different results if Higgins
had been in his place: but assuredly constitutional liberty would have
had one chance more. There are two works of his by which he was known,
apart from his paradoxes. First, An apology for the life and character
of the celebrated prophet of Arabia, called Mohamed, or the
Illustrious. London, 8vo. 1829. The reader will look at this writing
of our English Buddhist with suspicious eye, but he will not be able to
avoid confessing that the Arabian prophet has some reparation to demand
at the hands of Christians. Next, Horæ Sabaticæ; or an attempt to
correct certain superstitions and vulgar errors respecting the
Sabbath. Second edition, with a large appendix. London, 12mo. 1833.
This book was very heterodox at the time, but it has furnished material
for some of the clergy of our day.
I never could quite make out whether Godfrey Higgins took that system
which he traced to the Buddhists to have a Divine origin, or to be the
result of good men's meditations. Himself a strong theist, and believer
in a future state, one would suppose that he would
refer a universal religion, spread in different forms over the
whole earth from one source, directly to the universal Parent. And this I
suspect he did, whether he knew it or not. The external evidence is
balanced. In his preface he says:
"I cannot help smiling when I consider that the priests have objected
to admit my former book, The Celtic Druids, into libraries,
because it was antichristian; and it has been attacked by Deists, because
it was superfluously religious. The learned Deist, the Rev. R. Taylor
[already mentioned], has designated me as the religious Mr.
Higgins."
The time will come when some profound historian of literature will
make himself much clearer on the point than I am.
ON POPE'S DIPPING NEEDLE.
The triumphal Chariot of Friction: or a familiar elucidation of the
origin of magnetic attraction, &c. &c. By William Pope.[604] London, 1829, 4to.
Part of this work is on a dipping-needle of the author's construction.
It must have been under the impression that a book of naval magnetism was
proposed, that a great many officers, the Royal Naval Club, etc. lent
their names to the subscription list. How must they have been surprised
to find, right opposite to the list of subscribers, the plate presenting
"the three emphatic letters, J. A. O." And how much more when they saw it
set forth that if a square be inscribed in a circle, a circle within
that, then a square again, &c., it is impossible to have more than
fourteen circles, let the first circle be as large as you please. From
this the seven attributes of God are unfolded; and further, that all
matter was moral, until Lucifer churned it into
physical "as far as the third circle in Deity": this Lucifer,
called Leviathan in Job, being thus the moving cause of chaos. I shall
say no more, except that the friction of the air is the cause of
magnetism.
Remarks on the Architecture, Sculpture, and Zodiac of Palmyra; with a
Key to the Inscriptions. By B. Prescot.[605] London, 1830, 8vo.
Mr. Prescot gives the signs of the zodiac a Hebrew origin.
THE JACOTOT METHOD.
Epitomé de mathématiques. Par F. Jacotot,[606] Avocat. 3ième edition, Paris, 1830,
8vo. (pp. 18).
Méthode Jacotot. Choix de propositions mathématiques. Par P. Y.
Séprés.[607] 2nde
édition. Paris, 1830, 8vo. (pp. 82).
Of Jacotot's method, which had some vogue in Paris, the principle was
Tout est dans tout,[608] and the process Apprendre quelque
chose, et à y rapporter tout le reste.[609] The first tract has a proposition in
conic sections and its preliminaries: the second has twenty exercises, of
which the first is finding the greatest common measure of two numbers,
and the last is the motion of a point on a surface, acted on by given
forces. This is topped up with the problem of sound in a tube, and a
slice of Laplace's theory of the tides. All to be studied until known by
heart, and all the rest will come, or at least join on easily when it
comes. There is much truth in the assertion that new knowledge hooks on
easily to a little of the old, thoroughly mastered. The day is coming
when it will be found out that crammed erudition, got up for
examinations, does not cast out any hooks for more.
Lettre à MM. les Membres de l'Académie Royale des Sciences, contenant
un développement de la réfutation du système de la gravitation
universelle, qui leur a été présentée le 30 août, 1830. Par Félix
Passot.[610] Paris, 1830,
8vo.
Works of this sort are less common in France than in England. In
France there is only the Academy of Sciences to go to: in England there
is a reading public out of the Royal Society, &c.
A DISCOURSE ON PROBABILITY.
About 1830 was published, in the Library of Useful Knowledge,
the tract on Probability, the joint work of the late Sir John
Lubbock[611] and Mr.
Drinkwater (Bethune).[612] It is one of the best elementary
openings of the subject. A binder put my name on the outside (the work
was anonymous) and the consequence was that nothing could drive out of
people's heads that it was written by me. I do not know how many denials
I have made, from a passage in one of my own works to a letter in the
Times: and I am not sure that I have succeeded in establishing the
truth, even now. I accordingly note the fact once more. But as a book has
no right here unless it contain a paradox—or thing counter to
general opinion or practice—I will produce two small ones. Sir John
Lubbock, with whom lay the executive arrangement, had a strong objection
to the last word in "Theory of Probabilities," he maintained that the
singular probability, should be used; and I hold him quite
right.
The second case was this: My friend Sir J. L., with a large cluster of
intellectual qualities, and another of social qualities, had one point of
character which I will not call bad and cannot call good; he never used a
slang expression. To such a length did he carry his dislike, that he
could not bear head and tail, even in a work on games of
chance: so he used obverse and reverse. I stared when I
first saw this: but, to my delight, I found that the force of
circumstances beat him at last. He was obliged to take an example from
the race-course, and the name of one of the horses was Bessy
Bedlam! And he did not put her down as Elizabeth Bethlehem,
but forced himself to follow the jockeys.
[Almanach Romain sur la Loterie Royale de France, ou les Etrennes
nécessaires aux Actionnaires et Receveurs de la dite Loterie. Par M.
Menut de St.-Mesmin. Paris, 1830. 12mo.
This book contains all the drawings of the French lottery (two or
three, each month) from 1758 to 1830. It is intended for those who
thought they could predict the future drawings from the past: and various
sets of sympathetic numbers are given to help them. The principle
is, that anything which has not happened for a long time must be soon to
come. At rouge et noir, for example, when the red has won five
times running, sagacious gamblers stake on the black, for they think the
turn which must come at last is nearer than it was. So it is: but
observation would have shown that if a large number of those cases had
been registered which show a run of five for the red, the next game would
just as often have made the run into six as have turned in favor of the
black. But the gambling reasoner is incorrigible: if he would but take to
squaring the circle, what a load of misery would be saved. A writer of
1823, who appeared to be thoroughly acquainted with the gambling of Paris
and London, says that the gamesters by profession are haunted
by a secret foreboding of their future destruction, and seem as if they
said to the banker at the table, as the gladiators said to the emperor,
Morituri te salutant.[613]
In the French lottery, five numbers out of ninety were drawn at a
time. Any person, in any part of the country, might stake any sum upon
any event he pleased, as that 27 should be drawn; that 42 and 81 should
be drawn; that 42 and 81 should be drawn, and 42 first; and so on up to a
quine déterminé, if he chose, which is betting on five given
numbers in a given order. Thus, in July, 1821, one of the drawings
was
A gambler had actually predicted the five numbers (but not their
order), and won 131,350 francs on a trifling stake. M. Menut seems to
insinuate that the hint what numbers to choose was given at his own
office. Another won 20,852 francs on the quaterne, 8, 16, 46, 64, in this
very drawing. These gains, of course, were widely advertised: of the
multitudes who lost nothing was said. The enormous number of those who
played is proved to all who have studied chances arithmetically by the
numbers of simple quaternes which were gained: in 1822, fourteen; in
1823, six; in 1824, sixteen; in 1825, nine, &c.
The paradoxes of what is called chance, or hazard, might themselves
make a small volume. All the world understands that there is a long run,
a general average; but great part of the world is surprised that this
general average should be computed and predicted. There are many
remarkable cases of verification; and one of them relates to the
quadrature of the circle. I give some account of this and another. Throw
a penny time after time until head arrives, which it will do
before long: let this be called a set. Accordingly, H is the
smallest set, TH the next smallest, then TTH, &c. For abbreviation,
let a set in which seven tails occur before
head turns up be T7H. In an immense number of trials of
sets, about half will be H; about a quarter TH; about an eighth,
T2H. Buffon[614] tried 2,048 sets; and several have
followed him. It will tend to illustrate the principle if I give all the
results; namely, that many trials will with moral certainty show an
approach—and the greater the greater the number of trials—to
that average which sober reasoning predicts. In the first column is the
most likely number of the theory: the next column gives Buffon's result;
the three next are results obtained from trial by correspondents of mine.
In each case the number of trials is 2,048.
| H | 1,024 | 1,061 | 1,048 | 1,017 | 1,039 |
| TH | 512 | 494 | 507 | 547 | 480 |
| T2H | 256 | 232 | 248 | 235 | 267 |
| T3H | 128 | 137 | 99 | 118 | 126 |
| T4H | 64 | 56 | 71 | 72 | 67 |
| T5H | 32 | 29 | 38 | 32 | 33 |
| T6H | 16 | 25 | 17 | 10 | 19 |
| T7H | 8 | 8 | 9 | 9 | 10 |
| T8H | 4 | 6 | 5 | 3 | 3 |
| T9H | 2 | | 3 | 2 | 4 |
| T10H | 1 | | 1 | 1 |
| T11H | | | 0 | 1 |
| T12H | | | 0 | 0 |
| T13H | 1 | | 1 | 0 |
| T14H | | | 0 | 0 |
| T15H | | | 1 | 1 |
| &c. | | | 0 | 0 |
| | —— | —— | —— | —— | —— |
| | 2,048 | 2,048 | 2,048 | 2,048 | 2,048 |
In very many trials, then, we may depend upon something like the
predicted average. Conversely, from many trials we may form a guess at
what the average will be. Thus, in Buffon's experiment the 2,048 first
throws of the sets gave head in 1,061 cases: we have a right to
infer that in the long run something like 1,061 out of 2,048 is the
proportion of heads, even before we know the reasons for the equality of
chance, which tell us that 1,024 out of 2,048 is the real truth. I now
come to the way in which such considerations have led to a mode in which
mere pitch-and-toss has given a more accurate approach to the quadrature
of the circle than has been reached by some of my paradoxers. What would
my friend[615] in No. 14
have said to this? The method is as follows: Suppose a planked floor of
the usual kind, with thin visible seams between the planks. Let there be
a thin straight rod, or wire, not so long as the breadth of the plank.
This rod, being tossed up at hazard, will either fall quite clear of the
seams, or will lay across one seam. Now Buffon, and after him Laplace,
proved the following: That in the long run the fraction of the whole
number of trials in which a seam is intersected will be the fraction
which twice the length of the rod is of the circumference of the circle
having the breadth of a plank for its diameter. In 1855 Mr.
Ambrose Smith, of Aberdeen, made 3,204 trials with a rod
three-fifths of the distance between the planks: there were 1,213 clear
intersections, and 11 contacts on which it was difficult to decide.
Divide these contacts equally, and we have 1,218½ to 3,204 for the ratio
of 6 to 5π, presuming that the greatness of
the number of trials gives something near to the final average, or result
in the long run: this gives π = 3.1553. If
all the 11 contacts had been treated as intersections, the result would
have been π = 3.1412,
exceedingly near. A pupil of mine made 600 trials with a rod of the
length between the seams, and got π =
3.137.
This method will hardly be believed until it has been repeated so
often that "there never could have been any doubt about it."
The first experiment strongly illustrates a truth of the theory, well
confirmed by practice: whatever can happen will happen if we make trials
enough. Who would undertake to throw tail eight times running?
Nevertheless, in the 8,192 sets tail 8 times running occurred 17 times; 9
times running, 9 times; 10 times running, twice; 11 times and 13 times,
each once; and 15 times twice.]
ON CURIOSITIES OF π.
1830. The celebrated interminable fraction 3.14159..., which the
mathematician calls π, is the ratio of the
circumference to the diameter. But it is thousands of things besides. It
is constantly turning up in mathematics: and if arithmetic and algebra
had been studied without geometry, π must
have come in somehow, though at what stage or under what name must have
depended upon the casualties of algebraical invention. This will readily
be seen when it is stated that π is nothing
but four times the series
1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...
ad infinitum.[616] It would be wonderful if so simple a
series had but one kind of occurrence. As it is,
our trigonometry being founded on the circle, π first appears as the ratio stated. If, for
instance, a deep study of probable fluctuation from average had preceded,
π might have emerged as a number perfectly
indispensable in such problems as: What is the chance of the number of
aces lying between a million + x and a million - x, when
six million of throws are made with a die? I have not gone into any
detail of all those cases in which the paradoxer finds out, by his
unassisted acumen, that results of mathematical investigation cannot
be: in fact, this discovery is only an accompaniment, though a
necessary one, of his paradoxical statement of that which must be.
Logicians are beginning to see that the notion of horse is
inseparably connected with that of non-horse: that the first
without the second would be no notion at all. And it is clear that the
positive affirmation of that which contradicts mathematical demonstration
cannot but be accompanied by a declaration, mostly overtly made, that
demonstration is false. If the mathematician were interested in punishing
this indiscretion, he could make his denier ridiculous by inventing
asserted results which would completely take him in.
More than thirty years ago I had a friend, now long gone, who was a
mathematician, but not of the higher branches: he was, inter alia,
thoroughly up in all that relates to mortality, life assurance, &c.
One day, explaining to him how it should be ascertained what the chance
is of the survivors of a large number of persons now alive lying between
given limits of number at the end of a certain time, I came, of course
upon the introduction of π, which I could
only describe as the ratio of the circumference of a circle to its
diameter. "Oh, my dear friend! that must be a delusion; what can the
circle have to do with the numbers alive at the end of a given
time?"—"I cannot demonstrate it to you; but it is
demonstrated."—"Oh! stuff! I think you can prove anything with your
differential calculus: figment, depend upon it." I said no more; but, a
few days afterwards, I went to him and very gravely told him that I had
discovered the law of human mortality in the Carlisle Table, of which he
thought very highly. I told him that the law was involved in this
circumstance. Take the table of expectation of life, choose any age, take
its expectation and make the nearest integer a new age, do the same with
that, and so on; begin at what age you like, you are sure to end at the
place where the age past is equal, or most nearly equal, to the
expectation to come. "You don't mean that this always
happens?"—"Try it." He did try, again and again; and found it as I
said. "This is, indeed, a curious thing; this is a discovery." I
might have sent him about trumpeting the law of life: but I contented
myself with informing him that the same thing would happen with any table
whatsoever in which the first column goes up and the second goes down;
and that if a proficient in the higher mathematics chose to palm a
figment upon him, he could do without the circle: à corsaire, corsaire
et demi,[617] the
French proverb says. "Oh!" it was remarked, "I see, this was Milne!"[618] It was not
Milne: I remember well showing the formula to him some time afterwards.
He raised no difficulty about π; he knew the
forms of Laplace's results, and he was much interested. Besides, Milne
never said stuff! and figment! And he would not have been taken in: he
would have quietly tried it with the Northampton and all the other
tables, and would have got at the truth.
EUCLID WITHOUT AXIOMS.
The first book of Euclid's Elements. With alterations and familiar
notes. Being an attempt to get rid of axioms altogether; and to establish
the theory of parallel lines, without the introduction of any principle
not common to other parts of the elements. By a member of the University
of Cambridge. Third edition. In usum serenissimæ filiolæ. London,
1830.
The author was Lieut. Col. (now General) Perronet Thompson,[619] the author of the
"Catechism on the Corn Laws." I reviewed the fourth edition—which
had the name of "Geometry without Axioms," 1833—in the quarterly
Journal of Education for January, 1834. Col. Thompson, who then
was a contributor to—if not editor of—the Westminster
Review, replied in an article the authorship of which could not be
mistaken.
Some more attempts upon the problem, by the same author, will be found
in the sequel. They are all of acute and legitimate speculation; but they
do not conquer the difficulty in the manner demanded by the conditions of
the problem. The paradox of parallels does not contribute much to my
pages: its cases are to be found for the most part in geometrical
systems, or in notes to them. Most of them consist in the proposal of
additional postulates; some are attempts to do without any new postulate.
Gen. Perronet Thompson, whose paradoxes are always constructed on much
study of previous writers, has collected in the work above named, a
budget of attempts, the heads of which are in the Penny and
English Cyclopædias, at "Parallels." He has given thirty
instances, selected from what he had found.[620]
Lagrange,[621] in one
of the later years of his life, imagined that he had overcome the
difficulty. He went so far as to write a paper, which he took with him to
the Institute, and began to read it. But in the first paragraph something
struck him which he had not observed: he muttered Il faut que j'y
songe encore,[622]
and put the paper in his pocket.
THE LUNAR CAUSTIC JOKE.
The following paragraph appeared in the Morning Post, May 4,
1831:
"We understand that although, owing to circumstances with which the
public are not concerned, Mr. Goulburn[623] declined becoming a candidate for
University honors, that his scientific attainments are far from
inconsiderable. He is well known to be the author of an essay in the
Philosophical Transactions on the accurate rectification of a circular
arc, and of an investigation of the equation of a lunar caustic—a
problem likely to become of great use in nautical astronomy."
This hoax—which would probably have succeeded with any
journal—was palmed upon the Morning Post, which supported
Mr. Goulburn, by some Cambridge wags who supported Mr. Lubbock, the other
candidate for the University of Cambridge. Putting on the usual
concealment, I may say that I always suspected Dr-nkw-t-r B-th-n-[624] of having a share in
the matter. The skill of the hoax lies in avoiding the words "quadrature
of the circle," which all know, and speaking of "the accurate
rectification of a circular arc," which all do not know for its synonyme.
The Morning Post next day gave a reproof to hoaxers in general,
without referring to any particular case. It must be added, that although
there are caustics in mathematics, there is no lunar
caustic.
So far as Mr. Goulburn was concerned, the above was poetic justice. He
was the minister who, in old time, told a deputation from the
Astronomical Society that the Government "did not care twopence for all
the science in the country." There may be some still alive who remember
this: I heard it from more than one of those who were present, and are
now gone. Matters are much changed. I was thirty years in office at the
Astronomical Society; and, to my certain knowledge, every Government of
that period, Whig and Tory, showed itself ready to help with influence
when wanted, and with money whenever there was an answer for the House of
Commons. The following correction subsequently appeared. Referring to the
hoax about Mr. Goulburn, Messrs. C. H. and Thompson Cooper[625] have corrected an
error, by stating that the election which gave rise to the hoax was that
in which Messrs. Goulburn and Yates Peel[626] defeated Lord Palmerston[627] and Mr. Cavendish.[628] They add that Mr.
Gunning, the well-known Esquire Bedell of the University, attributed the
hoax to the late Rev. R. Sheepshanks, to whom, they state, are also
attributed certain clever fictitious biographies—of public men, as
I understand it—which were palmed upon the editor of the
Cambridge Chronicle, who never suspected their genuineness to the
day of his death. Being in most confidential intercourse with Mr.
Sheepshanks,[629] both at
the time and all the rest of his life (twenty-five years), and never
heard him allude to any such things—which were not in his line,
though he had satirical power of quite another kind—I feel
satisfied he had nothing to do with them. I may add that others, his
nearest friends, and also members of his family, never heard him allude
to these hoaxes as their author, and disbelieve his authorship as much as
I do myself. I say this not as imputing any blame to the true author,
such hoaxes being fair election jokes in all time, but merely to put the
saddle off the wrong horse, and to give one more instance of the
insecurity of imputed authorship. Had Mr. Sheepshanks ever told me that
he had perpetrated the hoax, I should have had no hesitation in giving it
to him. I consider all clever election squibs, free from bitterness and
personal imputation, as giving the multitude good channels for the vent
of feelings which but for them would certainly find bad ones.
[But I now suspect that Mr. Babbage[630] had some hand in the hoax. He gives
it in his "Passages, &c." and is evidently writing from memory, for
he gives the wrong year. But he has given the paragraph, though not
accurately, yet with such a recollection of the points as brings
suspicion of the authorship upon him, perhaps in conjunction with D. B.[631] Both were on
Cavendish's committee. Mr. Babbage adds, that "late one evening a cab
drove up in hot haste to the office of the Morning Post, delivered
the copy as coming from Mr. Goulburn's committee, and at the same time
ordered fifty extra copies of the Post to be sent next morning to
their committee-room." I think the man—the only one I ever heard
of—who knew all about the cab and the extra copies must have known
more.]
ON M. DEMONVILLE.
Demonville.—A Frenchman's Christian name is his own
secret, unless there be two of the surname. M. Demonville is a very good
instance of the difference between a French and English
discoverer. In England there is a public to listen to discoveries in
mathematical subjects made without mathematics: a public which will hear,
and wonder, and think it possible that the pretensions of the discoverer
have some foundation. The unnoticed man may possibly be right: and the
old country-town reputation which I once heard of, attaching to a man who
"had written a book about the signs of the zodiac which all the
philosophers in London could not answer," is fame as far as it goes.
Accordingly, we have plenty of discoverers who, even in astronomy,
pronounce the learned in error because of mathematics. In France, beyond
the sphere of influence of the Academy of Sciences, there is no one to
cast a thought upon the matter: all who take the least interest repose
entire faith in the Institute. Hence the French discoverer turns all his
thoughts to the Institute, and looks for his only hearing in that
quarter. He therefore throws no slur upon the means of knowledge, but
would say, with M. Demonville: "A l'égard de M. Poisson,[632] j'envie loyalement la millième partie
de ses connaissances mathématiques, pour prouver mon systême d'astronomie
aux plus incrédules."[633] This system is that the only bodies
of our system are the earth, the sun, and the moon; all the others being
illusions, caused by reflection of the sun and moon from the ice of the
polar regions. In mathematics, addition and subtraction are for men;
multiplication and division, which are in truth creation and destruction,
are prerogatives of deity. But nothing multiplied by
nothing is one. M. Demonville obtained an introduction to
William the Fourth, who desired the opinion of the Royal Society upon his
system: the answer was very brief. The King was quite
right; so was the Society: the fault lay with those who advised His
Majesty on a matter they knew nothing about. The writings of M.
Demonville in my possession are as follows.[634] The dates—which were only on
covers torn off in binding—were about 1831-34:
Petit cours d'astronomie[635] followed by Sur l'unité
mathématique.—Principes de la physique de la création
implicitement admis dans la notice sur le tonnerre par M.
Arago.—Question de longitude sur mer.[636]—Vrai système du monde[637] (pp. 92). Same title,
four pages, small type. Same title, four pages, addressed to the British
Association. Same title, four pages, addressed to M. Mathieu. Same title,
four pages, on M. Bouvard's report.—Résumé de la physique de la
création; troisième partie du vrai système du monde.[638]
PARSEY'S PARADOX.
The quadrature of the circle discovered, by Arthur Parsey,[639] author of the 'art of
miniature painting.' Submitted to the consideration of the Royal Society,
on whose protection the author humbly throws himself. London, 1832,
8vo.
Mr. Parsey was an artist, who also made himself conspicuous by a new
view of perspective. Seeing that the sides of a tower, for instance,
would appear to meet in a point if the tower were high enough, he thought
that these sides ought to slope to one another in the picture. On this
theory he published a small work, of which
I have not the title, with a Grecian temple in the frontispiece, stated,
if I remember rightly, to be the first picture which had ever been drawn
in true perspective. Of course the building looked very Egyptian, with
its sloping sides. The answer to his notion is easy enough. What is
called the picture is not the picture from which the mind takes its
perception; that picture is on the retina. The intermediate
picture, as it may be called—the human artist's work—is
itself seen perspectively. If the tower were so high that the sides,
though parallel, appeared to meet in a point, the picture must also be so
high that the picture-sides, though parallel, would appear to meet
in a point. I never saw this answer given, though I have seen and heard
the remarks of artists on Mr. Parsey's work. I am inclined to think it is
commonly supposed that the artist's picture is the representation which
comes before the mind: this is not true; we might as well say the same of
the object itself. In July 1831, reading an article on squaring the
circle, and finding that there was a difficulty, he set to work, got a
light denied to all mathematicians in—some would say
through—a crack, and advertised in the Times that he had
done the trick. He then prepared this work, in which, those who read it
will see how, he showed that 3.14159... should be 3.0625. He might have
found out his error by stepping a draughtsman's circle with the
compasses.
Perspective has not had many paradoxes. The only other one I remember
is that of a writer on perspective, whose name I forget, and whose four
pages I do not possess. He circulated remarks on my notes on the subject,
published in the Athenæum, in which he denies that the
stereographic projection is a case of perspective, the reason being that
the whole hemisphere makes too large a picture for the eye conveniently
to grasp at once. That is to say, it is no perspective because there is
too much perspective.
ON A COUPLE OF GEOMETRIES.
Principles of Geometry familiarly illustrated. By the Rev. W.
Ritchie,[640] LL.D.
London, 1833, 12mo.
A new Exposition of the system of Euclid's Elements, being an attempt
to establish his work on a different basis. By Alfred Day,[641] LL.D. London, 1839,
12mo.
These works belong to a small class which have the peculiarity of
insisting that in the general propositions of geometry a proposition
gives its converse: that "Every B is A" follows from "Every A is B." Dr.
Ritchie says, "If it be proved that the equality of two of the angles of
a triangle depends essentially upon the equality of the opposite
sides, it follows that the equality of opposite sides depends
essentially on the equality of the angles." Dr. Day puts it as
follows:
"That the converses of Euclid, so called, where no particular
limitation is specified or implied in the leading proposition, more than
in the converse, must be necessarily true; for as by the nature of the
reasoning the leading proposition must be universally true, should the
converse be not so, it cannot be so universally, but has at least all the
exceptions conveyed in the leading proposition, and the case is therefore
unadapted to geometric reasoning; or, what is the same thing, by the very
nature of geometric reasoning, the particular exceptions to the extended
converse must be identical with some one or other of the cases under the
universal affirmative proposition with which we set forth, which is
absurd."
On this I cannot help transferring to my reader the words of the Pacha
when he orders the bastinado,—May it do you good! A rational study
of logic is much wanted to show many mathematicians, of all degrees of
proficiency, that there is nothing in the reasoning of mathematics
which differs from other reasoning. Dr. Day repeated his argument in A
Treatise on Proportion, London, 1840, 8vo. Dr. Ritchie was a very
clear-headed man. He published, in 1818, a work on arithmetic, with
rational explanations. This was too early for such an improvement, and
nearly the whole of his excellent work was sold as waste paper. His
elementary introduction to the Differential Calculus was drawn up while
he was learning the subject late in life. Books of this sort are often
very effective on points of difficulty.
NEWTON AGAIN OBLITERATED.
Letter to the Royal Astronomical Society in refutation of Mistaken
Notions held in common, by the Society, and by all the Newtonian
philosophers. By Capt. Forman,[642] R.N. Shepton-Mallet, 1833, 8vo.
Capt. Forman wrote against the whole system of gravitation, and got no
notice. He then wrote to Lord Brougham, Sir J. Herschel, and others I
suppose, desiring them to procure notice of his books in the reviews:
this not being acceded to, he wrote (in print) to Lord John Russell[643] to complain of their
"dishonest" conduct. He then sent a manuscript letter to the Astronomical
Society, inviting controversy: he was answered by a recommendation to
study dynamics. The above pamphlet was the
consequence, in which, calling the Council of the Society "craven
dunghill cocks," he set them right about their doctrines. From all I can
learn, the life of a worthy man and a creditable officer was completely
embittered by his want of power to see that no person is bound in reason
to enter into controversy with every one who chooses to invite him to the
field. This mistake is not peculiar to philosophers, whether of orthodoxy
or paradoxy; a majority of educated persons imply, by their modes of
proceeding, that no one has a right to any opinion which he is not
prepared to defend against all comers.
David and Goliath, or an attempt to prove that the Newtonian system of
Astronomy is directly opposed to the Scriptures. By Wm. Lauder,[644] Sen., Mere, Wilts.
Mere, 1833, 12mo.
Newton is Goliath; Mr. Lauder is David. David took five pebbles; Mr.
Lauder takes five arguments. He expects opposition; for Paul and Jesus
both met with it.
Mr. Lauder, in his comparison, seems to put himself in the divinely
inspired class. This would not be a fair inference in every case; but we
know not what to think when we remember that a tolerable number of
cyclometers have attributed their knowledge to direct revelation. The
works of this class are very scarce; I can only mention one or two from
Montucla.[645] Alphonso
Cano de Molina,[646] in
the last century, upset all Euclid, and squared the circle upon the
ruins; he found a follower, Janson, who translated him from Spanish into
Latin. He declared that he believed in Euclid, until God, who humbles the
proud, taught him better. One Paul Yvon, called from his estate de la
Leu, a merchant at Rochelle, supported by his book-keeper, M. Pujos, and
a Scotchman, John Dunbar, solved the problem
by divine grace, in a manner which was to convert all Jews, Infidels,
etc. There seem to have been editions of his work in 1619 and 1628, and a
controversial "Examen" in 1630, by Robert Sara. There was a noted
discussion, in which Mydorge,[647] Hardy,[648] and others took part against de la
Leu. I cannot find this name either in Lipenius[649] or Murhard,[650] and I should not have known the dates
if it had not been for one of the keenest bibliographers of any time, my
friend Prince Balthasar Boncompagni,[651] who is trying to find copies of the
works, and has managed to find copies of the titles. In 1750, Henry
Sullamar, an Englishman, squared the circle by the number of the Beast:
he published a pamphlet every two or three years; but I cannot find any
mention of him in English works.[652] In France, in 1753, M. de Causans,[653] of the Guards, cut a
circular piece of turf, squared it, and deduced original sin
and the Trinity. He found out that the circle was equal to the square in
which it is inscribed; and he offered a reward for detection of any
error, and actually deposited 10,000 francs as earnest of 300,000. But
the courts would not allow any one to recover.
SIR JOHN HERSCHEL.
1834. In this year Sir John Herschel[654] set up his telescope at Feldhausen,
Cape of Good Hope. He did much for astronomy, but not much for the
Budget of Paradoxes. He gives me, however, the following story. He
showed a resident a remarkable blood-red star, and some little time after
he heard of a sermon preached in those parts in which it was asserted
that the statements of the Bible must be true, for that Sir J. H. had
seen in his telescope "the very place where wicked people go."
But red is not always the color. Sir J. Herschel has in his possession
a letter written to his father, Sir W. H.,[655] dated April 3, 1787, and signed
"Eliza Cumyns," begging to know if any of the stars be indigo in
color, "because, if there be, I think it may be deemed a strong
conjectural illustration of the expression, so often used by our Saviour
in the Holy Gospels, that 'the disobedient shall be cast into outer
darkness'; for as the Almighty Being can doubtless confine any of his
creatures, whether corporeal or spiritual, to what part of his creation
He pleases, if therefore any of the stars (which are beyond all doubt so
many suns to other systems) be of so dark a color as that above
mentioned, they may be calculated to give the most insufferable heat to
those dolorous systems dependent upon them (and to reprobate spirits
placed there), without one ray of cheerful light; and may therefore be
the scenes of future punishments." This letter is addressed to Dr.
Heirschel at Slow. Some have placed the infernal regions inside the
earth, but others have filled this internal
cavity—for cavity they will have—with refulgent light, and
made it the abode of the blessed. It is difficult to build without
knowing the number to be provided for. A friend of mine heard the
following (part) dialogue between two strong Scotch Calvinists: "Noo! hoo
manny d'ye thank there are of the alact on the arth at this
moment?—Eh! mabbee a doozen—Hoot! mon! nae so mony as
thot!"
THE NAUTICAL ALMANAC.
1834. From 1769 to 1834 the Nautical Almanac was published on a
plan which gradually fell behind what was wanted. In 1834 the new series
began, under a new superintendent (Lieut. W. S. Stratford).[656] There had been a long
scientific controversy, which would not be generally intelligible. To set
some of the points before the reader, I reprint a cutting which I have by
me. It is from the Nautical Magazine, but I did hear that some had
an idea that it was in the Nautical Almanac itself. It certainly
was not, and I feel satisfied the Lords of the Admiralty would not have
permitted the insertion; they are never in advance of their age. The
Almanac for 1834 was published in July 1833.
The New Nautical Almanac—Extract from
the 'Primum Mobile,' and 'Milky Way Gazette.' Communicated by Aerolith.
A meeting of the different bodies composing the Solar System was this
day held at the Dragon's Tail, for the purpose of taking into
consideration the alterations and amendments introduced into the New
Nautical Almanac. The honorable luminaries had been individually summoned
by fast-sailing comets, and there was a
remarkably full attendance. Among the visitors we observed several
nebulæ, and almost all the stars whose proper motions would admit of
their being present.
The Sun was unanimously called to the focus.
The small planets took the oaths, and their places, after a short
discussion, in which it was decided that the places should be those of
the Almanac itself, with leave reserved to move for corrections.
Petitions were presented from α and
δ Ursæ Minoris, complaining of being put
on daily duty, and praying for an increase of salary.—Laid on the
plane of the ecliptic.
The trustees of the eccentricity[657] and inclination funds reported a
balance of .00001 in the former, and a deficit of 0".009 in the latter.
This announcement caused considerable surprise, and a committee was moved
for, to ascertain which of the bodies had more or less than his share.
After some discussion, in which the small planets offered to consent to a
reduction, if necessary, the motion was carried.
The Focal Body then rose to address the
meeting. He remarked that the subject on which they were assembled was
one of great importance to the routes and revolutions of the heavenly
bodies. For himself, though a private arrangement between two of his
honourable neighbours (here he looked hard at the Earth and Venus) had
prevented his hitherto paying that close attention to the predictions of
the Nautical Almanac which he declared he always had wished to do; yet he
felt consoled by knowing that the conductors of that work had every
disposition to take his peculiar circumstances into consideration. He
declared that he had never passed the wires of a transit without deeply
feeling his inability to adapt himself to the present state of his
theory; a feeling which he was afraid had sometimes caused a slight
tremor in his limb. Before he sat down, he expressed a hope that
honourable luminaries would refrain as much as possible from eclipsing
each other, or causing mutual perturbations. Indeed, he should be very sorry to see any
interruption of the harmony of the spheres. (Applause.)
The several articles of the New Nautical Almanac were then read over
without any comment; only we observed that Saturn shook his ring at every
novelty, and Jupiter gave his belt a hitch, and winked at the satellites
at page 21 of each month.
The Moon rose to propose a resolution. No one,
he said, would be surprised at his bringing this matter forward in the
way he did, when it was considered in how complete and satisfactory a
manner his motions were now represented. He must own he had trembled when
the Lords of the Admiralty dissolved the Board of Longitude, but his
tranquillity was more than reestablished by the adoption of the new
system. He did not know but that any little assistance he could give in
Nautical Astronomy was becoming of less and less value every day, owing
to the improvement of chronometers. But there was one thing, of which
nothing could deprive him—he meant the regulation of the tides.
And, perhaps, when his attention was not occupied by more than the
latter, he should be able to introduce a little more regularity into the
phenomena. (Here the honourable luminary gave a sort of modest libration,
which convulsed the meeting with laughter.) They might laugh at his
natural infirmity if they pleased, but he could assure them it arose only
from the necessity he was under, when young, of watching the motions of
his worthy primary. He then moved a resolution highly laudatory of the
alterations which appeared in the New Nautical Almanac.
The Earth rose, to second the motion. His
honourable satellite had fully expressed his opinions on the subject. He
joined his honourable friend in the focus in wishing to pay every
attention to the Nautical Almanac, but, really, when so
important an alteration had taken place in his magnetic pole[658] (hear) and there
might, for aught he knew, be a successful attempt to reach his pole of
rotation, he thought he could not answer for the preservation of the
precession in its present state. (Here the hon. luminary, scratching his
side, exclaimed, as he sat down, "More steamboats—confound
'em!")
An honourable satellite (whose name we could not learn) proposed that
the resolution should be immediately despatched, corrected for
refraction, when he was called to order by the Focal Body, who reminded
him that it was contrary to the moving orders of the system to take
cognizance of what passed inside the atmosphere of any planet.
Saturn and Pallas rose
together. (Cries of "New member!" and the former gave way.) The latter,
in a long and eloquent speech, praised the liberality with which he and
his colleagues had at length been relieved from astronomical
disqualifications. He thought that it was contrary to the spirit of the
laws of gravitation to exclude any planet from office on account of the
eccentricity or inclination of his orbit. Honourable luminaries need not
talk of the want of convergency of his series. What had they to do with
any private arrangements between him and the general equations of the
system? (Murmurs from the opposition.) So long as he obeyed the laws of
motion, to which he had that day taken a solemn oath, he would ask, were
old planets, which were now so well known that nobody trusted them,
to....
The Focal Body said he was sorry to break the
continuity of the proceedings, but he thought that remarks upon
character, with a negative sign, would introduce differences of too high
an order. The honourable luminary must eliminate the expression which he
had brought out, in finite terms, and use smaller inequalities in future.
(Hear, hear.)
Pallas explained, that he was far from meaning
to reflect upon the orbital character of any planet present. He only
meant to protest against being judged by any laws but those of
gravitation, and the differential calculus: he thought it most unjust
that astronomers should prevent the small planets from being observed,
and then reproach them with the imperfections of the tables, which were
the result of their own narrow-minded policy. (Cheers.)
Saturn thought that, as an old planet, he had
not been treated with due respect. (Hear, from his satellites.) He had
long foretold the wreck of the system from the friends of innovation.
Why, he might ask, were his satellites to be excluded, when small
planets, trumpery comets, which could not keep their mean distances
(cries of oh! oh!), double stars, with graphical approximations, and such
obscure riff-raff of the heavens (great uproar) found room enough. So
help him Arithmetic, nothing could come of it, but a stoppage of all
revolution. His hon. friend in the focus might smile, for he would be a
gainer by such an event; but as for him (Saturn), he had something to
lose, and hon. luminaries well knew that, whatever they might think
under an atmosphere, above it continual revolution was the
only way of preventing perpetual anarchy. As to the hon. luminary who had
risen before him, he was not surprised at his remarks, for he had
invariably observed that he and his colleagues allowed themselves too
much latitude. The stability of the system required that they should
be brought down, and he, for one, would exert all his powers of
attraction to accomplish that end. If other bodies would cordially unite
with him, particularly his noble friend next him, than whom no luminary
possessed greater weight—
Jupiter rose to order. He conceived his noble
friend had no right to allude to him in that
manner, and was much surprised at his proposal, considering the matters
which remained in dispute between them. In the present state of affairs,
he would take care never to be in conjunction with his hon. neighbour one
moment longer than he could help. (Cries of "Order, order, no long
inequalities," during which he sat down.)
Saturn proceeded to say, that he did not know
till then that a planet with a ring could affront one who had only a
belt, by proposing mutual co-operation. He would now come to the subject
under discussion. He should think meanly of his hon. colleagues if they
consented to bestow their approbation upon a mere astronomical
production. Had they forgotten that they once were considered the
arbiters of fate, and the prognosticators of man's destiny? What had lost
them that proud position? Was it not the infernal march of intellect,
which, after having turned the earth topsy-turvy, was now disturbing the
very universe? For himself (others might do as they pleased), but he
stuck to the venerable Partridge,[659] and the Stationers' Company, and
trusted that they would outlive infidels and anarchists, whether of
Astronomical or Diffusion of Knowledge Societies. (Cries of oh! oh!)
Mars said he had been told, for he must
confess he had not seen the work, that the places of the planets were
given for Sundays. This, he must be allowed to say, was an indecorum he
had not expected; and he was convinced the Lords of the Admiralty had
given no orders to that effect. He hoped this point would be considered
in the measure which had been introduced in another place, and that some
one would move that the prohibition
against travelling on Sundays extend to the heavenly as well as earthly
bodies.
Several of the stars here declared, that they had been much annoyed by
being observed on Sunday evenings, during the hours of divine
service.
The room was then cleared for a division, but we are unable to state
what took place. Several comets-at-arms were sent for, and we heard
rumors of a personal collision having taken place between two luminaries
in opposition. We were afterwards told that the resolution was carried by
a majority, and the luminaries elongated at 2 h. 15 m. 33,41 s. sidereal
time.
* * * It is reported, but we hope without foundation, that Saturn, and
several other discontented planets, have accepted an invitation from
Sirius to join his system, on the most liberal appointments. We believe
the report to have originated in nothing more than the discovery of the
annual parallax of Sirius from the orbit of Saturn; but we may safely
assure our readers that no steps have as yet been taken to open any
communication.
We are also happy to state, that there is no truth in the rumor of the
laws of gravitation being about to be repealed. We have traced this
report, and find it originated with a gentleman living near Bath (Captain
Forman, R.N),[660] whose
name we forbear to mention.
A great excitement has been observed among the nebulæ, visible to the
earth's southern hemisphere, particularly among those which have not yet
been discovered from thence. We are at a loss to conjecture the cause,
but we shall not fail to report to our readers the news of any movement
which may take place. (Sir J. Herschel's visit. He could just see this
before he went out.)
WOODLEY'S DIVINE SYSTEM.
A Treatise on the Divine System of the Universe, by Captain Woodley,
R.N.,[661] and as
demonstrated by his Universal Time-piece, and universal method of
determining a ship's longitude by the apparent true place of the moon;
with an introduction refuting the solar system of Copernicus, the
Newtonian philosophy, and mathematics. 1834.[662] 8vo.
Description of the Universal Time-piece. (4pp. 12mo.)
I think this divine system was published several years before, and was
republished with an introduction in 1834.[663] Capt. Woodley was very sure that the
earth does not move: he pointed out to me, in a conversation I had with
him, something—I forget what—in the motion of the Great Bear,
visible to any eye, which could not possibly be if the earth moved. He
was exceedingly ignorant, as the following quotation from his account of
the usual opinion will show:
"The north pole of the Earth's axis deserts, they say, the north star
or pole of the Heavens, at the rate of 1° in 71¾ years.... The fact is,
nothing can be more certain than that the Stars have not changed their
latitudes or declinations one degree in the last 71¾ years."
This is a strong specimen of a class of men by whom all accessible
persons who have made any name in science are hunted. It is a pity that
they cannot be admitted into scientific societies, and allowed fairly to
state their cases, and stand quiet cross-examination, being kept in their
answers very close to the questions, and the answers written down. I am
perfectly satisfied that if one meeting in the year were devoted to the
hearing of those who chose to come forward on such conditions, much good
would be done. But I strongly suspect few would come forward at first,
and none in a little while: and I have had some experience of the method
I recommend, privately tried. Capt. Woodley was proposed, a little after
1834, as a Fellow of the Astronomical Society; and, not caring whether he
moved the sun or the earth, or both—I could not have stood
neither—I signed the proposal. I always had a sneaking
kindness for paradoxers, such a one, perhaps, as Petit André had for his
lambs, as he called them. There was so little feeling against his
opinions, that he only failed by a fraction of a ball. Had I myself
voted, he would have been elected; but being engaged in conversation, and
not having heard the slightest objection to him, I did not think it worth
while to cross the room for the purpose. I regretted this at the time,
but had I known how ignorant he was I should not have supported him.
Probably those who voted against him knew more of his book than I
did.
I remember no other instance of exclusion from a scientific society on
the ground of opinion, even if this be one; of which it may be that
ignorance had more to do with it than paradoxy. Mr. Frend,[664] a strong
anti-Newtonian, was a Fellow of the Astronomical Society, and for some
years in the Council. Lieut. Kerigan[665] was elected to the Royal Society at a
time when his proposers must have known that his immediate object was to
put F.R.S. on the title-page of a work against the tides. To give all I
know, I may add that the editor of some very ignorant bombast about the
"forehead of the solar sky," who did not know the difference between
Bailly[666] and
Baily,[667]
received hints which induced him to withdraw his proposal for election
into the Astronomical Society. But this was an act of kindness; for if he
had seen Mr. Baily in the chair, with his head on, he might have been
political historian enough to faint away.
De la formation des Corps. Par Paul Laurent.[668] Nancy, 1834, 8vo.
Atoms, and ether, and ovules or eggs, which are planets, and their
eggs, which are satellites. These speculators can create worlds, in which
they cannot be refuted; but none of them dare attack the problem of a
grain of wheat, and its passage from a seed to a plant, bearing scores of
seeds like what it was itself.
ON JOHN FLAMSTEED.
An account of the Rev. John Flamsteed,[669] the First Astronomer-Royal.... By
Francis Baily,[670] Esq.
London, 1835, 4to. Supplement, London, 1837, 4to.
My friend Francis Baily was a paradoxer: he brought forward things
counter to universal opinion. That Newton was impeccable in every point
was the national creed; and failings of temper and conduct would have
been utterly disbelieved, if the paradox had not come supported by very
unusual evidence. Anybody who impeached Newton on existing evidence might
as well have been squaring the circle, for any attention he would have
got. About this book I will tell a story. It was published by the
Admiralty for distribution; and the distribution was entrusted to Mr.
Baily. On the eve of its appearance, rumors of its extraordinary
revelations got about, and persons of influence applied to the Admiralty
for copies. The Lords were in a difficulty: but on looking at the list
they saw names, as they thought, which were so obscure that they
had a right to assume Mr. Baily had included persons who had no claim to
such a compliment as presentation from the Admiralty. The Secretary
requested Mr. Baily to call upon him. "Mr. Baily, my Lords are inclined
to think that some of the persons in this list are perhaps not of that
note which would justify their Lordships in presenting this
work."—"To whom does your observation apply, Mr.
Secretary?"—"Well, now, let us examine the list; let me see;
now,—now,—now,—come!—here's Gauss[671]—who's
Gauss?"—"Gauss, Mr. Secretary, is the oldest mathematician now
living, and is generally thought to be the greatest."—"O-o-oh!
Well, Mr. Baily, we will see about it, and I will write you a letter."
The letter expressed their Lordships' perfect satisfaction with the
list.
There was a controversy about the revelations made in this work; but
as the eccentric anomalies took no part in it, there is nothing for my
purpose. The following valentine from Mrs. Flamsteed,[672] which I found among Baily's papers,
illustrates some of the points:
"3 Astronomers' Row, Paradise: February 14, 1836.
"Dear Sir,—I suppose you hardly expected to receive a letter
from me, dated from this place; but the truth is, a gentleman from our
street was appointed guardian angel to the American Treaty, in which
there is some astronomical question about boundaries. He has got leave to
go back to fetch some instruments which he left behind, and I take this
opportunity of making your acquaintance. That America has become a
wonderful place since I was down among you; you have no idea how grand
the fire at New York looked up here. Poor dear Mr. Flamsteed
does not know I am writing a letter to a gentleman on Valentine's day; he
is walked out with Sir Isaac Newton (they are pretty good friends now,
though they do squabble a little sometimes) and Sir William Herschel, to
see a new nebula. Sir Isaac says he can't make out at all how it is
managed; and I am sure I cannot help him. I never bothered my head about
those things down below, and I don't intend to begin here.
"I have just received the news of your having written a book about my
poor dear man. It's a chance that I heard it at all; for the truth is,
the scientific gentlemen are somehow or other become so wicked, and go so
little to church, that very few of them are considered fit company for
this place. If it had not been for Dr. Brinkley,[673] who came here of course, I should not
have heard about it. He seems a nice man, but is not yet used to our
ways. As to Mr. Halley,[674] he is of course not here; which is
lucky for him, for Mr. Flamsteed swore the moment he caught him in a
place where there are no magistrates, he would make a sacrifice of him to
heavenly truth. It was very generous in Mr. F. not appearing against Sir
Isaac when he came up, for I am told that if he had, Sir Isaac would not
have been allowed to come in at all. I should have been sorry for that,
for he is a companionable man enough, only holds his head rather higher
than he should do. I met him the other day walking with Mr. Whiston,[675] and disputing about
the deluge. 'Well, Mrs. Flamsteed,' says he, 'does old Poke-the-Stars
understand gravitation yet?' Now you must know that is rather a sore
point with poor dear Mr. Flamsteed. He says that Sir Isaac is as
crochetty about the moon as ever; and as to what some people say
about what has been done since his time, he says he should like to see
somebody who knows something about it of himself. For it is very singular
that none of the people who have carried on Sir Isaac's notions have been
allowed to come here.
"I hope you have not forgotten to tell how badly Sir Isaac used Mr.
Flamsteed about that book. I have never quite forgiven him; as for Mr.
Flamsteed, he says that as long as he does not come for observations, he
does not care about it, and that he will never trust him with any papers
again as long as he lives. I shall never forget what a rage he came home
in when Sir Isaac had called him a puppy. He struck the stairs all the
way up with his crutch, and said puppy at every step, and all the
evening, as soon as ever a star appeared in the telescope, he called it
puppy. I could not think what was the matter, and when I asked, he only
called me puppy.
"I shall be very glad to see you if you come our way. Pray keep up
some appearances, and go to church a little. St. Peter is always
uncommonly civil to astronomers, and indeed to all scientific persons,
and never bothers them with many questions. If they can make anything out
of the case, he is sure to let them in. Indeed, he says, it is perfectly
out of the question expecting a mathematician to be as religious as an
apostle, but that it is as much as his place is worth to let in the
greater number of those who come. So try if you cannot manage it, for I
am very curious to know whether you found all the letters. I remain, dear
sir, your faithful servant,
"Margaret Flamsteed.
"P.S. Mr. Flamsteed has come in, and says he left Sir Isaac riding
cockhorse upon the nebula, and poring over it as if it were a book. He
has brought in his old acquaintance Ozanam,[676] who says that it was always his maxim
on earth, that 'il appartient aux docteurs de
Sorbonne de disputer, au Pape de prononcer, et au mathématicien d'aller
en Paradis en ligne perpendiculaire.'"[677]
ON STEVIN.
The Secretary of the Admiralty was completely extinguished. I can
recall but two instances of demolition as complete, though no doubt there
are many others. The first is in
Simon Stevin[678] and M. Dumortier. Nieuport, 1845, 12mo.
M. Dumortier was a member of the Academy of Brussels: there was a
discussion, I believe, about a national Pantheon for Belgium. The name of
Stevinus suggested itself as naturally as that of Newton to an
Englishman; probably no Belgian is better known to foreigners as
illustrious in science. Stevinus is great in the Mécanique
Analytique of Lagrange;[679] Stevinus is great in the Tristram
Shandy of Sterne. M. Dumortier, who believed that not one Belgian in
a thousand knew Stevinus, and who confesses with ironical shame that he
was not the odd man, protested against placing the statue of an obscure
man in the Pantheon, to give foreigners the notion that Belgium could
show nothing greater. The work above named is a slashing retort: any one
who knows the history of science ever so little may imagine what a
dressing was given, by mere extract from foreign writers. The tract is a
letter signed J. du Fan, but this is a pseudonym of Mr. Van de Weyer.[680] The Academician says
Stevinus was a man who was not without merit for the time at which he
lived: Sir! is the answer, he was as much before his own time as you are
behind yours. How came a man who had never heard of Stevinus to be a
member of the Brussels Academy?
The second story was told me by Mr. Crabb Robinson,[681] who was long connected with the
Times, and intimately acquainted with Mr. W***.[682] When W*** was an undergraduate at
Cambridge, taking a walk, he came to a stile, on which sat a bumpkin who
did not make way for him: the gown in that day looked down on the town.
"Why do you not make way for a gentleman?"—"Eh?"—"Yes, why do
you not move? You deserve a good hiding, and you shall get it if you
don't take care!" The bumpkin raised his muscular figure on its feet,
patted his menacer on the head, and said, very quietly,—"Young man!
I'm Cribb."[683] W***
seized the great pugilist's hand, and shook it warmly, got him to his own
rooms in college, collected some friends, and had a symposium which
lasted until the large end of the small hours.
FINLEYSON AS A PARADOXER.
God's Creation of the Universe as it is, in support of the Scriptures.
By Mr. Finleyson.[684]
Sixth Edition, 1835, 8vo.
This writer, by his own account, succeeded in delivering the famous
Lieut. Richard Brothers[685] from the lunatic asylum, and tending
him, not as a keeper but as a disciple, till he died. Brothers was, by
his own account, the nephew of the Almighty, and Finleyson ought to have
been the nephew of Brothers. For Napoleon came to him in a vision, with a
broken sword and an arrow in his side, beseeching help: Finleyson pulled
out the arrow, but refused to give a new sword; whereby poor Napoleon,
though he got off with life, lost the battle of Waterloo. This story was
written to the Duke of Wellington, ending with "I pulled out the arrow,
but left the broken sword. Your Grace can supply the rest, and what
followed is amply recorded in history." The book contains a long account
of applications to Government to do three things: to pay 2,000l.
for care taken of Brothers, to pay 10,000l. for discovery of the
longitude, and to prohibit the teaching of the Newtonian system, which
makes God a liar. The successive administrations were threatened that
they would have to turn out if they refused, which, it is remarked, came
to pass in every case. I have heard of a joke of Lord Macaulay, that the
House of Commons must be the Beast of the Revelations, since 658 members,
with the officers necessary for the action of the House, make 666.
Macaulay read most things, and the greater part of the rest: so that he
might be suspected of having appropriated as a joke one of Finleyson's
serious points—"I wrote Earl Grey[686] upon the 13th of July, 1831,
informing him that his Reform Bill could not be carried, as it reduced
the members below the present amount of 658, which, with the eight
principal clerks or officers of the House, make the number 666." But a
witness has informed me that Macaulay's joke was made in his hearing a
great many years before the Reform Bill was proposed; in fact, when both
were students at Cambridge. Earl Grey was, according to Finleyson, a
descendant of Uriah the Hittite. For a specimen of Lieut. Brothers, this
book would be worth picking up. Perhaps a specimen of the Lieutenant's
poetry may be acceptable: Brothers loquitur, remember:
"Jerusalem ! Jerusalem! shall be built again!
More rich, more grand then ever;
And through it shall Jordan flow!(!)
My people's favourite river.
There I'll erect a splendid throne,
And build on the wasted place;
To fulfil my ancient covenant
To King David and his race.
* * * * * *
"Euphrates' stream shall flow with ships,
And also my wedded Nile;
And on my coast shall cities rise,
Each one distant but a mile.
* * * * * *
"My friends the Russians on the north
With Persees and Arabs round,
Do show the limits of my land,
Here! Here! then I mark the ground."
ON THEOLOGICAL PARADOXERS.
Among the paradoxers are some of the theologians who in their own
organs of the press venture to criticise science. These may hold their
ground when they confine themselves to the geology of long past periods
and to general cosmogony: for it is the tug of Greek against Greek; and
both sides deal much in what is grand when called hypothesis,
petty when called supposition. And very often they are not
conspicuous when they venture upon things within knowledge; wrong, but not
quite wrong enough for a Budget of Paradoxes. One case, however, is
destined to live, as an instance of a school which finds writers,
editors, and readers. The double stars have been seen from the
seventeenth century, and diligently observed by many from the time of Wm.
Herschel, who first devoted continuous attention to them. The year 1836
was that of a remarkable triumph of astronomical prediction. The theory
of gravitation had been applied to the motion of binary stars about each
other, in elliptic orbits, and in that year the two stars of γ Virginis, as had been predicted should happen
within a few years of that time—for years are small quantities in
such long revolutions—the two stars came to their nearest: in fact,
they appeared to be one as much with the telescope as without it. This
remarkable turning-point of the history of a long and widely-known branch
of astronomy was followed by an article in the Church of England
Quarterly Review for April 1837, written against the Useful Knowledge
Society. The notion that there are any such things as double stars is (p.
460) implied to be imposture or delusion, as in the following extract. I
suspect that I myself am the Sidrophel, and that my companion to
the maps of the stars, written for the Society and published in 1836, is
the work to which the writer refers:
"We have forgotten the name of that Sidrophel who lately discovered
that the fixed stars were not single stars, but appear in the heavens
like soles at Billingsgate, in pairs; while a second astronomer, under
the influence of that competition in trade which the political economists
tell us is so advantageous to the public, professes to show us, through
his superior telescope, that the apparently single stars are really
three. Before such wondrous mandarins of science, how continually must
homunculi like ourselves keep in the background, lest we come
between the wind and their nobility."
If the homunculus who wrote this be still above ground, how
devoutly must he hope he may be able to keep in the background! But the
chief blame falls on the editor. The title of the article is:
"The new school of superficial pantology; a speech intended to be
delivered before a defunct Mechanics' Institute. By Swallow Swift, late
M.P. for the Borough of Cockney-Cloud, Witsbury: reprinted Balloon
Island, Bubble year, month Ventose. Long live Charlatan!"
As a rule, orthodox theologians should avoid humor, a weapon which all
history shows to be very difficult to employ in favor of establishment,
and which, nine times out of ten, leaves its wielder fighting on the side
of heterodoxy. Theological argument, when not enlivened by bigotry, is
seldom worse than narcotic: but theological fun, when not covert heresy,
is almost always sialagogue. The article in question is a craze, which no
editor should have admitted, except after severe inspection by qualified
persons. The author of this wit committed a mistake which occurs now and
then in old satire, the confusion between himself and the party aimed at.
He ought to be reviewing this fictitious book, but every now and then the
article becomes the book itself; not by quotation, but by the writer
forgetting that he is not Mr. Swallow Swift, but his reviewer. In
fact he and Mr. S. Swift had each had a dose of the Devil's
Elixir. A novel so called, published about forty years ago, proceeds
upon a legend of this kind. If two parties both drink of the elixir,
their identities get curiously intermingled; each turns up in the
character of the other throughout the three volumes, without having his
ideas clear as to whether he be himself or the other. There is a similar
confusion in the answer made to the famous Epistolæ Obscurorum
Virorum:[687] it is
headed Lamentationes Obscurorum Virorum.[688] This is not a retort of
the writer, throwing back the imputation: the obscure men who had been
satirized are themselves made, by name, to wince under the disapprobation
which the Pope had expressed at the satire upon themselves.
Of course the book here reviewed is a transparent forgery. But I do
not know how often it may have happened that the book, in the journals
which always put a title at the head, may have been written after the
review. About the year 1830 a friend showed me the proof of an article of
his on the malt tax, for the next number of the Edinburgh Review.
Nothing was wanting except the title of the book reviewed; I asked what
it was. He sat down, and wrote as follows at the head, "The Maltster's
Guide (pp. 124)," and said that would do as well as anything.
But I myself, it will be remarked, have employed such humor as I can
command "in favor of establishment." What it is worth I am not to judge;
as usual in such cases, those who are of my cabal pronounce it good, but
cyclometers and other paradoxers either call it very poor, or commend it
as sheer buffoonery. Be it one or the other, I observe that all the
effective ridicule is, in this subject, on the side of establishment.
This is partly due to the difficulty of quizzing plain and sober
demonstration; but so much, if not more, to the ignorance of the
paradoxers. For that which cannot be ridiculed, can be turned
into ridicule by those who know how. But by the time a person is deep
enough in negative quantities, and impossible quantities,
to be able to satirize them, he is caught, and being inclined to become a
user, shrinks from being an abuser. Imagine a person with a
gift of ridicule, and knowledge enough, trying his hand on the junction
of the assertions which he will find in various books of algebra. First,
that a negative quantity has no logarithm; secondly, that a negative
quantity has no square root; thirdly, that the first non-existent is to
the second as the circumference of a circle to its diameter. One great
reason of the allowance of such unsound modes of expression is the
confidence felt by the writers that √-1 and log(-1) will make their
way, however inaccurately described. I heartily wish that the cyclometers
had knowledge enough to attack the weak points of algebraical diction:
they would soon work a beneficial change.[689]
AN EARLY METEOROLOGIST.
Recueil de ma vie, mes ouvrages et mes pensées. Par Thomas Ignace
Marie Forster.[690]
Brussels, 1836, 12mo.
Mr. Forster, an Englishman settled at Bruges, was an observer in many
subjects, but especially in meteorology. He communicated to the
Astronomical Society, in 1848, the information that, in the registers
kept by his grandfather, his father, and himself, beginning in 1767, new
moon on Saturday was followed, nineteen times out of twenty, by twenty
days of rain and wind. This statement being published in the
Athenæum, a cluster of correspondents averred that the belief is
common among seamen, in all parts of the world, and among landsmen too.
Some one quoted a distich:
"Saturday's moon and Sunday's full
Never were fine and never wull."
Another brought forward:
"If a Saturday's moon
Comes once in seven years it comes too soon."
Mr. Forster did not say he was aware of the proverbial character of
the phenomenon. He was a very eccentric man. He treated his dogs as
friends, and buried them with ceremony. He quarrelled with the
curé of his parish, who remarked that he could not take his dogs
to heaven with him. I will go nowhere, said he, where I cannot take my
dog. He was a sincere Catholic: but there is a point beyond which even
churches have no influence.
The following is some account of the announcement of 1849. The
Athenæum (Feb. 17), giving an account of the meeting of the
Astronomical Society in December, 1858, says:
"Dr. Forster of Bruges, who is well known as a meteorologist, made a
communication at which our readers will stare: he declares that by
journals of the weather kept by his grandfather, father, and himself,
ever since 1767, to the present time, whenever the new moon has fallen
on a Saturday, the following twenty days have been wet and windy, in
nineteen cases out of twenty. In spite of our friend Zadkiel[691] and the others who
declare that we would smother every truth that does not happen to agree
with us, we are glad to see that the Society had the sense to publish
this communication, coming, as it does, from a veteran observer, and one
whose love of truth is undoubted. It must be that the fact is so set down
in the journals, because Dr. Forster says it: and whether it be only a
fact of the journals, or one of the heavens, can soon be tried. The new
moon of March next, falls on Saturday the 24th, at 2 in the
afternoon. We shall certainly look out."
The following appeared in the number of March 31:
"The first Saturday Moon since Dr. Forster's announcement came
off a week ago. We had previously received a number of letters from
different correspondents—all to the effect that the notion of new
moon on Saturday bringing wet weather is one of widely extended currency.
One correspondent (who gives his name) states that he has constantly
heard it at sea, and among the farmers and peasantry in Scotland,
Ireland, and the North of England. He proceeds thus: 'Since 1826,
nineteen years of the time I have spent in a seafaring life. I have
constantly observed, though unable to account for, the phenomenon. I have
also heard the stormy qualities of a Saturday's moon remarked by
American, French, and Spanish seamen; and, still more distant, a Chinese
pilot, who was once doing duty on board my vessel seemed to be perfectly
cognizant of the fact.' So that it seems we have, in giving currency to
what we only knew as a very curious communication from an earnest
meteorologist, been repeating what is common enough among sailors and
farmers. Another correspondent affirms that the thing is most devoutly
believed in by seamen; who would as soon sail on a Friday as be in the
Channel after a Saturday moon.—After a tolerable course of dry
weather, there was some snow, accompanied by wind on Saturday last, here
in London; there were also heavy louring clouds. Sunday was cloudy and
cold, with a little rain; Monday was louring, Tuesday unsettled;
Wednesday quite overclouded, with rain in the morning. The present
occasion shows only a general change of weather with a tendency towards
rain. If Dr. Forster's theory be true, it is decidedly one of the minor
instances, as far as London weather is concerned.—It will take a
good deal of evidence to make us believe in the omen of a Saturday Moon.
But, as we have said of the Poughkeepsie Seer, the thing is very curious
whether true or false. Whence comes this universal proverb—and a
hundred others—while the meteorological observer cannot, when
he puts down a long series of results, detect any weather cycles at all?
One of our correspondents wrote us something of a lecture for
encouraging, he said, the notion that names could influence the
weather. He mistakes the question. If there be any weather cycles
depending on the moon, it is possible that one of them may be so related
to the week cycle of seven days, as to show recurrences which are of the
kind stated, or any other. For example, we know that if the new moon of
March fall on a Saturday in this year, it will most probably fall on a
Saturday nineteen years hence. This is not connected with the spelling of
Saturday—but with the connection between the motions of the sun and
moon. Nothing but the Moon can settle the question—and we are
willing to wait on her for further information. If the adage be true,
then the philosopher has missed what lies before his eyes; if false, then
the world can be led by the nose in spite of the eyes. Both these things
happen sometimes; and we are willing to take whichever of the two
solutions is borne out by future facts. In the mean time, we announce the
next Saturday Moon for the 18th of August."
How many coincidences are required to establish a law of connection?
It depends on the way in which the mind views the matter in question.
Many of the paradoxers are quite set up by a very few instances. I will
now tell a story about myself, and then ask them a question.
So far as instances can prove a law, the following is proved: no
failure has occurred. Let a clergyman be known to me, whether by personal
acquaintance or correspondence, or by being frequently brought before me
by those with whom I am connected in private life: that clergyman does
not, except in few cases, become a bishop; but if he become a
bishop, he is sure, first or last, to become an arch-bishop. This has
happened in every case. As follows:
1. My last schoolmaster, a former Fellow of Oriel, was a very
intimate college friend of Richard Whately[692], a younger man. Struck by his
friend's talents, he used to talk of him perpetually, and predict his
future eminence. Before I was sixteen, and before Whately had even given
his Bampton Lectures, I was very familiar with his name, and some of his
sayings. I need not say that he became Archbishop of Dublin.
2. When I was a child, a first cousin of John Bird Sumner[693] married a sister of my
mother. I cannot remember the time when I first heard his name, but it
was made very familiar to me. In time he became Bishop of Chester, and
then, Archbishop of Canterbury. My reader may say that Dr. C. R.
Sumner,[694] Bishop of
Winchester, has just as good a claim: but it is not so: those connected
with me had more knowledge of Dr. J. B. Sumner;[695] and said nothing, or next to nothing,
of the other. Rumor says that the Bishop of Winchester has
declined an Archbishopric: if so, my rule is a rule of
gradations.
3. Thomas Musgrave,[696] Fellow of Trinity College, Cambridge,
was Dean of the college when I was an undergraduate: this brought
me into connection with him, he giving impositions for not going to
chapel, I writing them out according. We had also friendly intercourse in
after life; I forgiving, he probably forgetting. Honest Tom Musgrave, as
he used to be called, became Bishop of Hereford, and Archbishop of
York.
4. About the time when I went to Cambridge, I heard a great deal about
Mr. C. T. Longley,[697]
of Christchurch, from a cousin of my own of the same college, long since
deceased, who spoke of him much, and most affectionately. Dr. Longley
passed from Durham to York, and thence to Canterbury. I cannot quite make
out the two Archbishoprics; I do not remember any other private channel
through which the name came to me: perhaps Dr. Longley, having two
strings to his bow, would have been one archbishop if I had never heard
of him.
5. When Dr. Wm. Thomson[698] was appointed to the see of
Gloucester in 1861, he and I had been correspondents on the subject of
logic—on which we had both written—for about fourteen years.
On his elevation I wrote to him, giving the preceding instances, and
informing him that he would certainly be an Archbishop. The case was a
strong one, and the law acted rapidly; for Dr. Thomson's elevation to the
see of York took place in 1862.
Here are five cases; and there is no opposing instance. I have
searched the almanacs since 1828, and can find no instance of a Bishop
not finally Archbishop of whom I had known through private sources,
direct or indirect. Now what do my paradoxers say? Is this a
pre-established harmony, or a chain of coincidences? And how many
instances will it require to establish a law?[699]
THE HERSCHEL HOAX.
Some account of the great astronomical discoveries lately made by Sir
John Herschel at the Cape of Good Hope. Second Edition. London, 12mo.
1836.
This is a curious hoax, evidently written by a person versed in
astronomy and clever at introducing probable circumstances and undesigned
coincidences.[700] It
first appeared in a newspaper. It makes Sir J. Herschel discover men,
animals, etc. in the moon, of which much detail is given. There seems to
have been a French edition, the original, and English editions in
America, whence the work came into Britain: but whether the French was
published in America or at Paris I do not know. There is no doubt that it
was produced in the United States, by M. Nicollet,[701] an astronomer, once of Paris, and a
fugitive of some kind. About him I have heard two stories. First that he
fled to America with funds not his own, and that this book was a mere
device to raise the wind. Secondly, that he was a protégé of Laplace, and
of the Polignac party, and also an outspoken man. That after the
revolution he was so obnoxious to the republican party that he judged it
prudent to quit France; which he did in debt, leaving money for his
creditors, but not enough, with M. Bouvard. In America he connected
himself with an assurance office. The moon-story was
written, and sent to France, chiefly with the intention of entrapping M.
Arago, Nicollet's especial foe, into the belief of it. And those who
narrate this version of the story wind up by saying that M. Arago
was entrapped, and circulated the wonders through Paris, until a
letter from Nicollet to M. Bouvard[702] explained the hoax. I have no
personal knowledge of either story: but as the poor man had to endure the
first, it is but right that the second should be told with it.
SOME MORE METEOROLOGY.
The Weather Almanac for the Year 1838. By P. Murphy,[703] Esq., M.N.S.
By M. N. S. is meant member of no society.. This almanac bears
on the title-page two recommendations. The Morning Post calls it
one of the most important-if-true publications of our generation. The
Times says: "If the basis of his theory prove sound, and its
principles be sanctioned by a more extended experience, it is not too
much to say that the importance of the discovery is equal to that of the
longitude." Cautious journalist! Three times that of the longitude would
have been too little to say. That the landsman might predict the weather
of all the year, at its beginning, Jack would cheerfully give up
astronomical longitude—the problem—altogether, and
fall back on chronometers with the older Ls, lead, latitude, and
look-out, applied to dead-reckoning. Mr. Murphy attempted to give the
weather day by day: thus the first seven days of March bore
Changeable; Rain; Rain; Rain-wind; Changeable; Fair; Changeable.
To aim at such precision as to put a fair day between two changeable ones
by weather theory was going very near the wind and weather too. Murphy
opened the year with cold and frost; and the weather did the same. But
Murphy, opposite to Saturday, January 20, put down "Fair, Probable lowest
degree of winter temperature." When this Saturday came, it was not merely
the probably coldest of 1838, but certainly the coldest of many
consecutive years. Without knowing anything of Murphy, I felt it prudent
to cover my nose with my glove as I walked the street at eight in the
morning. The fortune of the Almanac was made. Nobody waited to see
whether the future would dement the prophecy: the shop was beset in a
manner which brought the police to keep order; and it was said that the
Almanac for 1838 was a gain of 5,000l. to the owners. It very soon
appeared that this was only a lucky hit: the weather-prophet had a
modified reputation for a few years; and is now no more heard of. A work
of his will presently appear in the list.
THE GREAT PYRAMIDS.
Letter from Alexandria on the evidence of the practical application of
the quadrature of the circle in the great pyramids of Gizeh. By H. C.
Agnew,[704] Esq. London,
1838, 4to.
Mr. Agnew detects proportions which he thinks were suggested by those
of the circumference and diameter of a circle.
THE MATHEMATICS OF A CREED.
The creed of St. Athanasius proved by a mathematical parallel. Before
you censure, condemn, or approve; read, examine, and understand. E. B. Revilo.[705] London, 1839, 8vo.
This author really believed himself, and was in earnest. He is not the
only person who has written nonsense by confounding the mathematical
infinite (of quantity) with what speculators now more correctly express
by the unlimited, the unconditioned, or the absolute. This tract is worth
preserving, as the extreme case of a particular kind. The following is a
specimen. Infinity being represented by ∞, as usual, and f,
s, g, being finite integers, the three Persons are denoted
by ∞f, (m ∞)s,
∞g, the finite fraction m representing
human nature, as opposed to ∞. The clauses of the Creed are then
given with their mathematical parallels. I extract a couple:
|
"But the Godhead of the
Father, of the Son, and of
the Holy Ghost, is all one:
the glory equal, the Majesty
co-eternal.
|
"It has been shown that
∞f, ∞g, and (m ∞)s, together,
are but ∞, and that
each is ∞, and any magnitude
in existence represented
by ∞ always was and always
will be: for it cannot
be made, or destroyed, and
yet exists.
|
|
"Equal to the Father, as
touching his Godhead: and
inferior to the Father,
touching his Manhood."
|
"(m ∞)s is equal to ∞f as
touching ∞, but inferior to
∞f as touching m: because
m is not infinite."
|
I might have passed this over, as beneath even my present subject, but
for the way in which I became acquainted with it. A bookseller, not
the publisher, handed it to me over his counter: one who had
published mathematical works. He said, with an air of important
communication, Have you seen this, Sir! In reply, I recommended
him to show it to my friend Mr.——, for whom he had published
mathematics. Educated men, used to books and to the converse of learned
men, look with mysterious wonder on such productions as this: for which
reason I have made a quotation which many will judge had better have been
omitted. But it would have been an imposition on the public if I were,
omitting this and some other uses of the Bible and Common Prayer, to
pretend that I had given a true picture of my school.
[Since the publication of the above, it has been stated that the
author is Mr. Oliver Byrne, the author of the Dual Arithmetic
mentioned further on: E. B. Revilo seems to be obviously a reversal.]
LOGIC HAS NO PARADOXERS.
Old and new logic contrasted: being an attempt to elucidate, for
ordinary comprehension, how Lord Bacon delivered the human mind from its
2,000 years' enslavement under Aristotle. By Justin Brenan.[706] London, 1839,
12mo.
Logic, though the other exact science, has not had the sort of
assailants who have clustered about mathematics. There is a sect which
disputes the utility of logic, but there are no special points, like the
quadrature of the circle, which excite dispute among those who admit other
things. The old story about Aristotle having one logic to trammel us, and
Bacon another to set us free,—always laughed at by those who really
knew either Aristotle or Bacon,—now begins to be understood by a
large section of the educated world. The author of this tract connects
the old logic with the indecencies of the classical writers, and the new
with moral purity: he appeals to women, who, "when they see plainly the
demoralizing tendency of syllogistic logic, they will no doubt exert
their powerful influence against it, and support the Baconian method."
This is the only work against logic which I can introduce, but it is a
rare one, I mean in contents. I quote the author's idea of a
syllogism:
"The basis of this system is the syllogism. This is a form of couching
the substance of your argument or investigation into one short line or
sentence—then corroborating or supporting it in another, and
drawing your conclusion or proof in a third."
On this definition he gives an example, as follows: "Every sin
deserves death," the substance of the "argument or investigation." Then
comes, "Every unlawful wish is a sin," which "corroborates or supports"
the preceding: and, lastly, "therefore every unlawful wish deserves
death," which is the "conclusion or proof." We learn, also, that
"sometimes the first is called the premises (sic), and sometimes
the first premiss"; as also that "the first is sometimes called the
proposition, or subject, or affirmative, and the next the predicate, and
sometimes the middle term." To which is added, with a mark of exclamation
at the end, "but in analyzing the syllogism, there is a middle term, and
a predicate too, in each of the lines!" It is clear that Aristotle never
enslaved this mind.
I have said that logic has no paradoxers, but I was speaking of old
time. This science has slept until our own day: Hamilton[707] says there has been "no progress made
in the general development of the
syllogism since the time of Aristotle; and in regard to the few
partial improvements, the professed historians seem altogether
ignorant." But in our time, the paradoxer, the opponent of common
opinion, has appeared in this field. I do not refer to Prof. Boole,[708] who is not a
paradoxer, but a discoverer: his system could neither
oppose nor support common opinion, for its grounds were not in the
conception of any one. I speak especially of two others, who fought like
cat and dog: one was dogmatical, the other categorical. The first was
Hamilton himself—Sir William Hamilton of Edinburgh, the
metaphysician, not Sir William Rowan Hamilton[709] of Dublin, the mathematician, a
combination of peculiar genius with unprecedented learning, erudite in
all he could want except mathematics, for which he had no turn, and in
which he had not even a schoolboy's knowledge, thanks to the Oxford of
his younger day. The other was the author of this work, so fully
described in Hamilton's writings that there is no occasion to describe
him here. I shall try to say a few words in common language about the
paradoxers.
Hamilton's great paradox was the quantification of the
predicate; a fearful phrase, easily explained. We all know that when
we say "Men are animals," a form wholly unquantified in phrase, we speak
of all men, but not of all animals: it is some or all, some
may be all for aught the proposition says. This
some-may-be-all-for-aught-we-say, or not-none, is the logician's
some. One would suppose that "all men are some animals," would
have been the logical phrase in all time: but the predicate never was
quantified. The few who alluded to the possibility of such a thing found
reasons for not adopting it over and above the great reason, that
Aristotle did not adopt it. For Aristotle never ruled in physics or
metaphysics in the old time with near so much of absolute sway as
he has ruled in logic down to our own time. The logicians knew
that in the proposition "all men are animals" the "animal" is not
universal, but particular yet no one dared to say that
all men are some animals, and to invent the phrase,
"some animals are all men" until Hamilton leaped the ditch,
and not only completed a system of enunciation, but applied it to
syllogism.
My own case is as peculiar as his: I have proposed to introduce
mathematical thought into logic to an extent which makes the old
stagers cry:
"St. Aristotle! what wild notions!
Serve a ne exeat regno[710] on him!"
Hard upon twenty years ago, a friend and opponent who stands high in
these matters, and who is not nearly such a sectary of Aristotle and
establishment as most, wrote to me as follows: "It is said that next to
the man who forms the taste of the nation, the greatest genius is the man
who corrupts it. I mean therefore no disrespect, but very much the
reverse, when I say that I have hitherto always considered you as a great
logical heresiarch." Coleridge says he thinks that it was Sir Joshua
Reynolds who made the remark: which, to copy a bull I once heard, I
cannot deny, because I was not there when he said it. My friend did not
call me to repentance and reconciliation with the church: I think he had
a guess that I was a reprobate sinner. My offences at that time were but
small: I went on spinning syllogism systems, all alien from the common
logic, until I had six, the initial letters of which, put together, from
the names I gave before I saw what they would
make, bar all repentance by the words
leaving to the followers of the old school the comfortable option of
placing the letters thus:
It should however be stated that the question is not about absolute
truth or falsehood. No one denies that anything I call an inference is an
inference: they say that my alterations are extra-logical; that
they are material, not formal; and that logic is a
formal science.
The distinction between material and formal is easily made, where the
usual perversions are not required. A form is an empty machine,
such as "Every X is Y"; it may be supplied with matter, as in
"Every man is animal." The logicians will not see that
their formal proposition, "Every X is Y," is material in three
points, the degree of assertion, the quantity of the proposition, and the
copula. The purely formal proposition is "There is the probability α that X stands in the relation L to Y." The
time will come when it will be regretted that logic went without
paradoxers for two thousand years: and when much that has been said on
the distinction of form and matter will breed jokes.
I give one instance of one mood of each of the systems, in the order
of the letters first written above.
Relative.—In this system the formal relation is taken,
that is, the copula may be any whatever. As a material instance, in which
the relations are those of consanguinity (of men understood), take
the following: X is the brother of Y; X is not the uncle of Z; therefore,
Z is not the child of Y. The discussion of relation, and of the
objections to the extension, is in the Cambridge Transactions,
Vol. X, Part 2; a crabbed conglomerate.
Undecided.—In this system one premise, and want of power
over another, infer want of power over a conclusion. As "Some men
are not capable of tracing consequences; we cannot be sure that there are
beings responsible for consequences who are incapable of tracing
consequences; therefore, we cannot be sure that all men are responsible
for the consequences of their actions."
Exemplar.—This, long after it suggested itself to me as a
means of correcting a defect in Hamilton's system, I saw to be the very
system of Aristotle himself, though his followers have drifted into
another. It makes its subject and predicate examples, thus: Any one man
is an animal; any one animal is a mortal; therefore, any one man is a
mortal.
Numerical.—Suppose 100 Ys to exist: then if 70 Xs be Ys,
and 40 Zs be Ys, it follows that 10 Xs (at least) are Zs. Hamilton, whose
mind could not generalize on symbols, saw that the word most would
come under this system, and admitted, as valid, such a syllogism as "most
Ys are Xs; most Ys are Zs; therefore, some Xs are Zs."
Onymatic.—This is the ordinary system much enlarged in
propositional forms. It is fully discussed in my Syllabus of
Logic.
Transposed.—In this syllogism the quantity in one premise
is transposed into the other. As, some Xs are not Ys; for every X there
is a Y which is Z; therefore, some Zs are not Xs.
Sir William Hamilton of Edinburgh was one of the best friends and
allies I ever had. When I first began to publish speculation on this
subject, he introduced me to the logical world as having plagiarized from
him. This drew their attention: a mathematician might have written about
logic under forms which had something of mathematical look long enough
before the Aristotelians would have troubled themselves with him: as was
done by John Bernoulli,[711] James Bernoulli,[712] Lambert,[713] and Gergonne;[714] who, when our
discussion began, were not known even to omnilegent Hamilton. He
retracted his accusation of wilful theft in a manly way when he
found it untenable; but on this point he wavered a little, and was
convinced to the last that I had taken his principle unconsciously. He
thought I had done the same with Ploucquet[715] and Lambert. It was his pet notion
that I did not understand the commonest principles of logic, that I did
not always know the difference between the middle term of a syllogism and
its conclusion. It went against his grain to imagine that a mathematician
could be a logician. So long as he took me to be riding my own hobby, he
laughed consumedly: but when he thought he could make out that I was
mounted behind Ploucquet or Lambert, the current ran thus: "It would
indeed have been little short of a miracle had he, ignorant even of the
common principles of logic, been able of himself to rise to
generalization so lofty and so accurate as are supposed in the peculiar
doctrines of both the rival logicians, Lambert and Ploucquet—how
useless soever these may in practice prove to be." All this has been
sufficiently discussed elsewhere: "but, masters, remember that I am an
ass."
I know that I never saw Lambert's work until after all Hamilton
supposed me to have taken was written: he himself, who read almost
everything, knew nothing about it until after I did. I cannot prove what
I say about my knowledge of Lambert: but the means of doing it may turn
up. For, by the casual turning up of an old letter, I have found
the means of clearing myself as to Ploucquet. Hamilton assumed that
(unconsciously) I took from Ploucquet the notion of a logical notation in
which the symbol of the conclusion is seen in the joint symbols of the
premises. For example, in my own fashion I write down ( . ) ( . ), two
symbols of premises. By these symbols I see that there is a valid
conclusion, and that it may be written in symbol by striking out the two
middle parentheses, which gives ( . . ) and reading the two negative dots
as an affirmative. And so I see in ( . ) ( . ) that ( ) is the
conclusion. This, in full, is the perception that "all are either Xs or
Ys" and "all are either Ys or Zs" necessitates "some Xs are Zs." Now in
Ploucquet's book of 1763, is found, "Deleatur in præmissis medius; id
quod restat indicat conclusionem."[716] In the paper in which I explain my
symbols—which are altogether different from Ploucquet's—there
is found "Erase the symbols of the middle term; the remaining symbols
show the inference." There is very great likeness: and I would have
excused Hamilton for his notion if he had fairly given reference to the
part of the book in which his quotation was found. For I had shown in my
Formal Logic what part of Ploucquet's book I had used: and a fair
disputant would either have strengthened his point by showing that I had
been at his part of the book, or allowed me the advantage of it being
apparent that I had not given evidence of having seen that part of the
book. My good friend, though an honest man, was sometimes unwilling to
allow due advantage to controversial opponents.
But to my point. The only work of Ploucquet I ever saw was lent me by
my friend Dr. Logan,[717]
with whom I have often corresponded on logic, etc. I chanced (in 1865)
to turn up the letter which he sent me
(Sept. 12, 1847) with the book. Part of it runs thus: "I
congratulate you on your success in your logical researches [that is, in
asking for the book, I had described some results]. Since the reading of
your first paper I have been satisfied as to the possibility of inventing
a logical notation in which the rationale of the inference is contained
in the symbol, though I never attempted to verify it [what I
communicated, then, satisfied the writer that I had done and communicated
what he, from my previous paper, suspected to be practicable]. I send you
Ploucquet's dissertation....'
It now being manifest that I cannot be souring grapes which have been
taken from me, I will say what I never said in print before. There is not
the slightest merit in making the symbols of the premises yield that of
the conclusion by erasure: the thing must do itself in every system
which symbolises quantities. For in every syllogism (except the
inverted Bramantip of the Aristotelians) the conclusion is
manifest in this way without symbols. This Bramantip destroys
system in the Aristotelian lot: and circumstances which I have pointed
out destroy it in Hamilton's own collection. But in that enlargement of
the reputed Aristotelian system which I have called onymatic, and
in that correction of Hamilton's system which I have called
exemplar, the rule of erasure is universal, and may be seen
without symbols.
Our first controversy was in 1846. In 1847, in my Formal Logic,
I gave him back a little satire for satire, just to show, as I stated,
that I could employ ridicule if I pleased. He was so offended with the
appendix in which this was contained, that he would not accept the copy
of the book I sent him, but returned it. Copies of controversial works,
sent from opponent to opponent, are not presents, in the usual
sense: it was a marked success to make him angry enough to forget this.
It had some effect however: during the rest of his life I wished to avoid
provocation; for I could not feel sure that excitement might
not produce consequences. I allowed his slashing account of me in the
Discussions to pass unanswered: and before that, when he proposed
to open a controversy in the Athenæum upon my second Cambridge
paper, I merely deferred the dispute until the next edition of my
Formal Logic. I cannot expect the account in the
Discussions to amuse an unconcerned reader as much as it amused
myself: but for a cut-and-thrust, might-and-main, tooth-and-nail,
hammer-and-tongs assault, I can particularly recommend it. I never knew,
until I read it, how much I should enjoy a thundering onslought on
myself, done with racy insolence by a master hand, to whom my good genius
had whispered Ita feri ut se sentiat emori.[718] Since that time I have, as the
Irishman said, become "dry moulded for want of a bating." Some of my
paradoxers have done their best: but theirs is mere twopenny—"small
swipes," as Peter Peebles said. Brandy for heroes! I hope a reviewer or
two will have mercy on me, and will give me as good discipline as
Strafford would have given Hampden and his set: "much beholden," said he,
"should they be to any one that should thoroughly take pains with them in
that kind"—meaning objective flagellation. And I shall be
the same to any one who will serve me so—but in a literary and
periodical sense: my corporeal cuticle is as thin as my neighbors'.
Sir W. H. was suffering under local paralysis before our controversy
commenced: and though his mind was quite unaffected, a retort of as
downright a character as the attack might have produced serious effect
upon a person who had shown himself sensible of ridicule. Had a second
attack of his disorder followed an answer from me, I should have been
held to have caused it: though, looking at Hamilton's genial love of
combat, I strongly suspected that a retort in kind
"Would cheer his heart, and warm his blood,
And make him fight, and do him good."
But I could not venture to risk it. So all I did, in reply to the
article in the Discussions, was to write to him the following
note: which, as illustrating an etiquette of controversy, I insert.
"I beg to acknowledge and thank you for.... It is necessary that I
should say a word on my retention of this work, with reference to your
return of the copy of my Formal Logic, which I presented to you on
its publication: a return made on the ground of your disapproval of the
account of our controversy which that work contained. According to my
view of the subject, any one whose dealing with the author of a book is
specially attacked in it, has a right to expect from the author that part
of the book in which the attack is made, together with so much of the
remaining part as is fairly context. And I hold that the acceptance by
the party assailed of such work or part of a work does not imply any
amount of approval of the contents, or of want of disapproval. On this
principle (though I am not prepared to add the word alone) I
forwarded to you the whole of my work on Formal Logic and my
second Cambridge Memoir. And on this principle I should have held you
wanting in due regard to my literary rights if you had not forwarded to
me your asterisked pages, with all else that was necessary to a full
understanding of their scope and meaning, so far as the contents of the
book would furnish it. For the remaining portion, which it would be a
hundred pities to separate from the pages in which I am directly
concerned, I am your debtor on another principle; and shall be glad to
remain so if you will allow me to make a feint of balancing the account
by the offer of two small works on subjects as little connected with our
discussion as the Epistolæ Obscurorum Virorum, or the Lutheran
dispute. I trust that by accepting my Opuscula you will enable me
to avoid the use of the knife, and leave me to cut you
up with the pen as occasion shall serve, I remain, etc. (April 21,
1852)."
I received polite thanks, but not a word about the body of the letter:
my argument, I suppose, was admitted.
SOME DOGGEREL AND COUNTER DOGGEREL.
I find among my miscellaneous papers the following jeu
d'esprit, or jeu de bêtise,[719] whichever the reader pleases—I
care not—intended, before I saw ground for abstaining, to have, as
the phrase is, come in somehow. I think I could manage to bring anything
into anything: certainly into a Budget of Paradoxes. Sir W. H. rather
piqued himself upon some caniculars, or doggerel verses, which he had put
together in memoriam [technicam] of the way in which
A E I O are used in logic: he added U, Y, for the addition of
meet, etc., to the system. I took the liberty of concocting some
counter-doggerel, just to show that a mathematician may have
architectonic power as well as a metaphysician.
DOGGEREL.
BY SIR W. HAMILTON.
A it affirms of this, these, all,
Whilst E denies of any;
I it affirms (whilst O denies)
Of some (or few, or many).
Thus A affirms, as E denies,
And definitely either;
Thus I affirms, as O denies,
And definitely neither.
A half, left semidefinite,
Is worthy of its score;
U, then, affirms, as Y denies,
This, neither less nor more.
Indefinito-definites,
I, UI, YO, last we come;
And this affirms, as that denies
Of more, most (half, plus, some).
COUNTER DOGGEREL.
BY PROF. DE MORGAN.
(1847.)
Great A affirms of all;
Sir William does so too:
When the subject is "my suspicion,"
And the predicate "must be true."
Great E denies of all;
Sir William of all but one:
When he speaks about this present time,
And of those who in logic have done.
Great I takes up but some;
Sir William! my dear soul!
Why then in all your writings,
Does "Great I" fill[720] the whole!
Great O says some are not;
Sir William's readers catch,
That some (modern) Athens is not without
An Aristotle to match.
"A half, left semi-definite,
Is worthy of its score:"
This looked very much like balderdash,
And neither less nor more.
It puzzled me like anything;
In fact, it puzzled me worse:
Isn't schoolman's logic hard enough,
Without being in Sibyl's verse?
At last, thinks I, 'tis German;
And I'll try it with some beer!
The landlord asked what bothered me so,
And at once he made it clear.
It's half-and-half, the gentleman means;
Don't you see he talks of score?
That's the bit of memorandum
That we chalk behind the door.
Semi-definite's outlandish;
But I see, in half a squint,
That he speaks of the lubbers who call for a quart,
When they can't manage more than a pint.
Now I'll read it into English,
And then you'll answer me this:
If it isn't good logic all the world round,
I should like to know what is?
When you call for a pot of half-and-half,
If you're lost to sense of shame,
You may leave it semi-definite,
But you pay for it all just the same.
* * * * * *
I am unspeakably comforted when I look over the above in remembering
that the question is not whether it be Pindaric or Horatian, but whether
the copy be as good as the original. And I say it is: and will take no
denial.
Long live—long will live—the glad memory of William
Hamilton, Good, Learned, Acute, and Disputatious! He fought upon
principle: the motto of his book is:
"Truth, like a torch, the more it's shook it shines."
There is something in this; but metaphors, like puddings, quarrels,
rivers, and arguments, always have two sides to them. For instance,
"Truth, like a torch, the more it's shook it shines;
But those who want to use it, hold it steady.
They shake the flame who like a glare to gaze at,
They keep it still who want a light to see by."
ANOTHER THEORY OF PARALLELS.
Theory of Parallels. The proof of Euclid's axiom looked for in the
properties of the Equiangular Spiral. By Lieut-Col. G. Perronet
Thompson.[721] The same,
second edition, revised and corrected. The same, third edition,
shortened, and freed from dependence on the theory of limits. The same,
fourth edition, ditto, ditto. All London, 1840, 8vo.
To explain these editions it should be noted that General Thompson
rapidly modified his notions, and republished his tracts accordingly.
SOME PRIMITIVE DARWINISM.
Vestiges of the Natural History of Creation.[722] London, 1840, 12mo.
This is the first edition of this celebrated work. Its form is a case
of the theory: the book is an undeniable duodecimo, but the size of its
paper gives it the look of not the smallest of octavos. Does not this
illustrate the law of development, the gradation of families, the
transference of species, and so on? If so, I claim the discovery of this
esoteric testimony of the book to its own contents; I defy any one to
point out the reviewer who has mentioned it. The work itself is described by its
author as "the first attempt to connect the natural sciences into a
history of creation." The attempt was commenced, and has been carried on,
both with marked talent, and will be continued. Great advantage will
result: at the worst we are but in the alchemy of some new chemistry, or
the astrology of some new astronomy. Perhaps it would be as well not to
be too sure on the matter, until we have an antidote to possible
consequences as exhibited under another theory, on which it is as
reasonable to speculate as on that of the Vestiges. I met long ago
with a splendid player on the guitar, who assured me, and was confirmed
by his friends, that he never practised, except in thought, and
did not possess an instrument: he kept his fingers acting in his mind,
until they got their habits; and thus he learnt the most difficult
novelties of execution. Now what if this should be a minor segment of a
higher law? What if, by constantly thinking of ourselves as descended
from primeval monkeys, we should—if it be true—actually
get our tails again? What if the first man who was detected with
such an appendage should be obliged to confess himself the author of the
Vestiges—a person yet unknown—who would naturally get
the start of his species by having had the earliest habit of thinking on
the matter? I confess I never hear a man of note talk fluently about it
without a curious glance at his proportions, to see whether there may be
ground to conjecture that he may have more of "mortal coil" than others,
in anaxyridical concealment. I do not feel sure that even a paternal love
for his theory would induce him, in the case I am supposing, to exhibit
himself at the British Association,
With a hole behind which his tail peeped through.
The first sentence of this book (1840) is a cast of the log, which
shows our rate of progress. "It is familiar knowledge that the earth
which we inhabit is a globe of somewhat less than 8,000 miles in
diameter, being one of a series of eleven which revolve at different
distances around the sun." The eleven! Not to mention the Iscariot
which Le Verrier and Adams calculated into existence, there is more than
a septuagint of new planetoids.
ON RELIGIOUS INSURANCE.
The Constitution and Rules of the Ancient and Universal 'Benefit
Society' established by Jesus Christ, exhibited, and its advantages and
claims maintained, against all Modern and merely Human
Institutions of the kind: A Letter very respectfully addressed to the
Rev. James Everett,[723]
and occasioned by certain remarks made by him, in a speech to the Members
of the 'Wesleyan Centenary Institute' Benefit Society. Dated York, Dec.
7, 1840. By Thomas Smith.[724] 12mo, (pp. 8.)
The Wesleyan minister addressed had advocated provision against old
age, etc.: the writer declares all private provision un-Christian.
After decent maintenance and relief of family claims of indigence, he
holds that all the rest is to go to the "Benefit Society," of which he
draws up the rules, in technical form, with chapters of "Officers,"
"Contributors" etc., from the Acts of the Apostles, etc., and some of the
early Fathers. He holds that a Christian may not "make a private
provision against the contingencies of the future": and that the great
"Benefit Society" is the divinely-ordained recipient of all the surplus
of his income; capital, beyond what is necessary for business, he is to
have none. A real good speculator shuts his eyes by instinct, when
opening them would not serve the purpose: he has the vizor of the Irish
fairy tale, which fell of itself over the eyes of the wearer the moment
he turned them upon the enchanted light which would have destroyed him if
he had caught sight of it. "Whiles it remained, was it not thine own? and
after it was sold, was it (the purchase-money) not in thine own power?"
would have been awkward to quote, and accordingly nothing is stated
except the well-known result, which is rule 3, cap. 5, "Prevention of
Abuses." By putting his principles together, the author can be made,
logically, to mean that the successors of the apostles should put to
death all contributors who are detected in not paying their full
premiums.
I have known one or two cases in which policy-holders have surrendered
their policies through having arrived at a conviction that direct
provision is unlawful. So far as I could make it out, these parties did
not think it unlawful to lay by out of income, except when this was done
in a manner which involved calculation of death-chances. It is singular
they did not see that the entrance of chance of death was the entrance of
the very principle of the benefit society described in the Acts of the
Apostles. The family of the one who died young received more in
proportion to premiums paid than the family of one who died old.
Every one who understands life assurance sees that—bonus
apart—the difference between an assurance office and a savings bank
consists in the adoption, pro tanto, of the principle of community
of goods. In the original constitution of the oldest assurance office,
the Amicable Society, the plan with which they started was nothing
but this: persons of all ages under forty-five paid one common premium,
and the proceeds were divided among the representatives of those who died
within the year.
THE TWO OLD PARADOXES AGAIN.
[I omitted from its proper place a manuscript quadrature (3.1416
exactly) addressed to an eminent mathematician, dated in 1842 from the
debtor's ward of a country gaol. The unfortunate speculator says, "I have
labored many years to find the precise ratio." I have heard of several
cases in which squaring the circle has produced an inability to square
accounts. I remind those who feel a kind of inspiration to employ native
genius upon difficulties, without gradual progression from elements, that
the call is one which becomes stronger and stronger, and may lead, as it
has led, to abandonment of the duties of life, and all the consequences.]
1842. Provisional Prospectus of the Double Acting Rotary Engine
Company. Also Mechanic's Magazine, March 26, 1842.
Perpetual motion by a drum with one vertical half in mercury, the
other in a vacuum: the drum, I suppose, working round forever to find an
easy position. Steam to be superseded: steam and electricity convulsions
of nature never intended by Providence for the use of man. The price of
the present engines, as old iron, will buy new engines that will work
without fuel and at no expense. Guaranteed by the Count de Predaval,[725] the discoverer. I was
to have been a Director, but my name got no further than ink, and not so
far as official notification of the honor, partly owing to my having
communicated to the Mechanic's Magazine information privately
given to me, which gave premature publicity, and knocked up the plan.
An Exposition of the Nature, Force, Action, and other properties of
Gravitation on the Planets. London, 1842, 12mo.
An Investigation of the principles of the Rules for determining the
Measures of the Areas and Circumferences of Circular Plane Surfaces ...
London, 1844, 8vo.
These are anonymous; but the author (whom I believe to be Mr.
Denison,[726] presently
noted) is described as author of a new system of mathematics, and also of
mechanics. He had need have both, for he shows that the line which has a
square equal to a given circle, has a cube equal to the sphere on the
same diameter: that is, in old mathematics, the diameter is to the
circumference as 9 to 16! Again, admitting that the velocities of planets
in circular orbits are inversely as the square roots of their distances,
that is, admitting Kepler's law, he manages to prove that gravitation is
inversely as the square root of the distance: and suspects
magnetism of doing the difference between this and Newton's law. Magnetism and electricity are, in physics,
the member of parliament and the cabman—at every man's bidding, as
Henry Warburton[727]
said.
The above is an outrageous quadrature. In the preceding year, 1841,
was published what I suppose at first to be a Maori quadrature, by
Maccook. But I get it from a cutting out of some French periodical, and I
incline to think that it must be by a Mr. McCook. He makes
π to be 2 + 2√(8√2 - 11).
THE DUPLICATION PROBLEM.
Refutation of a Pamphlet written by the Rev. John Mackey, R.C.P.,[728] entitled "A method of
making a cube double of a cube, founded on the principles of elementary
geometry," wherein his principles are proved erroneous, and the required
solution not yet obtained. By Robert Murphy.[729] Mallow, 1824, 12mo.
This refutation was the production of an Irish boy of eighteen years
old, self-educated in mathematics, the son of a shoemaker at Mallow. He
died in 1843, leaving a name which is well known among mathematicians.
His works on the theory of equations and on electricity, and his papers
in the Cambridge Transactions, are all of high genius. The only
account of him which I know of is that which I wrote for the
Supplement of the Penny Cyclopædia. He was thrown by his
talents into a good income at Cambridge, with no social training except
penury, and very little intellectual training except mathematics. He fell
into dissipation, and his scientific career was almost arrested: but he
had great good in him, to my knowledge. A sentence in a letter from
the late Dean Peacock[730] to me—giving some advice about
the means of serving Murphy—sets out the old case: "Murphy is a man
whose special education is in advance of his general; and
such men are almost always difficult subjects to manage." This article
having been omitted in its proper place, I put it at 1843, the date of
Murphy's death.
A NEW VALUE OF π.
The Invisible Universe disclosed; or, the real Plan and Government of
the Universe. By Henry Coleman Johnson, Esq. London, 1843, 8vo.
The book opens abruptly with:
"First demonstration. Concerning the centre: showing that, because the
centre is an innermost point at an equal distance between two extreme
points of a right line, and from every two relative and opposite
intermediate points, it is composed of the two extreme internal points of
each half of the line; each extreme internal point attracting towards
itself all parts of that half to which it belongs...."
Of course the circle is squared: and the circumference is 3-1/21
diameters.
SOME MODERN ASTROLOGY.
Combination of the Zodiacal and Cometical Systems. Printed for the
London Society, Exeter Hall. Price Sixpence. (n. d. 1843.)
What this London Society was, or the "combination," did not appear.
There was a remarkable comet in 1843, the tail of which was at first
confounded with what is called the zodiacal light. This
nicely-printed little tract, evidently got up with less care for expense
than is usual in such works, brings together all the announcements of the
astronomers, and adds a short head and tail piece, which I shall quote
entire. As the announcements are very ordinary astronomy, the reader
will be able to detect, if detection be possible, what is the meaning and
force of the "Combination of the Zodiacal and Cometical Systems":
"Premonition. It has pleased the Author
of Creation to cause (to His human and
reasoning Creatures of this generation, by a 'combined'
appearance in His Zodiacal and Cometical system) a
'warning Crisis' of universal concernment to this our Globe. It is this 'Crisis' that has so generally
'ROUSED' at this moment the 'nations
throughout the Earth' that no equal interest has ever before been
excited by Man; unless it be in that caused by
the 'Pagan-Temple in Rome,' which is recorded by
the elder Pliny, 'Nat. Hist.' i. 23. iii. 3. Hardouin."
After the accounts given by the unperceiving astronomers, comes what
follows:
"Such has been (hitherto) the only object discerned by the
'Wise of this World,' in this twofold union of the
'Zodiacal' and 'Cometical' systems: yet it is nevertheless
a most 'Thrilling Warning,' to all the inhabitants of this
precarious and transitory Earth. We have no
authorized intimation or reasonable prospective contemplation, of
'current time' beyond a year 1860, of the present century; or
rather, except 'the interval which may now remain from the present
year 1843, to a year 1860' (ἡμέρας
ἙΞΗΚΟΝΤΑ—'threescore
or sixty days'—'I have appointed each "Day" for a "Year,"'
Ezek. iv. 6): and we know, from our 'common experience,'
how speedily such a measure of time will pass away.
"No words can be 'more explicit' than these of our blessed Lord: viz. 'This
Gospel of the Kingdom shall be preached in ALL the Earth, for a
Witness to all Nations; and then, shall
the End come.' The 'next 18 years'
must therefore supply the interval of the 'special Episcopal
forerunners.'
(Matt. xxiv. 14.)
"See the 'Jewish Intelligencer' of the present
month (April), p. 153, for the 'Debates in Parliament,'
respecting the Bishop of
Jerusalem, viz. Dr. Bowring,[731] Mr. Hume,[732] Sir R. Inglis,[733] Sir R. Peel,[734] Viscount Palmerston.[735]"
I have quoted this at length, to show the awful threats which were
published at a time of some little excitement about the phenomenon, under
the name of the London Society. The assumption of a corporate
appearance is a very unfair trick: and there are junctures at which harm
might be done by it.
THE NUMBER OF THE BEAST.
Wealth the name and number of the Beast, 666, in the Book of
Revelation. [by John Taylor.[736]] London, 1844, 8vo.
Whether Junius or the Beast be the more difficult to identify, must be
referred to Mr. Taylor, the only person who has attempted both. His
cogent argument on the political secret is not unworthily matched in his
treatment of the theological riddle. He sees the solution in εὐπορία, which occurs
in the Acts of the Apostles as the word for wealth in one of its most
disgusting forms, and makes 666 in the most straightforward way. This
explanation has as good a chance as any other. The work contains a
general attempt at explanation of the Apocalypse,
and some history of opinion on the subject. It has not the prolixity
which is so common a fault of apocalyptic commentators.
A practical Treatise on Eclipses ... with remarks on the anomalies of
the present Theory of the Tides. By T. Kerigan,[737] F.R.S. 1844, 8vo.
Containing also a refutation of the theory of the tides, and
afterwards increased by a supplement, "Additional facts and arguments
against the theory of the tides," in answer to a short notice in the
Athenæum journal. Mr. Kerigan was a lieutenant in the Navy: he
obtained admission to the Royal Society just before the publication of
his book.
A new theory of Gravitation. By Joseph Denison,[738] Esq. London, 1844, 12mo.
Commentaries on the Principia. By the author of 'A new theory of
Gravitation.' London, 1846, 8vo.
Honor to the speculator who can be put in his proper place by one
sentence, be that place where it may.
"But we have shown that the velocities are inversely as the square
roots of the mean distances from the sun; wherefore, by equality of
ratios, the forces of the sun's gravitation upon them are also inversely
as the square roots of their distances from the sun."
EASTER DAY PARADOXERS.
In the years 1818 and 1845 the full moon fell on Easter Day, having
been particularly directed to fall before it in the act for the change of
style and in the English missals and prayer-books of all time: perhaps it
would be more correct to say that Easter Day was directed to fall after
the full moon; "but the principle is the same." No explanation was given
in 1818, but Easter was kept by the tables, in defiance of the
rule, and of several protests. A chronological panic was beginning in
December 1844, which was stopped by the Times newspaper printing
extracts from an article of mine in the Companion to the Almanac
for 1845, which had then just appeared. No one had guessed the true
reason, which is that the thing called the moon in the Gregorian Calendar
is not the moon of the heavens, but a fictitious imitation put wrong on
purpose, as will presently appear, partly to keep Easter out of the way
of the Jews' Passover, partly for convenience of calculation. The
apparent error happens but rarely; and all the work will perhaps have to
be gone over next time. I now give two bits of paradox.
Some theologians were angry at this explanation. A review called the
Christian Observer (of which Christianity I do not know) got up a
crushing article against me. I did not look at it, feeling sure that an
article on such a subject which appeared on January 1, 1845, against a
publication made in December 1844, must be a second-hand job. But some
years afterwards (Sept. 10, 1850), the reviews, etc. having been just
placed at the disposal of readers in the old reading-room of the
Museum, I made a tour of inspection, came upon my critic on his perch,
and took a look at him. I was very glad to remember this, for, though
expecting only second-hand, yet even of this there is good and bad; and I
expected to find some hints in the good second-hand of a respectable
clerical publication. I read on, therefore, attentively, but not long: I
soon came to the information that some additions to Delambre's[739] statement of the rule
for finding Easter, belonging to distant years, had been made by Sir
Harris Nicolas![740] Now
as I myself furnished my friend Sir H. N. with Delambre's digest of Clavius's[741] rule, which I translated out of
algebra into common language for the purpose, I was pretty sure this was
the ignorant reading of a person to whom Sir H. N. was the highest
arithmetical authority on the subject. A person pretending to
chronology, without being able to distinguish the historical
points—so clearly as they stand out—in which Sir H. N. speaks
with authority, from the arithmetical points of pure reckoning on which
he does not pretend to do more than directly repeat others, must be as
fit to talk about the construction of Easter Tables as the Spanish are to
talk French. I need hardly say that the additions for distant years are
as much from Clavius as the rest: my reviewer was not deep enough in his
subject to know that Clavius made and published, from his rules, the full
table up to A.D. 5000, for all the movable feasts of every year! I gave
only a glance at the rest: I found I was either knave or fool, with a
leaning to the second opinion; and I came away satisfied that my critic
was either ignoramus or novice, with a leaning to the first. I afterwards
found an ambiguity of expression in Sir H. N.'s account—whether his
or mine I could not tell—which might mislead a novice or content an
ignoramus, but would have been properly read or further inquired into by
a competent person.
The second case is this. Shortly after the publication of my article,
a gentleman called at my house, and, finding I was not at home, sent up
his card—with a stylish west-end club on it—to my wife,
begging for a few words on pressing business. With many well-expressed
apologies, he stated that he had been alarmed by hearing that Prof. De M.
had an intention of altering Easter next year. Mrs. De M. kept her
countenance, and assured him that I had no such intention, and further,
that she greatly doubted my having the power to do it. Was she quite
sure? his authority was very good: fresh assurances given. He was greatly
relieved, for he had some horses training for after Easter, which would
not be ready to run if it were altered the wrong way. A doubt comes over
him: would Mrs. De M., in the event of her being mistaken, give him the
very earliest information? Promise given; profusion of thanks; more
apologies; and departure.
Now, candid reader!—or uncandid either!—which most
deserves to be laughed at? A public instructor, who undertakes to settle
for the world whether a reader of Clavius, the constructor of the
Gregorian Calendar, is fool or knave, upon information derived from a
compiler—in this matter—of his own day; or a gentleman of
horse and dog associations, who, misapprehending something which he heard
about a current topic, infers that the reader of Clavius had the ear of
the Government on a proposed alteration. I suppose the querist had heard
some one say, perhaps, that the day ought to be set right, and some one
else remark that I might be consulted, as the only person who had
discussed the matter from the original source of the Calendar.
To give a better chance of the explanation being at once produced,
next time the real full moon and Easter Day shall fall together, I insert
here a summary which was printed in the Irish Prayer-book of the
Ecclesiastical Society. If the amusement given by paradoxers should
prevent a useless discussion some years hence, I and the paradoxers shall
have done a little good between us—at any rate, I have done my best
to keep the heavy weight afloat by tying bladders to it. I think the next
occurrence will be in 1875.
EASTER DAY.
In the years 1818 and 1845, Easter Day, as given by the rules
in 24 Geo. II cap. 23. (known as the act for the change of
style) contradicted the precept given in the preliminary
explanations. The precept is as follows:
"Easter Day, on which the rest" of the moveable feasts "depend,
is always the First Sunday after the Full Moon, which happens upon or
next after the Twenty-first Day of March; and if
the Full Moon happens upon a Sunday, Easter Day is the Sunday
after."
But in 1818 and 1845, the full moon fell on a Sunday, and yet the
rules gave that same Sunday for Easter Day. Much discussion was
produced by this circumstance in 1818: but a repetition of it in 1845 was
nearly altogether prevented by a timely[742] reference to the intention of those
who conducted the Gregorian reformation of the Calendar. Nevertheless,
seeing that the apparent error of the Calendar is due to the precept in
the Act of Parliament, which is both erroneous and insufficient, and that
the difficulty will recur so often as Easter Day falls on the day of full
moon, it may be advisable to select from the two articles cited in the
note such of their conclusions and rules, without proof or controversy,
as will enable the reader to understand the main points of the Easter
question, and, should he desire it, to calculate for himself the Easter
of the old or new style, for any given year.
1. In the very earliest age of Christianity, a controversy arose as to
the mode of keeping Easter, some desiring to perpetuate the
Passover, others to keep the festival of the Resurrection.
The first afterwards obtained the name of Quartadecimans, from
their Easter being always kept on the fourteenth day of the moon
(Exod. xii. 18, Levit. xxiii. 5.). But though it is unquestionable that a
Judaizing party existed, it is also likely that many dissented on
chronological grounds. It is clear that no perfect anniversary can
take place, except when the fourteenth of the moon, and with it the
passover, falls on a Friday. Suppose, for instance, it falls on a
Tuesday: one of three things must be done. Either (which
seems never to have been proposed) the crucifixion and resurrection must
be celebrated on Tuesday and Sunday, with a wrong interval; or the former
on Tuesday, the latter on Thursday, abandoning the first day of the week;
or the former on Friday, and the latter on Sunday, abandoning the paschal
commemoration of the crucifixion.
The last mode has been, as every one knows, finally adopted. The
disputes of the first three centuries did not turn on any calendar
questions. The Easter question was merely the symbol of the struggle
between what we may call the Jewish and Gentile sects of Christians: and
it nearly divided the Christian world, the Easterns, for the most part,
being Quartadecimans. It is very important to note that there is
no recorded dispute about a method of predicting the new moon, that is,
no general dispute leading to formation of sects: there may have been
difficulties, and discussions about them. The Metonic cycle, presently
mentioned, must have been used by many, perhaps most, churches.
2. The question came before the Nicene Council (A.D. 325) not as an
astronomical, but as a doctrinal, question: it was, in fact, this, Shall
the passover[743]
be treated as a part of Christianity? The Council resolved this question
in the negative, and the only information on its premises and conclusion,
or either, which comes from itself, is contained in the following
sentence of the synodical epistle, which epistle is preserved by
Socrates[744] and
Theodoret.[745] "We also
send you the good news concerning the unanimous
consent of all in reference to the celebration of the most solemn feast
of Easter, for this difference also has been made up by the assistance of
your prayers: so that all the brethren in the East, who formerly
celebrated this festival at the same time as the Jews, will in
future conform to the Romans and to us, and to all who have of old
observed our manner of celebrating Easter." This is all that can
be found on the subject: none of the stories about the Council ordaining
the astronomical mode of finding Easter, and introducing the Metonic
cycle into ecclesiastical reckoning, have any contemporary evidence: the
canons which purport to be those of the Nicene Council do not contain a
word about Easter; and this is evidence, whether we suppose those canons
to be genuine or spurious.
3. The astronomical dispute about a lunar cycle for the prediction of
Easter either commenced, or became prominent, by the extinction of
greater ones, soon after the time of the Nicene Council. Pope Innocent
I[746] met with
difficulty in 414. S. Leo,[747] in 454, ordained that Easter of 455
should be April 24; which is right. It is useless to record details of
these disputes in a summary: the result was, that in the year 463, Pope
Hilarius[748] employed
Victorinus[749] of
Aquitaine to correct the Calendar, and Victorinus formed a rule which
lasted until the sixteenth century. He combined the Metonic cycle and the
solar cycle presently described. But this cycle bears the
name of Dionysius Exiguus,[750] a Scythian settled at Rome, about
A.D. 530, who adapted it to his new yearly reckoning, when he abandoned
the era of Diocletian as a commencement, and constructed that which is
now in common use.
4. With Dionysius, if not before, terminated all difference as to the
mode of keeping Easter which is of historical note: the increasing
defects of the Easter Cycle produced in time the remonstrance of persons
versed in astronomy, among whom may be mentioned Roger Bacon,[751] Sacrobosco,[752] Cardinal Cusa,[753] Regiomontanus,[754] etc. From the middle
of the sixth to that of the sixteenth century, one rule was observed.
5. The mode of applying astronomy to chronology has always involved
these two principles. First, the actual position of the heavenly body is
not the object of consideration, but what astronomers call its mean
place, which may be described thus. Let a fictitious sun or moon move
in the heavens, in such manner as to revolve among the fixed stars at an
average rate, avoiding the alternate accelerations and retardations which
take place in every planetary motion. Thus the fictitious (say
mean) sun and moon are always very near to the real sun and moon.
The ordinary clocks show time by the mean, not the real, sun: and it was
always laid down that Easter depends on the opposition (or full moon) of
the mean sun and moon, not of the real ones. Thus we see that, were the
Calendar ever so correct as to the mean moon, it would be
occasionally false as to the true one: if, for instance, the
opposition of the mean sun and moon took place at one second before
midnight, and that of the real bodies only two seconds afterwards, the
calendar day of full moon would be one day before that of the common
almanacs. Here is a way in which the discussions of 1818 and 1845 might
have arisen: the British legislature has defined the moon as the
regulator of the paschal calendar. But this was only a part of the
mistake.
6. Secondly, in the absence of perfectly accurate knowledge of the
solar and lunar motion (and for convenience, even if such knowledge
existed), cycles are, and always have been taken, which serve to
represent those motions nearly. The famous Metonic cycle, which is
introduced into ecclesiastical chronology under the name of the cycle of
the golden numbers, is a period of 19 Julian[755] years. This period, in the old
Calendar, was taken to contain exactly 235 lunations, or intervals
between new moons, of the mean moon. Now the state of the case is:
19 average Julian years make 6939 days 18 hours.
235 average lunations make 6939 days 16 hours 31 minutes.
So that successive cycles of golden numbers, supposing the first to
start right, amount to making the new moons fall too late, gradually, so
that the mean moon of this cycle gains 1 hour 29 minutes in 19
years upon the mean moon of the heavens, or about a day in 300 years.
When the Calendar was reformed, the calendar new moons were four days in
advance of the mean moon of the heavens: so that, for instance, calendar
full moon on the 18th usually meant real full moon on the 14th.
7. If the difference above had not existed, the moon of the heavens
(the mean moon at least), would have returned permanently to the same
days of the month in 19 years; with an occasional slip arising from the
unequal distribution of the leap years, of which a period contains
sometimes five and sometimes four. As a general rule, the days of new and
full moon in any one year would have been also the days of new and full
moon of a year having 19 more units in its date. Again, if there had been
no leap years, the days of the month would have returned to the same days
of the week every seven years. The introduction of occasional 29ths of
February disturbs this, and makes the permanent return of month days to
week days occur only after 28 years. If all had been true, the lapse of
28 times 19, or 532 years, would have restored the year in every point:
that is, A.D. 1, for instance, and A.D. 533, would have had the same
almanac in every matter relating to week days, month days, sun, and moon
(mean sun and moon at least). And on the supposition of its truth, the
old system of Dionysius was framed. Its errors, are, first, that the
moments of mean new moon advance too much by 1 h. 29 m. in 19 average
Julian years; secondly, that the average Julian year of 365¼ days is too
long by 11 m. 10 s.
8. The Council of Trent, moved by the representations made on the
state of the Calendar, referred the consideration of it to the Pope. In
1577, Gregory XIII[756]
submitted to the Roman Catholic Princes and Universities a plan presented
to him by the representatives of Aloysius Lilius,[757] then deceased. This plan being
approved of, the Pope nominated a commission to consider its details, the
working member of which was the Jesuit Clavius. A short work was prepared
by Clavius, descriptive of the new Calendar: this was published[758] in 1582, with the
Pope's bull (dated February 24, 1581) prefixed. A larger work was
prepared by Clavius, containing fuller explanation, and entitled
Romani Calendarii a Gregorio XIII. Pontifice Maximo restituti
Explicatio. This was published at Rome in 1603, and again in the
collection of the works of Clavius in 1612.
9. The following extracts from Clavius settle the question of the
meaning of the term moon, as used in the Calendar:
"Who, except a few who think they are very sharp-sighted in this
matter, is so blind as not to see that the 14th of the moon and the full
moon are not the same things in the Church of God?... Although the
Church, in finding the new moon, and from it the 14th day, uses
neither the true nor the mean motion of the moon, but measures only
according to the order of a cycle, it is nevertheless undeniable that the
mean full moons found from astronomical tables are of the greatest use in
determining the cycle which is to be preferred ... the new moons of which
cycle, in order to the due celebration of Easter, should be so arranged
that the 14th days of those moons, reckoning from the day of new moon
inclusive, should not fall two or more days before the mean full
moon, but only one day, or else on the very day itself, or not long
after. And even thus far the Church need not take very great pains ...
for it is sufficient that all should reckon by the 14th day of the moon
in the cycle, even though sometimes it should be more than one day
before or after the mean full moon.... We have taken pains that in
our cycle the new moons should follow the real new moons, so that
the 14th of the moon should fall either the day before the mean full
moon, or on that day, or not long after; and this was done on purpose,
for if the new moon of the cycle fell on the same day as the mean new
moon of the astronomers, it might chance that we
should celebrate Easter on the same day as the Jews or the Quartadeciman
heretics, which would be absurd, or else before them, which would be
still more absurd."
From this it appears that Clavius continued the Calendar of his
predecessors in the choice of the fourteenth day of the moon. Our
legislature lays down the day of the full moon: and this mistake
appears to be rather English than Protestant; for it occurs in missals
published in the reign of Queen Mary. The calendar lunation being 29½
days, the middle day is the fifteenth day, and this is and was
reckoned as the day of the full moon. There is every right to presume
that the original passover was a feast of the real full moon: but
it is most probable that the moons were then reckoned, not from the
astronomical conjunction with the sun, which nobody sees except at an
eclipse, but from the day of first visibility of the new moon. In
fine climates this would be the day or two days after conjunction; and
the fourteenth day from that of first visibility inclusive, would very
often be the day of full moon. The following is then the proper
correction of the precept in the Act of Parliament:
Easter Day, on which the rest depend, is always the First Sunday after
the fourteenth day of the calendar moon which happens upon
or next after the Twenty-first day of March, according to the rules
laid down for the construction of the Calendar; and if the
fourteenth day happens upon a Sunday, Easter Day is the Sunday
after.
10. Further, it appears that Clavius valued the celebration of the
festival after the Jews, etc., more than astronomical correctness. He
gives comparison tables which would startle a believer in the
astronomical intention of his Calendar: they are to show that a calendar
in which the moon is always made a day older than by him, represents
the heavens better than he has done, or meant to do. But it must be
observed that this diminution of the real moon's age has a tendency to
make the English explanation often practically accordant with the
Calendar. For the fourteenth day of Clavius is generally the
fifteenth day of the mean moon of the heavens, and therefore most often
that of the real moon. But for this, 1818 and 1845 would not have been
the only instances of our day in which the English precept would have
contradicted the Calendar.
11. In the construction of the Calendar, Clavius adopted the ancient
cycle of 532 years, but, we may say, without ever allowing it to run out.
At certain periods, a shift is made from one part of the cycle into
another. This is done whenever what should be Julian leap year is made a
common year, as in 1700, 1800, 1900, 2100, etc. It is also done at
certain times to correct the error of 1 h. 19 m., before referred to, in
each cycle of golden numbers: Clavius, to meet his view of the amount of
that error, put forward the moon's age a day 8 times in 2,500 years. As
we cannot enter at full length into the explanation, we must content
ourselves with giving a set of rules, independent of tables, by which the
reader may find Easter for himself in any year, either by the old
Calendar or the new. Any one who has much occasion to find Easters and
movable feasts should procure Francœur's[759] tables.
12. Rule for determining Easter Day of the Gregorian Calendar in
any year of the new style. To the several parts of the rule
are annexed, by way of example, the results for the year 1849.
I. Add 1 to the given year. (1850).
II. Take the quotient of the given year divided by 4, neglecting the
remainder. (462).
III. Take 16 from the centurial figures of the given year, if it can
be done, and take the remainder. (2).
IV. Take the quotient of III. divided by 4, neglecting the remainder.
(0).
V. From the sum of I, II, and IV., subtract III. (2310).
VI. Find the remainder of V. divided by 7. (0).
VII. Subtract VI. from 7; this is the number of the dominical
letter
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | (7; dominical letter G). |
| A | B | C | D | E | F | G |
VIII. Divide I. by 19, the remainder (or 19, if no remainder) is the
golden number. (7).
IX. From the centurial figures of the year subtract 17, divide by 25,
and keep the quotient. (0).
X. Subtract IX. and 15 from the centurial figures, divide by 3, and
keep the quotient. (1).
XI. To VIII. add ten times the next less number, divide by 30, and
keep the remainder. (7).
XII. To XI. add X. and IV., and take away III., throwing out thirties,
if any. If this give 24, change it into 25. If 25, change it into 26,
whenever the golden number is greater than 11. If 0, change it into 30.
Thus we have the epact, or age of the Calendar moon at the
beginning of the year. (6).
|
When the Epact is 23, or less.
XIII. Subtract XII., the epact, from 45. (39).
XIV. Subtract the epact from 27, divide by 7, and keep the remainder,
or 7, if there be no remainder. (7)
|
When the Epact is greater than 23.
XIII. Subtract XII., the epact, from 75.
XIV. Subtract the epact from 57, divide by 7, and keep the remainder,
or 7, if there be no remainder.
|
XV. To XIII. add VII., the dominical number, (and 7 besides, if XIV.
be greater than VII.,) and subtract XIV., the result is the day of March,
or if more than 31, subtract 31, and the result is the day
of April, on which Easter Sunday falls. (39; Easter Day is April 8).
In the following examples, the several results leading to the final
conclusion are tabulated.
| Given Year | 1592 | 1637 | 1723 | 1853 | 2018 | 4686 |
| I. | 1593 | 1638 | 1724 | 1854 | 2019 | 4687 |
| II. | 398 | 409 | 430 | 463 | 504 | 1171 |
| III. | — | 0 | 1 | 2 | 4 | 30 |
| IV. | — | 0 | 0 | 0 | 1 | 7 |
| V. | 1991 | 2047 | 2153 | 2315 | 2520 | 5835 |
| VI. | 3 | 3 | 4 | 5 | 0 | 4 |
| VII. | 4 | 4 | 3 | 2 | 7 | 3 |
| VIII. | 16 | 4 | 14 | 11 | 5 | 13 |
| IX. | — | — | 0 | 0 | 0 | 1 |
| X. | 0 | 0 | 0 | 1 | 1 | 10 |
| XI. | 16 | 4 | 24 | 21 | 15 | 13 |
| XII. | 16 | 4 | 23 | 20 | 13 | 0 say 30 |
| XIII. | 29 | 41 | 22 | 25 | 32 | 45 |
| XIV. | 4 | 2 | 4 | 7 | 7 | 6 |
| XV. | 29 | 43 | 28 | 27 | 32 | 49 |
| Easter Day | Mar.29 | Apr.12 | Mar.28 | Mar.27 | Apr.1 | Apr.18 |
13. Rule for determining Easter Day of the Antegregorian Calendar
in any year of the old style. To the several parts of the rule are
annexed, by way of example, the results for the year 1287. The steps are
numbered to correspond with the steps of the Gregorian rule, so that it
can be seen what augmentations the latter requires.
I. Set down the given year. (1287).
II. Take the quotient of the given year divided by 4, neglecting the
remainder (321).
V. Take 4 more than the sum of I. and II. (1612).
VI. Find the remainder of V. divided by 7. (2).
VII. Subtract VI. from 7; this is the number of the dominical
letter
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | (5; dominical letter E). |
| A | B | C | D | E | F | G |
VIII. Divide one more than the given year by 19, the remainder (or 19
if no remainder) is the golden number. (15).
XII. Divide 3 less than 11 times VIII. by 30; the remainder (or 30 if
there be no remainder) is the epact. (12).
|
When the Epact is 23, or less.
XIII. Subtract XII., the epact, from 45. (33).
XIV. Subtract the epact from 27, divide by 7, and keep the remainder,
or 7, if there be no remainder, (1).
|
When the Epact is greater than 23.
XIII. Subtract XII., the epact, from 75.
XIV. Subtract the epact from 57, divide by 7, and keep the remainder,
or 7, if there be no remainder.
|
XV. To XIII. add VII., the dominical number, (and 7 besides if XIV. be
greater than VII.,) and subtract XIV., the result is the day of March, or
if more than 31, subtract 31, and the result is the day of April, on
which Easter Sunday (old style) falls. (37; Easter Day is April 6).
These rules completely represent the old and new Calendars, so far as
Easter is concerned. For further explanation we must refer to the
articles cited at the commencement.
The annexed is the table of new and full moons of the Gregorian
Calendar, cleared of the errors made for the purpose of preventing Easter
from coinciding with the Jewish Passover.
The second table (page 370) contains
epacts, or ages of the moon at the beginning of the year: thus in
1913, the epact is 22, in 1868 it is 6. This table goes from 1850 to
1999: should the New Zealander not have arrived by that time, and should
the churches of England and Rome then survive, the epact table may be
continued from their liturgy-books. The way of using the table is as
follows: Take the epact of the required year, and find it in the first or
last column of the first table, in line with it are seen the calendar
days of new and full moon. Thus, when the epact is 17, the new and full
moons of March fall on the 13th and 28th. The result is, for the most
part, correct: but in a minority of cases there is an error of a day.
When this happens, the error is almost always a fraction of a day much
less than twelve hours. Thus, when the table gives full moon on the 27th,
and the real truth is the 28th, we may be sure it is early on the
28th.
| | Jan. | Feb. | Mar. | Apr. | May | June | July | Aug. | Sep. | Oct. | Nov. | Dec. | |
| 1 | 29 | 27 | 29 | 27 | 27 | 25 | 25 | 23 | 22 | 21 | 20 | 19 | 1 |
| | 14 | 13 | 14 | 13 | 12 | 11 | 10 | 9 | 7 | 7 | 5 | 5 | |
| 2 | 28 | 26 | 28 | 26 | 26 | 24 | 24 | 22 | 21 | 20 | 19 | 18 | 2 |
| | 13 | 12 | 13 | 12 | 11 | 10 | 9 | 8 | 6 | 6 | 4 | 4 | |
| 3 | 27 | 25 | 27 | 25 | 25 | 23 | 23 | 21 | 20 | 19 | 18 | 17 | 3 |
| | 12 | 11 | 12 | 11 | 10 | 9 | 8 | 7 | 5 | 5 | 3 | 3 | |
| 4 | 26 | 24 | 26 | 24 | 24 | 22 | 22 | 20 | 19 | 18 | 17 | 16 | 4 |
| | 11 | 10 | 11 | 10 | 9 | 8 | 7 | 6 | 4 | 4 | 2 | 2,31 | |
| 5 | 25 | 23 | 25 | 23 | 23 | 21 | 21 | 19 | 18 | 17 | 16 | 15 | 5 |
| | 10 | 9 | 10 | 9 | 8 | 7 | 6 | 5 | 3 | 3 | 1 | 1,30 | |
| 6 | 24 | 22 | 24 | 22 | 22 | 20 | 20 | 18 | 17 | 16 | 15 | 14 | 6 |
| | 9 | 8 | 9 | 8 | 7 | 6 | 5 | 4 | 2 | 2,31 | 30 | 29 | |
| 7 | 23 | 21 | 23 | 21 | 21 | 19 | 19 | 17 | 16 | 15 | 14 | 13 | 7 |
| | 8 | 7 | 8 | 7 | 6 | 5 | 4 | 3 | 1 | 1,30 | 29 | 28 | |
| 8 | 22 | 20 | 22 | 20 | 20 | 18 | 18 | 16 | 15 | 14 | 13 | 12 | 8 |
| | 7 | 6 | 7 | 6 | 5 | 4 | 3 | 2,31 | 30 | 29 | 28 | 27 | |
| 9 | 21 | 19 | 21 | 19 | 19 | 17 | 17 | 15 | 14 | 13 | 12 | 11 | 9 |
| | 6 | 5 | 6 | 5 | 4 | 3 | 2 | 1,30 | 29 | 28 | 27 | 26 | |
| 10 | 20 | 18 | 20 | 18 | 18 | 16 | 16 | 14 | 13 | 12 | 11 | 10 | 10 |
| | 5 | 4 | 5 | 4 | 3 | 2 | 1,31 | 29 | 28 | 27 | 26 | 25 | |
| 11 | 19 | 17 | 19 | 17 | 17 | 15 | 15 | 13 | 12 | 11 | 10 | 9 | 11 |
| | 4 | 3 | 4 | 3 | 2 | 1,30 | 30 | 28 | 27 | 26 | 25 | 24 | |
| 12 | 18 | 16 | 18 | 16 | 16 | 14 | 14 | 12 | 11 | 10 | 9 | 8 | 12 |
| | 3 | 2 | 3 | 2 | 1,31 | 29 | 29 | 27 | 26 | 25 | 24 | 23 | |
| 13 | 17 | 15 | 17 | 15 | 15 | 13 | 13 | 11 | 10 | 9 | 8 | 7 | 13 |
| | 2 | 1 | 2 | 1,30 | 30 | 28 | 28 | 26 | 25 | 24 | 23 | 22 | |
| 14 | 16 | 14 | 16 | 14 | 14 | 12 | 12 | 10 | 9 | 8 | 7 | 6 | 14 |
| | 1,31 | — | 1,31 | 29 | 29 | 27 | 27 | 25 | 24 | 23 | 22 | 21 | |
| 15 | 15 | 13 | 15 | 13 | 13 | 11 | 11 | 9 | 8 | 7 | 6 | 5 | 15 |
| | 30 | 28 | 30 | 28 | 28 | 26 | 26 | 24 | 23 | 22 | 21 | 20 | |
| 16 | 14 | 12 | 14 | 12 | 12 | 10 | 10 | 8 | 7 | 6 | 5 | 4 | 16 |
| | 29 | 27 | 29 | 27 | 27 | 25 | 25 | 23 | 22 | 21 | 20 | 19 | |
| 17 | 13 | 11 | 13 | 11 | 11 | 9 | 9 | 7 | 6 | 5 | 4 | 3 | 17 |
| | 28 | 26 | 28 | 26 | 26 | 24 | 24 | 22 | 21 | 20 | 19 | 18 | |
| 18 | 12 | 10 | 12 | 10 | 10 | 8 | 8 | 6 | 5 | 4 | 3 | 2 | 18 |
| | 27 | 25 | 27 | 25 | 25 | 23 | 23 | 21 | 20 | 19 | 18 | 17 | |
| 19 | 11 | 9 | 11 | 9 | 9 | 7 | 7 | 5 | 4 | 3 | 2 | 1,31 | 19 |
| | 26 | 24 | 26 | 24 | 24 | 22 | 22 | 20 | 19 | 18 | 17 | 16 | |
| 20 | 10 | 8 | 10 | 8 | 8 | 6 | 6 | 4 | 3 | 2 | 1,31 | 30 | 20 |
| | 25 | 23 | 25 | 23 | 23 | 21 | 21 | 19 | 18 | 17 | 16 | 15 | |
| 21 | 9 | 7 | 9 | 7 | 7 | 5 | 5 | 3 | 2 | 1,31 | 29 | 29 | 21 |
| | 24 | 22 | 24 | 22 | 22 | 20 | 20 | 18 | 17 | 16 | 15 | 14 | |
| 22 | 8 | 6 | 8 | 6 | 6 | 4 | 4 | 2 | 1,30 | 30 | 28 | 28 | 22 |
| | 23 | 21 | 23 | 21 | 21 | 19 | 19 | 17 | 16 | 15 | 14 | 13 | |
| 23 | 7 | 5 | 7 | 5 | 5 | 3 | 3 | 1,31 | 29 | 29 | 27 | 27 | 23 |
| | 22 | 20 | 22 | 20 | 20 | 18 | 18 | 16 | 15 | 14 | 13 | 12 | |
| 24 | 6 | 5 | 6 | 5 | 4 | 3 | 2 | 1,30 | 29 | 28 | 27 | 26 | 24 |
| | 21 | 19 | 21 | 19 | 19 | 17 | 17 | 15 | 14 | 13 | 12 | 11 | |
| 25 | 5 | 4 | 5 | 4 | 3 | 2 | 1,31 | 29 | 28 | 27 | 26 | 25 | 25 |
| | 20 | 19 | 20 | 19 | 18 | 17 | 16 | 15 | 13 | 13 | 11 | 11 | |
| 26 | 4 | 3 | 4 | 3 | 2 | 1,30 | 30 | 28 | 27 | 26 | 25 | 24 | 26 |
| | 19 | 18 | 19 | 18 | 17 | 16 | 15 | 14 | 12 | 12 | 10 | 10 | |
| 27 | 3 | 2 | 3 | 2 | 1,31 | 29 | 29 | 27 | 26 | 25 | 24 | 23 | 27 |
| | 18 | 17 | 18 | 17 | 16 | 15 | 14 | 13 | 11 | 11 | 9 | 9 | |
| 28 | 2 | 1 | 2 | 1,30 | 30 | 28 | 28 | 26 | 25 | 24 | 23 | 22 | 28 |
| | 17 | 16 | 17 | 16 | 15 | 14 | 13 | 12 | 10 | 10 | 8 | 8 | |
| 29 | 1,31 | — | 1,31 | 29 | 29 | 27 | 27 | 25 | 24 | 23 | 22 | 21 | 29 |
| | 16 | 15 | 16 | 15 | 14 | 13 | 12 | 11 | 9 | 9 | 7 | 7 | |
| 30 | 30 | 28 | 30 | 28 | 28 | 26 | 26 | 24 | 23 | 22 | 21 | 20 | 30 |
| | 15 | 14 | 15 | 14 | 13 | 12 | 11 | 10 | 8 | 8 | 6 | 6 | |
| | Jan. | Feb. | Mar. | Apr. | May | June | July | Aug. | Sep. | Oct. | Nov. | Dec. | |
| | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 185 | 17 | 28 | 9 | 20 | 2 | 12 | 23 | 4 | 15 | 26 |
| 186 | 7 | 18 | 30 | 11 | 22 | 3 | 14 | 25 | 6 | 17 |
| 187 | 28 | 9 | 20 | 1 | 12 | 23 | 4 | 15 | 26 | 7 |
| 188 | 18 | 30 | 11 | 22 | 3 | 14 | 25 | 6 | 17 | 28 |
| 189 | 9 | 21 | 1 | 12 | 23 | 4 | 15 | 26 | 7 | 18 |
| 190 | 29 | 10 | 21 | 2 | 13 | 24 | 5 | 16 | 27 | 8 |
| 191 | 19 | 30 | 11 | 22 | 3 | 14 | 26 | 6 | 17 | 29 |
| 192 | 10 | 21 | 2 | 13 | 24 | 5 | 16 | 27 | 8 | 19 |
| 193 | 30 | 11 | 22 | 3 | 14 | 26 | 6 | 17 | 29 | 10 |
| 194 | 21 | 2 | 13 | 24 | 5 | 16 | 27 | 8 | 19 | 30 |
| 195 | 11 | 22 | 3 | 14 | 26 | 6 | 17 | 29 | 10 | 21 |
| 196 | 2 | 13 | 24 | 5 | 16 | 27 | 8 | 19 | 30 | 11 |
| 197 | 22 | 3 | 14 | 26 | 6 | 17 | 29 | 10 | 21 | 2 |
| 198 | 13 | 24 | 5 | 16 | 27 | 8 | 19 | 30 | 11 | 22 |
| 199 | 3 | 14 | 26 | 6 | 17 | 29 | 10 | 21 | 2 | 13 |
For example, the year 1867. The epact is 25, and we find in the
table:
| | J. | F. | M. | AP. | M. | JU. | JL. | AU. | S. | O. | N. | D. |
| New | 5+ | 4 | 5+ | 4 | 3+ | 2 | 1,31 | 29 | 28- | 27 | 26 | 25 |
| Full | 20 | 19- | 20 | 19- | 18 | 17 | 16 | 15 | 13- | 13 | 11+ | 11 |
When the truth is the day after + is written after the date; when the
day before, -. Thus, the new moon of March is on the 6th; the full moon
of April is on the 18th.
I now introduce a small paradox of my own; and as I am not able to
prove it, I am compelled to declare that any one who shall dissent must
be either very foolish or very dishonest, and will make me quite
uncomfortable about the state of his soul. This being settled once for
all, I proceed to say that the necessity of arriving at the truth about
the assertions that the Nicene Council laid down astronomical tests led
me to look at Fathers, Church histories, etc. to an extent which I never
dreamed of before. One conclusion which I arrived at was, that the Nicene
Fathers had a knack of sticking to the question which many later councils
could not acquire. In our own day, it is not permitted to Convocation
seriously to discuss any one of the points which are bearing so hard upon
their resources of defence—the cursing clauses of the Athanasian
Creed, for example. And it may be collected that the prohibition arises
partly from fear that there is no saying where a beginning, if allowed,
would end. There seems to be a suspicion that debate, once let loose,
would play up old Trent with the liturgy, and bring the whole book to
book. But if any one will examine the real Nicene Creed, without the
augmentation, he will admire the way in which the framers stuck to the
point, and settled what they had to decide, according to their view of
it. With such a presumption of good sense in their favor, it becomes
easier to believe in any claim which may be made on their behalf to tact
or sagacity in settling any other matter. And I strongly suspect such a
claim may be made for them on the Easter question.
I collect from many little indications, both before and after the
Council, that the division of the Christian world into Judaical and
Gentile, though not giving rise to a sectarian distinction expressed by
names, was of far greater force and meaning than historians prominently
admit. I took note of many indications of this, but not
notes, as it was not to my purpose. If it were so, we must admire
the discretion of the Council. The Easter question was the fighting
ground of the struggle: the Eastern or Judaical Christians, with some
varieties of usage and meaning, would have the Passover itself to be the
great feast, but taken in a Christian sense; the Western or Gentile
Christians, would have the commemoration of the Resurrection, connected
with the Passover only by chronology. To shift the Passover in time,
under its name, Pascha, without allusion to any of the force of
the change, was gently cutting away the ground from under the feet of the
Conservatives. And it was done in a very quiet way: no allusion to the
precise character of the change; no hint that the question was about two
different festivals: "all the brethren in the East, who formerly
celebrated this festival at the same time as the Jews, will in future
conform to the Romans and to us." The Judaizers meant to be keeping the
Passover as a Christian feast: they are gently assumed to be
keeping, not the Passover, but a Christian feast; and a
doctrinal decision is quietly, but efficiently, announced under the form
of a chronological ordinance. Had the Council issued theses of doctrine,
and excommunicated all dissentients, the rupture of the East and West
would have taken place earlier by centuries than it did. The only place
in which I ever saw any part of my paradox advanced, was in an article in
the Examiner newspaper, towards the end of 1866, after the above
was written.
A story about Christopher Clavius, the workman of the new Calendar. I
chanced to pick up "Albertus Pighius Campensis de æquinoctiorum
solsticiorumque inventione... Ejusdem de ratione Paschalis celebrationis,
De que Restitutione ecclesiastici Kalendarii," Paris, 1520, folio.[760] On the title-page were
decayed words followed by "..hristophor.. C..ii, 1556 (or 8)," the
last blank not entirely erased by time, but showing the lower halves of
an l and of an a, and rather too much room
for a v. It looked very like E Libris Christophori Clavii
1556. By the courtesy of some members of the Jesuit body in London, I
procured a tracing of the signature of Clavius from Rome, and the shapes
of the letters, and the modes of junction and disjunction, put the matter
beyond question. Even the extra space was explained; he wrote himself
Clauius. Now in 1556, Clavius was nineteen years old: it thus
appears probable that the framer of the Gregorian Calendar was selected,
not merely as a learned astronomer, but as one who had attended to the
calendar, and to works on its reformation, from early youth. When on the
subject I found reason to think that Clavius had really read this work,
and taken from it a phrase or two and a notion or two. Observe the
advantage of writing the baptismal name at full length.
A COUPLE OF MINOR PARADOXES.
The discovery of a general resolution of all superior finite
equations, of every numerical both algebraick and transcendent form. By
A. P. Vogel,[761]
mathematician at Leipzick. Leipzick and London, 1845, 8vo.
This work is written in the English of a German who has not mastered
the idiom: but it is always intelligible. It professes to solve equations
of every degree "in a more extent sense, and till to every degree of
exactness." The general solution of equations of all degrees is a
vexed question, which cannot have the mysterious interest of the circle
problem, and is of a comparatively modern date.[762] Mr. Vogel announces a forthcoming
treatise in which are resolved the "last impossibilities of pure
mathematics."
Elective Polarity the Universal Agent. By Frances Barbara Burton,
authoress of 'Astronomy familiarized,' 'Physical Astronomy,' &c.
London, 1845, 8vo.[763]
The title gives a notion of the theory. The first sentence states,
that 12,500 years ago α Lyræ was the
pole-star, and attributes the immense magnitude of the now fossil animals
to a star of such "polaric intensity as Vega pouring its magnetic streams
through our planet." Miss Burton was a lady of property, and of very
respectable acquirements, especially in Hebrew; she was eccentric in all
things.
1867.—Miss Burton is revived by the writer of a book on
meteorology which makes use of the planets: she is one of his leading
minds.[764]
SPECULATIVE THOUGHT IN ENGLAND.
In the year 1845 the old Mathematical Society was merged in the
Astronomical Society. The circle-squarers, etc., thrive more in England
than in any other country: there are most weeds where there is the
largest crop. Speculation, though not encouraged by our Government so
much as by those of the Continent, has had, not indeed such forcing, but
much wider diffusion: few tanks, but many rivulets. On this point I quote
from the preface to the reprint of the work of Ramchundra,[765] which I superintended
for the late Court of Directors of the East India Company.
"That sound judgment which gives men well to know what is best for
them, as well as that faculty of invention which leads to development of
resources and to the increase of wealth and comfort, are both materially
advanced, perhaps cannot rapidly be advanced without, a great taste for
pure speculation among the general mass of the people, down to the lowest
of those who can read and write. England is a marked example. Many
persons will be surprised at this assertion. They imagine that our
country is the great instance of the refusal of all unpractical
knowledge in favor of what is useful. I affirm, on the contrary,
that there is no country in Europe in which there has been so wide a
diffusion of speculation, theory, or what other unpractical word the
reader pleases. In our country, the scientific society is always
formed and maintained by the people; in every other, the scientific
academy—most aptly named—has been the creation of the
government, of which it has never ceased to be the nursling. In all the
parts of England in which manufacturing pursuits have given the artisan
some command of time, the cultivation of mathematics and other
speculative studies has been, as is well known, a very frequent
occupation. In no other country has the weaver at his loom bent over the
Principia of Newton; in no other country has the man of weekly
wages maintained his own scientific periodical. With us, since the
beginning of the last century, scores upon scores—perhaps hundreds,
for I am far from knowing all—of annuals have run, some their ten
years, some their half-century, some their century and a half, containing
questions to be answered, from which many of our examiners in the
universities have culled materials for the academical contests. And these
questions have always been answered, and in cases without number by the
lower order of purchasers, the mechanics, the weavers, and the printers'
workmen. I cannot here digress to point out the manner in which the
concentration of manufactures, and the general diffusion of education,
have affected the state of things; I speak of the time
during which the present system took its rise, and of the circumstances
under which many of its most effective promoters were trained. In all
this there is nothing which stands out, like the state-nourished academy,
with its few great names and brilliant single achievements. This country
has differed from all others in the wide diffusion of the disposition to
speculate, which disposition has found its place among the ordinary
habits of life, moderate in its action, healthy in its amount."
THE OLD MATHEMATICAL SOCIETY.
Among the most remarkable proofs of the diffusion of speculation was
the Mathematical Society, which flourished from 1717 to 1845. Its habitat
was Spitalfields, and I think most of its existence was passed in Crispin
Street. It was originally a plain society, belonging to the studious
artisan. The members met for discussion once a week; and I believe I am
correct in saying that each man had his pipe, his pot, and his problem.
One of their old rules was that, "If any member shall so far forget
himself and the respect due to the Society as in the warmth of debate to
threaten or offer personal violence to any other member, he shall be
liable to immediate expulsion, or to pay such fine as the majority of the
members present shall decide." But their great rule, printed large on the
back of the title page of their last book of regulations, was "By the
constitution of the Society, it is the duty of every member, if he be
asked any mathematical or philosophical question by another member, to
instruct him in the plainest and easiest manner he is able." We shall
presently see that, in old time, the rule had a more homely form.
I have been told that De Moivre[766] was a member of this Society. This
I cannot verify: circumstances render it unlikely; even though the French
refugees clustered in Spitalfields; many of them were of the Society,
which there is some reason to think was founded by them. But Dolland,[767] Thomas Simpson,[768] Saunderson,[769] Crossley,[770] and others of known
name, were certainly members. The Society gradually declined, and in 1845
was reduced to nineteen members. An arrangement was made by which sixteen
of these members, who where not already in the Astronomical Society
became Fellows without contribution, all the books and other property of
the old Society being transferred to the new one. I was one of the
committee which made the preliminary inquiries, and the reason of the
decline was soon manifest. The only question which could arise was
whether the members of the society of working men—for this repute
still continued—were of that class of educated men who could
associate with the Fellows of the Astronomical Society on terms agreeable
to all parties. We found that the artisan element had been extinct for
many years; there was not a man but might, as to education, manners, and
position, have become a Fellow in the usual way. The fact was that life
in Spitalfields had become harder: and the weaver could only live from
hand to mouth, and not up to the brain. The material of the old Society
no longer existed.
In 1798, experimental lectures were given, a small charge for
admission being taken at the door: by this hangs a tale—and a song.
Many years ago, I found among papers of a deceased friend, who certainly
never had anything to do with the Society, and who passed all his life
far from London, a song, headed "Song sung by the Mathematical Society in
London, at a dinner given Mr. Fletcher,[771] a solicitor, who had defended the
Society gratis." Mr. Williams,[772] the Assistant Secretary of the
Astronomical Society, formerly Secretary of the Mathematical Society,
remembered that the Society had had a solicitor named Fletcher among the
members. Some years elapsed before it struck me that my old friend
Benjamin Gompertz,[773]
who had long been a member, might have some recollection of the matter.
The following is an extract of a letter from him (July 9, 1861):
"As to the Mathematical Society, of which I was a member when only 18
years of age, [Mr. G. was born in 1779], having been, contrary to the
rules, elected under the age of 21. How I came to be a member of that
Society—and continued so until it joined the Astronomical Society,
and was then the President—was: I happened to pass a bookseller's
small shop, of second-hand books, kept by a poor taylor, but a good
mathematician, John Griffiths. I was very pleased to meet a
mathematician, and I asked him if he would give me some lessons; and his
reply was that I was more capable to teach him, but he belonged to a
society of mathematicians, and he would introduce me. I accepted the
offer, and I was elected, and had many scholars then to teach, as one
of the rules was, if a member asked for information, and applied to any
one who could give it, he was obliged to give it, or fine one penny.
Though I might say much with respect to the Society which would be
interesting, I will for the present reply only to your question. I well
knew Mr. Fletcher, who was a very clever and very scientific person. He
did, as solicitor, defend an action brought by an informer against the
Society—I think for 5,000l.—for giving lectures to the
public in philosophical subjects [i.e., for unlicensed public exhibition
with money taken at the doors]. I think the price for admission was one
shilling, and we used to have, if I rightly recollect, from two to three
hundred visitors. Mr. Fletcher was successful in his defence, and we got
out of our trouble. There was a collection made to reward his services,
but he did not accept of any reward: and I think we gave him a dinner, as
you state, and enjoyed ourselves; no doubt with astronomical songs and
other songs; but my recollection does not enable me to say if the
astronomical song was a drinking song. I think the anxiety caused by that
action was the cause of some of the members' death. [They had, no doubt,
broken the law in ignorance; and by the sum named, the informer must have
been present, and sued for a penalty on every shilling he could prove to
have been taken]."
I by no means guarantee that the whole song I proceed to give is what
was sung at the dinner: I suspect, by the completeness of the chain, that
augmentations have been made. My deceased friend was just the man to add
some verses, or the addition may have been made before it came into his
hands, or since his decease, for the scraps containing the verses passed
through several hands before they came into mine. We may, however, be
pretty sure that the original is substantially contained in what is
given, and that the character is therefore preserved. I have had myself
to repair damages every now and then, in the way of conjectural
restoration of defects caused by ill-usage.
THE ASTRONOMER'S DRINKING SONG.
"Whoe'er would search the starry sky,
Its secrets to divine, sir,
Should take his glass—I mean, should try
A glass or two of wine, sir!
True virtue lies in golden mean,
And man must wet his clay, sir;
Join these two maxims, and 'tis seen
He should drink his bottle a day, sir!
"Old Archimedes, reverend sage!
By trump of fame renowned, sir,
Deep problems solved in every page,
And the sphere's curved surface found,[774] sir:
Himself he would have far outshone,
And borne a wider sway, sir,
Had he our modern secret known,
And drank a bottle a day, sir!
"When Ptolemy,[775] now long ago,
Believed the earth stood still, sir,
He never would have blundered so,
Had he but drunk his fill, sir:
He'd then have felt[776] it circulate,
And would have learnt to say, sir,
The true way to investigate
Is to drink your bottle a day, sir!
"Copernicus,[777] that learned wight,
The glory of his nation,
With draughts of wine refreshed his sight,
And saw the earth's rotation;
Each planet then its orb described,
The moon got under way, sir;
These truths from nature he imbibed
For he drank his bottle a day, sir!
"The noble[778] Tycho placed the stars,
Each in its due location;
He lost his nose[779] by spite of Mars,
But that was no privation:
Had he but lost his mouth, I grant
He would have felt dismay, sir,
Bless you! he knew what he should want
To drink his bottle a day, sir!
"Cold water makes no lucky hits;
On mysteries the head runs:
Small drink let Kepler[780] time his wits
On the regular polyhedrons:
He took to wine, and it changed the chime,
His genius swept away, sir,
Through area varying[781] as the time
At the rate of a bottle a day, sir!
"Poor Galileo,[782] forced to rat
Before the Inquisition,
E pur si muove[783] was the pat
He gave them in addition:
He meant, whate'er you think you prove,
The earth must go its way, sirs;
Spite of your teeth I'll make it move,
For I'll drink my bottle a day, sirs!
"Great Newton, who was never beat
Whatever fools may think, sir;
Though sometimes he forgot to eat,
He never forgot to drink, sir:
Descartes[784] took nought but lemonade,
To conquer him was play, sir;
The first advance that Newton made
Was to drink his bottle a day, sir!
"D'Alembert,[785] Euler,[786] and Clairaut,[787]
Though they increased our store, sir,
Much further had been seen to go
Had they tippled a little more, sir!
Lagrange[788] gets mellow with Laplace,[789]
And both are wont to say, sir,
The philosophe who's not an ass
Will drink his bottle a day, sir!
"Astronomers! what can avail
Those who calumniate us;
Experiment can never fail
With such an apparatus:
Let him who'd have his merits known
Remember what I say, sir;
Fair science shines on him alone
Who drinks his bottle a day, sir!
"How light we reck of those who mock
By this we'll make to appear, sir,
We'll dine by the sidereal[790] clock
For one more bottle a year, sir:
But choose which pendulum you will,
You'll never make your way, sir,
Unless you drink—and drink your fill,—
At least a bottle a day, sir!"
Old times are changed, old manners gone!
There is a new Mathematical Society,[791] and I am, at this present writing
(1866), its first President. We are very high in the newest developments,
and bid fair to take a place among the scientific establishments.
Benjamin Gompertz, who was President of the old Society when it expired,
was the link between the old and new body: he was a member of ours
at his death. But not a drop of liquor is seen at our meetings, except a
decanter of water: all our heavy is a fermentation of symbols; and we do
not draw it mild. There is no penny fine for reticence or occult science;
and as to a song! not the ghost of a chance.
1826. The time may have come when the original documents connected
with the discovery of Neptune may be worth revising. The following are
extracts from the Athenæum of October 3 and October 17:
LE VERRIER'S[792] PLANET.
We have received, at the last moment before making up for press, the
following letter from Sir John Herschel,[793] in reference to the
matter referred to in the communication from Mr. Hind[794] given below:
"Collingwood, Oct. 1.
"In my address to the British Association assembled at Southampton, on
the occasion of my resigning the chair to Sir R. Murchison,[795] I stated, among the
remarkable astronomical events of the last twelvemonth, that it had added
a new planet to our list,—adding, 'it has done more,—it has
given us the probable prospect of the discovery of another. We see it as
Columbus saw America from the shores of Spain. Its movements have been
felt, trembling along the far-reaching line of our analysis, with a
certainty hardly inferior to that of ocular demonstration.'—These
expressions are not reported in any of the papers which profess to give
an account of the proceedings, but I appeal to all present whether they
were not used.
"Give me leave to state my reasons for this confidence; and, in so
doing, to call attention to some facts which deserve to be put on record
in the history of this noble discovery. On July 12, 1842, the late
illustrious astronomer, Bessel,[796] honored me with a visit at my present
residence. On the evening of that day, conversing on the great work of
the planetary reductions undertaken by the Astronomer Royal[797]—then in
progress, and since published,[798]—M. Bessel remarked that the
motions of Uranus, as he had satisfied himself by careful
examination of the recorded observations, could not be accounted for by
the perturbations of the known planets; and that the deviations far
exceeded any possible limits of error of observation. In reply to the
question, Whether the deviations in question might not be due to the
action of an unknown planet?—he stated that he considered it highly
probable that such was the case,—being systematic, and such as
might be produced by an exterior planet. I then inquired whether he had
attempted, from the indications afforded by these perturbations, to
discover the position of the unknown body,—in order that 'a hue and
cry' might be raised for it. From his reply, the words of which I do not
call to mind, I collected that he had not then gone into that inquiry;
but proposed to do so, having now completed certain works which had
occupied too much of his time. And, accordingly, in a letter which I
received from him after his return to Königsberg, dated November 14,
1842, he says,—'In reference to our conversation at Collingwood, I
announce to you (melde ich Ihnen) that Uranus is not
forgotten.' Doubtless, therefore, among his papers will be found some
researches on the subject.
"The remarkable calculations of M. Le Verrier—which have pointed
out, as now appears, nearly the true situation of the new planet, by
resolving the inverse problem of the perturbations—if
uncorroborated by repetition of the numerical calculations by another
hand, or by independent investigation from another quarter, would hardly
justify so strong an assurance as that conveyed by my expressions above
alluded to. But it was known to me, at that time, (I will take the
liberty to cite the Astronomer Royal as my authority) that a similar
investigation had been independently entered into, and a conclusion as to
the situation of the new planet very nearly coincident with M. Le
Verrier's arrived at (in entire ignorance of his conclusions), by a young
Cambridge mathematician, Mr. Adams;[799]—who will, I hope, pardon this
mention of his name (the matter being one of great historical
moment),—and who will, doubtless, in his own good time and manner,
place his calculations before the public.
"J. F. W. HERSCHEL."
Discovery of Le Verrier's Planet.
Mr. Hind announces to the Times that he has received a letter
from Dr. Brünnow, of the Royal Observatory at Berlin, giving the very
important information that Le Verrier's planet was found by M. Galle, on
the night of September 23. "In announcing this grand discovery," he says,
"I think it better to copy Dr. Brünnow's[800] letter."
"Berlin, Sept. 25.
"My dear Sir—M. Le Verrier's planet was discovered here the 23d
of September, by M. Galle.[801] It is a star of the 8th magnitude,
but with a diameter of two or three seconds. Here are its places:
| | h. | m. | s. | | R. A. | | Declination. |
| Sept. 23, | 12 | 0 | 14.6 M.T. | | 328° | 19' | 16.0" | | -13° | 24' | 8.2" |
| Sept. 24, | 8 | 54 | 40.9 M.T. | | 328° | 18' | 14.3" | | -13° | 24' | 29.7" |
The planet is now retrograde, its motion amounting daily to four
seconds of time.
"Yours most respectfully, Brünnow."
"This discovery," Mr. Hind says, "may be justly considered one of the
greatest triumphs of theoretical astronomy;" and he adds, in a
postscript, that the planet was observed at Mr. Bishop's[802] Observatory, in the Regent's Park,
on Wednesday night, notwithstanding the
moonlight and hazy sky. "It appears bright," he says, "and with a power
of 320 I can see the disc. The following position is the result of
instrumental comparisons with 33 Aquarii:
Sept. 30, at 8h. 16m. 21s. Greenwich mean time—
| Right ascension of planet | 21h. | 52m. | 47.15s. |
| South declination | 13° | 27' | 20"." |
THE NEW PLANET.
"Cambridge Observatory, Oct. 15.
"The allusion made by Sir John Herschel, in his letter contained in
the Athenæum of October 3, to the theoretical researches of Mr.
Adams, respecting the newly-discovered planet, has induced me to request
that you would make the following communication public. It is right that
I should first say that I have Mr. Adams's permission to make the
statements that follow, so far as they relate to his labors. I do not
propose to enter into a detail of the steps by which Mr. Adams was led,
by his spontaneous and independent researches, to a conclusion that a
planet must exist more distant than Uranus. The matter is of too great
historical moment not to receive a more formal record than it would be
proper to give here. My immediate object is to show, while the attention
of the scientific public is more particularly directed to the subject,
that, with respect to this remarkable discovery, English astronomers may
lay claim to some merit.
"Mr. Adams formed the resolution of trying, by calculation, to account
for the anomalies in the motion of Uranus on the hypothesis of a more
distant planet, when he was an undergraduate in this university, and when
his exertions for the academical distinction, which he obtained in
January 1843, left him no time for pursuing the research. In the course
of that year, he arrived at an approximation to the position of the
supposed planet; which, however, he did not consider to be worthy of
confidence, on account of his not having employed a
sufficient number of observations of Uranus. Accordingly, he requested my
intervention to obtain for him the early Greenwich observations, then in
course of reduction;—which the Astronomer Royal immediately
supplied, in the kindest possible manner. This was in February, 1844. In
September, 1845, Mr. Adams communicated to me values which he had
obtained for the heliocentric longitude, excentricity of orbit, longitude
of perihelion, and mass, of an assumed exterior planet,—deduced
entirely from unaccounted-for perturbations of Uranus. The same results,
somewhat corrected, he communicated, in October, to the Astronomer Royal.
M. Le Verrier, in an investigation which was published in June of 1846,
assigned very nearly the same heliocentric longitude for the probable
position of the planet as Mr. Adams had arrived at, but gave no results
respecting its mass and the form of its orbit. The coincidence as to
position from two entirely independent investigations naturally inspired
confidence; and the Astronomer Royal shortly after suggested the
employing of the Northumberland telescope of this observatory in a
systematic search after the hypothetical planet; recommending, at the
same time, a definite plan of operations. I undertook to make the
search,—and commenced observing on July 29. The observations were
directed, in the first instance, to the part of the heavens which theory
had pointed out as the most probable place of the planet; in selecting
which I was guided by a paper drawn up for me by Mr. Adams. Not having
hour xxi. of the Berlin star-maps—of the publication of which I was
not aware—I had to proceed on the principle of comparison of
observations made at intervals. On July 30, I went over a zone 9' broad,
in such a manner as to include all stars to the eleventh magnitude. On
August 4, I took a broader zone and recorded a place of the planet. My
next observations were on August 12; when I met with a star of the eighth
magnitude in the zone which I had gone over on July 30,—and which
did not then contain this star. Of course, this was the
planet;—the place of which was, thus, recorded a second time in
four days of observing. A comparison of the observations of July 30 and
August 12 would, according to the principle of search which I employed,
have shown me the planet. I did not make the comparison till after the
detection of it at Berlin—partly because I had an impression that a
much more extensive search was required to give any probability of
discovery—and partly from the press of other occupation. The
planet, however, was secured, and two positions of it recorded six
weeks earlier here than in any other observatory,—and in a
systematic search expressly undertaken for that purpose. I give now the
positions of the planet on August 4 and August 12.
| Greenwich mean time. |
| Aug. 4, 13h. 36m. 25s. ... |  | R.A. | 21h. | 58m. | 14.70s. |
| N.P.D. | 102° | 57' | 32.2" |
| Aug. 12, 13h. 3m. 26s. ... | | R.A. | 21h. | 57m. | 26.13s. |
| N.P.D. | 103° | 2' | 0.2" |
"From these places compared with recent observations Mr. Adams has
obtained the following results:
| Distance of the planet from the sun ... | 30.05 |
| Inclination of the orbit ... | 1° 45' |
| Longitude of the descending node ... | 309° 43' |
| Heliocentric longitude, Aug. 4 ... | 326° 39' |
"The present distance from the sun is, therefore, thirty times the
earth's mean distance;—which is somewhat less than the theory had
indicated. The other elements of the orbit cannot be approximated to till
the observations shall have been continued for a longer period.
"The part taken by Mr. Adams in the theoretical search after this
planet will, perhaps, be considered to justify the suggesting of a name.
With his consent, I mention Oceanus as one which may possibly
receive the votes of astronomers.—I have authority to state
that Mr. Adams's investigations will in a short time, be published in
detail.
"J. Challis."[803]
ASTRONOMICAL POLICE REPORT.
"An ill-looking kind of a body, who declined to give any name, was
brought before the Academy of Sciences, charged with having assaulted a
gentleman of the name of Uranus in the public highway. The prosecutor was
a youngish looking person, wrapped up in two or three great coats; and
looked chillier than anything imaginable, except the
prisoner,—whose teeth absolutely shook, all the time.
Policeman Le Verrier[804] stated that he saw the prosecutor
walking along the pavement,—and sometimes turning sideways, and
sometimes running up to the railings and jerking about in a strange way.
Calculated that somebody must be pulling his coat, or otherwise
assaulting him. It was so dark that he could not see; but thought, if he
watched the direction in which the next odd move was made, he might find
out something. When the time came, he set Brünnow, a constable in another
division of the same force, to watch where he told him; and Brünnow
caught the prisoner lurking about in the very spot,—trying to look
as if he was minding his own business. Had suspected for a long time that
somebody was lurking about in the neighborhood. Brünnow was then called,
and deposed to his catching the prisoner as described.
M. Arago.—Was the prosecutor sober?
Le Verrier.—Lord, yes, your worship; no man who had a
drop in him ever looks so cold as he did.
M. Arago.—Did you see the assault?
Le Verrier.—I can't say I did; but I told Brünnow exactly
how he'd be crouched down;—just as he was.
M. Arago (to Brünnow).—Did you see the
assault?
Brünnow.—No, your worship; but I caught the prisoner.
M. Arago.—How did you know there was any assault at
all?
Le Verrier.—I reckoned it couldn't be otherwise, when I
saw the prosecutor making those odd turns on the pavement.
M. Arago.—You reckon and you calculate! Why, you'll tell
me, next, that you policemen may sit at home and find out all that's
going on in the streets by arithmetic. Did you ever bring a case of this
kind before me till now?
Le Verrier.—Why, you see, your worship, the police are
growing cleverer and cleverer every day. We can't help it:—it grows
upon us.
M. Arago.—You're getting too clever for me. What does the
prosecutor know about the matter?
The prosecutor said, all he knew was that he was pulled behind by
somebody several times. On being further examined, he said that he had
seen the prisoner often, but did not know his name, nor how he got his
living; but had understood he was called Neptune. He himself had paid
rates and taxes a good many years now. Had a family of six,—two of
whom got their own living.
The prisoner being called on for his defence, said that it was a
quarrel. He had pushed the prosecutor—and the prosecutor had pushed
him. They had known each other a long time, and were always
quarreling;—he did not know why. It was their nature, he supposed.
He further said, that the prosecutor had given a false account of
himself;—that he went about under different names. Sometimes he was
called Uranus, sometimes Herschel, and sometimes Georgium Sidus; and he
had no character for regularity in the neighborhood. Indeed, he was
sometimes not to be seen for a long time at once.
The prosecutor, on being asked, admitted, after a little hesitation,
that he had pushed and pulled the prisoner too. In the altercation
which followed, it was found very difficult to make out which
began:—and the worthy magistrate seemed to think they must have
begun together.
M. Arago.—Prisoner, have you any family?
The prisoner declined answering that question at present. He said he
thought the police might as well reckon it out whether he had or not.
M. Arago said he didn't much differ from that opinion.—He
then addressed both prosecutor and prisoner; and told them that if they
couldn't settle their differences without quarreling in the streets, he
should certainly commit them both next time. In the meantime, he called
upon both to enter into their own recognizances; and directed the police
to have an eye upon both,—observing that the prisoner would be
likely to want it a long time, and the prosecutor would be not a hair the
worse for it."
This quib was written by a person who was among the astronomers: and
it illustrates the fact that Le Verrier had sole possession of the field
until Mr. Challis's letter appeared. Sir John Herschel's previous
communication should have paved the way: but the wonder of the discovery
drove it out of many heads. There is an excellent account of the whole
matter in Professor Grant's[805] History of Physical Astronomy.
The squib scandalized some grave people, who wrote severe admonitions to
the editor. There are formalists who spend much time in writing propriety
to journals, to which they serve as foolometers. In a letter to the
Athenæum, speaking of the way in which people hawk fine terms for
common things, I said that these people ought to have a new translation
of the Bible, which should contain the verse "gentleman and lady, created
He them." The editor was handsomely fired and brimstoned!
A NEW THEORY OF TIDES.
A new theory of the tides: in which the errors of the usual theory are
demonstrated; and proof shewn that the full moon is not the cause of a
concomitant spring tide, but actually the cause of the neaps.... By
Commr. Debenham,[806] R.N. London, 1846, 8vo.
The author replied to a criticism in the Athenæum, and I
remember how, in a very few words, he showed that he had read nothing on
the subject. The reviewer spoke of the forces of the planets (i.e., the
Sun and Moon) on the ocean, on which the author remarks, "But N.B. the
Sun is no planet, Mr. Critic." Had he read any of the actual
investigations on the usual theory, he would have known that to this day
the sun and moon continue to be called planets—though the
phrase is disappearing—in speaking of the tides; the sense, of
course, being the old one, wandering bodies.
A large class of the paradoxers, when they meet with something which
taken in their sense is absurd, do not take the trouble to find out the
intended meaning, but walk off with the words laden with their own first
construction. Such men are hardly fit to walk the streets without an
interpreter. I was startled for a moment, at the time when a recent
happy—and more recently happier—marriage occupied the public
thoughts, by seeing in a haberdasher's window, in staring large letters,
an unpunctuated sentence which read itself to me as "Princess Alexandra!
collar and cuff!" It immediately occurred to me that had I been any one
of some scores of my paradoxers, I should, no doubt, have proceeded to
raise the mob against the unscrupulous person who dared to hint to a
young bride such maleficent—or at least immellificent—conduct
towards her new lord. But, as it was, certain material contexts in the
shop window suggested a less savage explanation. A paradoxer should not
stop at reading the advertisements of Newton or Laplace; he should learn
to look at the stock of goods.
I think I must have an eye for double readings, when presented: though
I never guess riddles. On the day on which I first walked into the
Panizzi reading room[807]—as it ought to be
called—at the Museum, I began my circuit of the wall-shelves at the
ladies' end: and perfectly coincided in the propriety of the Bibles and
theological works being placed there. But the very first book I looked on
the back of had, in flaming gold letters, the following
inscription—"Blast the Antinomians!"[808] If a line had been drawn below the
first word, Dr. Blast's history of the Antinomians would not have been so
fearfully misinterpreted. It seems that neither the binder nor the
arranger of the room had caught my reading. The book was removed before
the catalogue of books of reference was printed.
AN ASTRONOMICAL PARADOXER.
Two systems of astronomy: first, the Newtonian system, showing the
rise and progress thereof, with a short historical account; the general
theory with a variety of remarks thereon: second, the system in
accordance with the Holy Scriptures, showing the rise and progress from
Enoch, the seventh from Adam, the prophets, Moses, and others, in the
first Testament; our Lord Jesus Christ, and his apostles, in the new or
second Testament; Reeve and Muggleton, in the third and last Testament;
with a variety of remarks thereon. By Isaac Frost.[809] London, 1846, 4to.
A very handsomely printed volume, with beautiful plates. Many readers
who have heard of Muggletonians have never had any distinct idea of
Lodowick Muggleton,[810]
the inspired tailor, (1608-1698) who about 1650 received his commission
from heaven, wrote a Testament, founded a sect, and descended to
posterity. Of Reeve[811]
less is usually said; according to Mr. Frost, he and Muggleton are the
two "witnesses." I shall content myself with one specimen of Mr. Frost's
science:
"I was once invited to hear read over 'Guthrie[812] on Astronomy,' and when the reading
was concluded I was asked my opinion thereon; when I said, 'Doctor, it
appears to me that Sir I. Newton has only given two proofs in support of
his theory of the earth revolving round the sun: all the rest is
assertion without any proofs.'—'What are they?' inquired the
Doctor.—'Well,' I said, 'they are, first, the power of attraction
to keep the earth to the sun; the second is the power of repulsion, by
virtue of the centrifugal motion of the earth: all the rest appears to me
assertion without proof.' The Doctor considered a short time and then
said, 'It certainly did appear so.' I said, 'Sir Isaac has certainly
obtained the credit of completing the system, but really he has only half
done his work.'—'How is that,' inquired my friend the Doctor. My
reply was this: 'You will observe his system shows the earth traverses
round the sun on an inclined plane; the consequence is, there are four
powers required to make his system complete:
1st. The power of attraction.
2ndly. The power of repulsion.
3rdly. The power of ascending the inclined plane.
4thly. The power of descending the inclined plane.
You will thus easily see the four powers required, and Newton
has only accounted for two; the work is therefore only half done.'
Upon due reflection the Doctor said, 'It certainly was necessary to have
these four points cleared up before the system could be said to be
complete.'"
I have no doubt that Mr. Frost, and many others on my list, have
really encountered doctors who could be puzzled by such stuff as this, or
nearly as bad, among the votaries of existing systems, and have been
encouraged thereby to print their objections. But justice requires me to
say that from the words "power of repulsion by virtue of the centrifugal
motion of the earth," Mr. Frost may be suspected of having something more
like a notion of the much-mistaken term "centrifugal force" than many
paradoxers of greater fame. The Muggletonian sect is not altogether
friendless: over and above this handsome volume, the works of Reeve and
Muggleton were printed, in 1832, in three quarto volumes. See Notes
and Queries, 1st Series, v, 80; 3d Series, iii, 303.
[The system laid down by Mr. Frost, though intended to be
substantially that of Lodowick Muggleton, is not so vagarious. It is
worthy of note how very different have been the fates of two contemporary
paradoxers, Muggleton and George Fox.[813] They were friends and associates,[814] and commenced their
careers about the same time, 1647-1650. The followers of Fox have made
their sect an institution, and deserve to be called the pioneers of
philanthropy. But though there must still be Muggletonians, since
expensive books are published by men who take the name, no sect of that
name is known to the world. Nevertheless, Fox and Muggleton are men of
one type, developed by the same circumstances: it is for those who
investigate such men to point out why their teachings have had fates so
different. Macaulay says it was because Fox found followers of more sense
than himself. True enough: but why did Fox find such followers and not
Muggleton? The two were equally crazy, to all appearance: and the
difference required must be sought in the doctrines themselves.
Fox was not a rational man: but the success of his sect and
doctrines entitles him to a letter of alteration of the phrase which I am
surprised has not become current. When Conduitt,[815] the husband of Newton's half-niece,
wrote a circular to Newton's friends, just after his death, inviting them
to bear their parts in a proper biography, he said, "As Sir I. Newton was
a national man, I think every one ought to contribute to a work
intended to do him justice." Here is the very phrase which is often
wanted to signify that celebrity which puts its mark, good or
bad, on the national history, in a manner which cannot be asserted of
many notorious or famous historical characters. Thus George Fox and
Newton are both national men. Dr. Roget's[816] Thesaurus gives more than
fifty synonyms—colleagues would be the better word—of
"celebrated," any one of which might be applied, either in prose
or poetry, to Newton or to his works, no one of which comes near to the
meaning which Conduitt's adjective immediately suggests.
The truth is, that we are too monarchical to be
national. We have the Queen's army, the Queen's navy, the Queen's
highway, the Queen's English, etc.; nothing is national except the
debt. That this remark is not new is an addition to its force; it
has hardly been repeated since it was first made. It is some excuse that
nation is not vernacular English: the country is our word,
and country man is appropriated.]
Astronomical Aphorisms, or Theory of Nature; founded on the immutable
basis of Meteoric Action. By P. Murphy,[817] Esq. London, 1847, 12mo.
This is by the framer of the Weather Almanac, who appeals to that work
as corroborative of his theory of planetary temperature, years after all
the world knew by experience that this meteorological theory was just as
good as the others.
The conspiracy of the Bullionists as it affects the present system of
the money laws. By Caleb Quotem. Birmingham, 1847, 8vo. (pp. 16).
This pamphlet is one of a class of which I know very little, in which
the effects of the laws relating to this or that political bone of
contention are imputed to deliberate conspiracy of one class to rob
another of what the one knew ought to belong to the other. The success of
such writers in believing what they have a bias to believe, would, if
they knew themselves, make them think it equally likely that the
inculpated classes might really believe what it is their interest
to believe. The idea of a guilty understanding existing among
fundholders, or landholders, or any holders, all the country over, and
never detected except by bouncing pamphleteers, is a theory which should
have been left for Cobbett[818] to propose, and for Apella to
believe.[819]
[August, 1866. A pamphlet shows how to pay the National Debt.
Advance paper to railways, etc., receivable in payment of taxes. The
railways pay interest and principal in money, with which you pay your
national debt, and redeem your notes. Twenty-five years of interest
redeems the notes, and then the principal pays the debt. Notes to be kept
up to value by penalties.]
THEISM INDEPENDENT OF REVELATION.
The Reasoner. No. 45. Edited by G.J. Holyoake.[820] Price 2d. Is there sufficient
proof of the existence of God? 8vo. 1847.
This acorn of the holy oak was forwarded to me with a manuscript note,
signed by the editor, on the part of the "London Society of
Theological Utilitarians," who say, "they trust you may be induced to
give this momentous subject your consideration." The supposition that a
middle-aged person, known as a student of thought on more subjects than
one, had that particular subject yet to begin, is a specimen of what I
will call the assumption-trick of controversy, a habit which
pervades all sides of all subjects. The tract is a proof of the good
policy of letting opinions find their level, without any assistance from
the Court of Queen's Bench. Twenty years earlier the thesis would have
been positive, "There is sufficient proof of the non-existence of God,"
and bitter in its tone. As it stands, we have a moderate and respectful
treatment—wrong only in making the opponent argue absurdly, as
usually happens when one side invents the other—of a question in
which a great many Christians have agreed with the atheist: that question
being—Can the existence of God be proved independently of
revelation? Many very religious persons answer this question in the
negative, as well as Mr. Holyoake. And, this point being settled, all who
agree in the negative separate into those who can endure scepticism, and
those who cannot: the second class find their way to Christianity. This
very number of The Reasoner announces the secession of one of its
correspondents, and his adoption of the Christian faith. This would not
have happened twenty years before: nor, had it happened, would it have
been respectfully announced.
There are people who are very unfortunate in the expression of their
meaning. Mr. Holyoake, in the name of the "London Society" etc.,
forwarded a pamphlet on the existence of God, and said that the Society
trusted I "may be induced to give" the subject my "consideration." How
could I know the Society was one person, who supposed I had arrived at a
conclusion and wanted a "guiding word"? But so it seems it was:
Mr. Holyoake, in the English Leader of October 15, 1864, and in a
private letter to me, writes as follows:
"The gentleman who was the author of the argument, and who asked me to
send it to Mr. De Morgan, never assumed that that gentleman had 'that
particular subject to begin'—on the contrary, he supposed that one
whom we all knew to be eminent as a thinker had come to a
conclusion upon it, and would perhaps vouchsafe a guiding word to one who
was, as yet, seeking the solution of the Great Problem of Theology. I
told my friend that 'Mr. De Morgan was doubtless preoccupied, and that he
must be content to wait. On some day of courtesy and leisure he might
have the kindness to write.' Nor was I wrong—the answer appears in
your pages at the lapse of seventeen years."
I suppose Mr. Holyoake's way of putting his request was the stylus
curiæ of the Society. A worthy Quaker who was sued for debt in the
King's Bench was horrified to find himself charged in the declaration
with detaining his creditor's money by force and arms, contrary to the
peace of our Lord the King, etc. It's only the stylus curiæ, said
a friend: I don't know curiæ, said the Quaker, but he shouldn't
style us peace-breakers.
The notion that the non-existence of God can be proved,
has died out under the light of discussion: had the only lights shone
from the pulpit and the prison, so great a step would never have been
made. The question now is as above. The dictum that Christianity is "part
and parcel of the law of the land" is also abrogated: at the same time,
and the coincidence is not an accident, it is becoming somewhat nearer
the truth that the law of the land is part and parcel of Christianity. It
must also be noticed that Christianity was part and parcel of the
articles of war; and so was duelling. Any officer speaking
against religion was to be cashiered; and any officer receiving an
affront without, in the last resort, attempting to kill his opponent, was
also to be cashiered. Though somewhat of a book-hunter, I have never
been able to ascertain the date of the collected remonstrances of the
prelates in the House of Lords against this overt inculcation of murder,
under the soft name of satisfaction: it is neither in Watt,[821] nor in Lowndes,[822] nor in any edition of
Brunet;[823] and there is
no copy in the British Museum. Was the collected edition really
published?
[The publication of the above in the Athenæum has not produced
reference to a single copy. The collected edition seems to be doubted. I
have even met one or two persons who doubt the fact of the Bishops having
remonstrated at all: but their doubt was founded on an absurd
supposition, namely, that it was no business of theirs; that it
was not the business of the prelates of the church in union with the
state to remonstrate against the Crown commanding murder! Some say that
the edition was published, but under an irrelevant title, which prevented
people from knowing what it was about. Such things have happened: for
example, arranged extracts from Wellington's general orders, which would
have attracted attention, fell dead under the title of "Principles of
War." It is surmised that the book I am looking for also contains the
protests of the Reverend bench against other things besides the
Thou-shalt-do-murder of the Articles (of war), and is called "First
Elements of Religion" or some similar title. Time clears up all
things.]
[1] See Mrs. De Morgan's Memoir of
Augustus De Morgan, London, 1882, p 61.
[2] In the first edition this
reference was to page 11.
[3] In the first edition this read
"at page 438," the work then appearing in a single volume.
[4] "Just as it would surely have
been better not to have considered it (i.e., the trinity) as a mystery,
and with Cl. Kleckermann to have investigated by the aid of philosophy
according to the teaching of true logic what it might be, before they
determined what it was; just so would it have been better to withdraw
zealously and industriously into the deepest caverns and darkest recesses
of metaphysical speculations and suppositions in order to establish their
opinion beyond danger from the weapons of their adversaries.... Indeed
that great man so explains and demonstrates this dogma (although to
theologians the word has not much charm) from the immovable foundations
of philosophy, that with but few changes and additions a mind sincerely
devoted to truth can desire nothing more."
[5] Mrs. Wititterly, in Nicholas
Nickleby.—A. De M.
[6] The brackets mean that the
paragraph is substantially from some one of the Athenæum
Supplements.—S. E. De M.
[7] "It is annoying that this
ingenious naturalist who has already given us more useful works and has
still others in preparation, uses for this odious task, a pen dipped in
gall and wormwood. It is true that many of his remarks have some
foundation, and that to each error that he points out he at the same time
adds its correction. But he is not always just and never fails to insult.
After all, what does his book prove except that a forty-fifth part of a
very useful review is not free from mistakes? Must we confuse him with
those superficial writers whose liberty of body does not permit them to
restrain their fruitfulness, that crowd of savants of the highest rank
whose writings have adorned and still adorn the Transactions? Has
he forgotten that the names of the Boyles, Newtons, Halleys, De Moivres,
Hans Sloanes, etc. have been seen frequently? and that still are found
those of the Wards, Bradleys, Grahams, Ellicots, Watsons, and of an
author whom Mr. Hill prefers to all others, I mean Mr. Hill himself?"
[8] "Let no free man be seized or
imprisoned or in any way harmed except by trial of his peers."
[9] "The master can rob, wreck and
punish his slave according to his pleasure save only that he may not maim
him."
[10] An Irish antiquary informs me
that Virgil is mentioned in annals at A.D. 784, as "Verghil, i.e., the
geometer, Abbot of Achadhbo [and Bishop of Saltzburg] died in Germany in
the thirteenth year of his bishoprick." No allusion is made to his
opinions; but it seems he was, by tradition, a mathematician. The Abbot
of Aghabo (Queen's County) was canonized by Gregory IX, in 1233. The
story of the second, or scapegoat, Virgil would be much damaged by the
character given to the real bishop, if there were anything in it to
dilapidate.—A. De M.
[11] "He performed many acts
befitting the Papal dignity, and likewise many excellent (to be sure!)
works."
[12] "After having been on the
throne during ten years of pestilence."
[13] The work is the Questiones
Joannis Buridani super X libros Aristotelis ad Nicomachum, curante Egidio
Delfo ... Parisiis, 1489, folio. It also appeared at Paris in
editions of 1499, 1513, and 1518, and at Oxford in 1637.
[14] Jean Buridan was born at
Béthune about 1298, and died at Paris about 1358. He was professor of
philosophy at the University of Paris and several times held the office
of Rector. As a philosopher he was classed among the nominalists.
[15] So in the original.
[16] Baruch Spinoza, or Benedict de
Spinoza as he later called himself, the pantheistic philosopher,
excommunicated from the Jewish faith for heresy, was born at Amsterdam in
1632 and died there in 1677.
[17] Michael Scott, or Scot, was
born about 1190, probably in Fifeshire, Scotland, and died about 1291. He
was one of the best known savants of the court of Emperor Frederick II,
and wrote upon astrology, alchemy, and the occult sciences. He was looked
upon as a great magician and is mentioned among the wizards in Dante's
Inferno.
"That other, round the loins
So slender of his shape, was Michael Scot,
Practised in every slight of magic wile." Inferno, XX.
Boccaccio also speaks of him: "It is not long since there was in this
city (Florence) a great master in necromancy, who was called Michele
Scotto, because he was a Scot." Decameron, Dec. Giorno.
Scott's mention of him in Canto Second of his Lay of the Last
Minstrel, is well known:
"In these fair climes, it was my lot
To meet the wondrous Michael Scott;
A wizard of such dreaded fame,
That when, in Salamanca's cave,
Him listed his magic wand to wave,
The bells would ring in Notre Dame!"
Sir Walter's notes upon him are of interest.
[18] These were some of the
forgeries which Michel Chasles (1793-1880) was duped into buying. They
purported to be a correspondence between Pascal and Newton and to show
that the former had anticipated some of the discoveries of the great
English physicist and mathematician. That they were forgeries was shown
by Sir David Brewster in 1855.
[19] "Let the serpent also break
from its appointed path."
[20] Guglielmo Brutus Icilius
Timoleon Libri-Carucci della Sommaja, born at Florence in 1803; died at
Fiesole in 1869. His Histoire des Sciences Mathématiques appeared
at Paris in 1838, the entire first edition of volume I, save some half
dozen that he had carried home, being burned on the day that the printing
was completed. He was a great collector of early printed works on
mathematics, and was accused of having stolen large numbers of them from
other libraries. This accusation took him to London, where he bitterly
attacked his accusers. There were two auction sales of his library, and a
number of his books found their way into De Morgan's collection.
[21] Philo of Gadara lived in the
second century B.C. He was a pupil of Sporus, who worked on the problem
of the two mean proportionals.
[22] In his Histoire des
Mathématiques, the first edition of which appeared in 1758. Jean
Etienne Montucla was born at Lyons in 1725 and died at Versailles in
1799. He was therefore only thirty-three years old when his great work
appeared. The second edition, with additions by D'Alembert, appeared in
1799-1802. He also wrote a work on the quadrature of the circle,
Histoire des recherches sur la Quadrature du Cercle, which
appeared in 1754.
[23] Eutocius of Ascalon was born
in 480 A.D. He wrote commentaries on the first four books of the conics
of Apollonius of Perga (247-222 B.C.). He also wrote on the Sphere and
Cylinder and the Quadrature of the Circle, and on the two books on
Equilibrium of Archimedes (287-212 B.C.)
[24] Edward Cocker was born in 1631
and died between 1671 and 1677. His famous arithmetic appeared in 1677
and went through many editions. It was written in a style that appealed
to teachers, and was so popular that the expression "According to Cocker"
became a household phrase. Early in the nineteenth century there was a
similar saying in America, "According to Daboll," whose arithmetic had
some points of analogy to that of Cocker. Each had a well-known prototype
in the ancient saying, "He reckons like Nicomachus of Gerasa."
[25] So in the original, for
Barrême. François Barrême was to France what Cocker was to England. He
was born at Lyons in 1640, and died at Paris in 1703. He published
several arithmetics, dedicating them to his patron, Colbert. One of the
best known of his works is L'arithmétique, ou le livre facile pour
apprendre l'arithmétique soi-mème, 1677. The French word
barême or barrême, a ready-reckoner, is derived from his
name.
[26] Born at Rome, about 480 A.D.;
died at Pavia, 524. Gibbon speaks of him as "the last of the Romans whom
Cato or Tully could have acknowledged for their countryman." His works on
arithmetic, music, and geometry were classics in the medieval
schools.
[27] Johannes Campanus, of Novarra,
was chaplain to Pope Urban IV (1261-1264). He was one of the early
medieval translators of Euclid from the Arabic into Latin, and the first
printed edition of the Elements (Venice, 1482) was from his
translation. In this work he probably depended not a little upon at least
two or three earlier scholars. He also wrote De computo ecclesiastico
Calendarium, and De quadratura circuli.
[28] Archimedes gave 3-1/7, and
3-10/71 as the limits of the ratio of the circumference to the diameter
of a circle.
[29] Friedrich W. A. Murhard was
born at Cassel in 1779 and died there in 1853. His Bibliotheca
Mathematica, Leipsic, 1797-1805, is ill arranged and inaccurate, but
it is still a helpful bibliography. De Morgan speaks somewhere of his
indebtedness to it.
[30] Abraham Gotthelf Kästner was
born at Leipsic in 1719, and died at Göttingen in 1800. He was professor
of mathematics and physics at Göttingen. His Geschichte der
Mathematik (1796-1800) was a work of considerable merit. In the text
of the Budget of Paradoxes the name appears throughout as Kastner
instead of Kästner.
[31] Lucas Gauricus, or Luca
Gaurico, born at Giffoni, near Naples, in 1476; died at Rome in 1558. He
was an astrologer and mathematician, and was professor of mathematics at
Ferrara in 1531. In 1545 he became bishop of Cività Ducale.
[32] John Couch Adams was born at
Lidcot, Cornwall, in 1819, and died in 1892. He and Leverrier predicted
the discovery of Neptune from the perturbations in Uranus.
[33] Urbain-Jean-Joseph Leverrier
was born at Saint-Lô, Manche, in 1811, and died at Paris in 1877. It was
his data respecting the perturbations of Uranus that were used by Adams
and himself in locating Neptune.
[34] Joseph-Juste Scaliger, the
celebrated philologist, was born at Agen in 1540, and died at Leyden in
1609. His Cyclometrica elementa, to which De Morgan refers,
appeared at Leyden in 1594.
[35] The title is: In hoc libra
contenta.... Introductio i geometriā.... Liber de quadratura
circuli. Liber de cubicatione sphere. Perspectiva introductio.
Carolus Bovillus, or Charles Bouvelles (Boüelles, Bouilles, Bouvel), was
born at Saucourt, Picardy, about 1470, and died at Noyon about 1533. He
was canon and professor of theology at Noyon. His Introductio
contains considerable work on star polygons, a favorite study in the
Middle Ages and early Renaissance. His work Que hoc volumine
continētur. Liber de intellectu. Liber de sensu, etc., appeared
at Paris in 1509-10.
[36] Nicolaus Cusanus, Nicolaus
Chrypffs or Krebs, was born at Kues on the Mosel in 1401, and died at
Todi, Umbria, August 11, 1464. He held positions of honor in the church,
including the bishopric of Brescia. He was made a cardinal in 1448. He
wrote several works on mathematics, his Opuscula varia appearing
about 1490, probably at Strasburg, but published without date or place.
His Opera appeared at Paris in 1511 and again in 1514, and at
Basel in 1565.
[37] Henry Stephens (born at Paris
about 1528, died at Lyons in 1598) was one of the most successful
printers of his day. He was known as Typographus Parisiensis, and
to his press we owe some of the best works of the period.
[38] Jacobus Faber Stapulensis
(Jacques le Fèvre d'Estaples) was born at Estaples, near Amiens, in 1455,
and died at Nérac in 1536. He was a priest, vicar of the bishop of Meaux,
lecturer on philosophy at the Collège Lemoine in Paris, and tutor to
Charles, son of Francois I. He wrote on philosophy, theology, and
mathematics.
[39] Claude-François Milliet de
Challes was born at Chambéry in 1621, and died at Turin in 1678. He
edited Euclidis Elementorum libri octo in 1660, and published a
Cursus seu mundus mathematicus, which included a short history of
mathematics, in 1674. He also wrote on mathematical geography.
[40] This date should be 1503, if
he refers to the first edition. It is well known that this is the first
encyclopedia worthy the name to appear in print. It was written by
Gregorius Reisch (born at Balingen, and died at Freiburg in 1487), prior
of the cloister at Freiburg and confessor to Maximilian I. The first
edition appeared at Freiburg in 1503, and it passed through many editions
in the sixteenth and seventeenth centuries. The title of the 1504 edition
reads: Aepitoma omnis phylosophiae. alias Margarita phylosophica
tractans de omni genere scibili: Cum additionibus: Quae in alijs non
habentur.
[41] This is the Introductio in
arithmeticam Divi S. Boetii.... Epitome rerum geometricarum ex geometrica
introductio C. Bovilli. De quadratura circuli demonstratio ex
Campano, that appeared without date about 1507.
[42] Born at Liverpool in 1805, and
died there about 1872. He was a merchant, and in 1865 he published, at
Liverpool, a work entitled The Quadrature of the Circle, or the True
Ratio between the Diameter and Circumference geometrically and
mathematically demonstrated. In this he gives the ratio as exactly
3⅛.
[43] "That it would be impossible
to tell him exactly, since no one had yet been able to find precisely the
ratio of the circumference to the diameter."
[44] This is the Paris edition:
"Parisiis: ex officina Ascensiana anno Christi ... MDXIIII," as appears
by the colophon of the second volume to which De Morgan refers.
[45] Regiomontanus, or Johann
Müller of Königsberg (Regiomontanus), was born at Königsberg in
Franconia, June 5, 1436, and died at Rome July 6, 1476. He studied at
Vienna under the great astronomer Peuerbach, and was his most famous
pupil. He wrote numerous works, chiefly on astronomy. He is also known by
the names Ioannes de Monte Regio, de Regiomonte, Ioannes Germanus de
Regiomonte, etc.
[46] Henry Cornelius Agrippa was
born at Cologne in 1486 and died either at Lyons in 1534 or at Grenoble
in 1535. He was professor of theology at Cologne and also at Turin. After
the publication of his De Occulta Philosophia he was imprisoned
for sorcery. Both works appeared at Antwerp in 1530, and each passed
through a large number of editions. A French translation appeared in
Paris in 1582, and an English one in London in 1651.
[47] Nicolaus Remegius was born in
Lorraine in 1554, and died at Nancy in 1600. He was a jurist and
historian, and held the office of procurator general to the Duke of
Lorraine.
[48] This was at the storming of
the city by the British on May 4, 1799. From his having been born in
India, all this appealed strongly to the interests of De Morgan.
[49] Orontius Finaeus, or Oronce
Finé, was born at Briançon in 1494 and died at Paris, October 6, 1555. He
was imprisoned by François I for refusing to recognize the concordat
(1517). He was made professor of mathematics in the Collège Royal (later
called the Collège de France) in 1532. He wrote extensively on astronomy
and geometry, but was by no means a great scholar. He was a pretentious
man, and his works went through several editions. His
Protomathesis appeared at Paris in 1530-32. The work referred to
by De Morgan is the Quadratura circuli tandem inventa & clarissime
demonstrata ... Lutetiae Parisiorum, 1544, fol. In the 1556 edition
of his De rebus mathematicis, hactenus desideratis, Libri IIII,
published at Paris, the subtitle is: Quibus inter cætera, Circuli
quadratura Centum modis, & suprà, per eundem Orontium recenter
excogitatis, demonstratus, so that he kept up his efforts until his
death.
[50] Johannes Buteo (Boteo, Butéon,
Bateon) was born in Dauphiné c. 1485-1489, and died in a cloister in 1560
or 1564. Some writers give Charpey as the place and 1492 as the date of
his birth, and state that he died at Canar in 1572. He belonged to the
order of St. Anthony, and wrote chiefly on geometry, exposing the
pretenses of Finaeus. His Opera geometrica appeared at Lyons in
1554, and his Logistica and De quadratura circuli libri duo
at Lyons in 1559.
[51] This is the great French
algebraist, François Viète (Vieta), who was born at Fontenay-le-Comte in
1540, and died at Paris, December 13, 1603. His well-known Isagoge in
artem analyticam appeared at Tours in 1591. His Opera
mathematica was edited by Van Schooten in 1646.
[52] This is the De Rebus
mathematicis hactenus desideratis, Libri IIII, that appeared in Paris
in 1556. For the title page see Smith, D. E., Rara Arithmetica,
Boston, 1908, p. 280.
[53] The title is correct except
for a colon after Astronomicum. Nicolaus Raimarus Ursus was born
in Henstede or Hattstede, in Dithmarschen, and died at Prague in 1599 or
1600. He was a pupil of Tycho Brahe. He also wrote De astronomis
hypothesibus (1597) and Arithmetica analytica vulgo Cosa oder
Algebra (1601).
[54] Born at Dôle, Franche-Comté,
about 1550, died in Holland about 1600. The work to which reference is
made is the Quadrature du cercle, ou manière de trouver un quarré égal
au cercle donné, which appeared at Delft in 1584. Duchesne had the
courage of his convictions, not only on circle-squaring but on religion
as well, for he was obliged to leave France because of his conversion to
Calvinism. De Morgan's statement that his real name is Van der Eycke is
curious, since he was French born. The Dutch may have translated his name
when he became professor at Delft, but we might equally well say, that
his real name was Quercetanus or à Quercu.
[55] This was the father of Adriaan
Metius (1571-1635). He was a mathematician and military engineer, and
suggested the ratio 355/113 for π, a ratio
afterwards published by his son. The ratio, then new to Europe, had long
been known and used in China, having been found by Tsu Ch'ung-chih
(428-499 A.D.).
[56] This was Jost Bürgi, or Justus
Byrgius, the Swiss mathematician of whom Kepler wrote in 1627: "Apices
logistici Justo Byrgio multis annis ante editionem Neperianam viam
præiverunt ad hos ipsissimos logarithmos." He constructed a table of
antilogarithms (Arithmetische und geometrische Progress-Tabulen),
but it was not published until after Napier's work appeared.
[57] Ludolphus Van Ceulen, born at
Hildesheim, and died at Leyden in 1610. It was he who first carried the
computation of π to 35 decimal places.
[58] Jens Jenssen Dodt, van
Flensburg, a Dutch historian, who died in 1847.
[59] I do not know this edition.
There was one "Antverpiae apud Petrum Bellerum sub scuto Burgundiae,"
4to, in 1591.
[60] Archytas of Tarentum (430-365
B.C.) who wrote on proportions, irrationals, and the duplication of the
cube.
[61]
The Circle Speaks.
"At first a circle I was called,
And was a curve around about
Like lofty orbit of the sun
Or rainbow arch among the clouds.
A noble figure then was I—
And lacking nothing but a start,
And lacking nothing but an end.
But now unlovely do I seem
Polluted by some angles new.
This thing Archytas hath not done
Nor noble sire of Icarus
Nor son of thine, Iapetus.
What accident or god can then
Have quadrated mine area?"
The Author Replies.
"By deepest mouth of Turia
And lake of limpid clearness, lies
A happy state not far removed
From old Saguntus; farther yet
A little way from Sucro town.
In this place doth a poet dwell,
Who oft the stars will closely scan,
And always for himself doth claim
What is denied to wiser men;—
An old man musing here and there
And oft forgetful of himself,
Not knowing how to rightly place
The compasses, nor draw a line,
As he doth of himself relate.
This craftsman fine, in sooth it is
Hath quadrated thine area."
[62] Pietro Bongo, or Petrus
Bungus, was born at Bergamo, and died there in 1601. His work on the
Mystery of Numbers is one of the most exhaustive and erudite ones of the
mystic writers. The first edition appeared at Bergamo in 1583-84; the
second, at Bergamo in 1584-85; the third, at Venice in 1585; the fourth,
at Bergamo in 1590; and the fifth, which De Morgan calls the second, in
1591. Other editions, before the Paris edition to which he refers,
appeared in 1599 and 1614; and the colophon of the Paris edition is dated
1617. See the editor's Rara Arithmetica, pp. 380-383.
[63] William Warburton (1698-1779),
Bishop of Gloucester, whose works got him into numerous literary
quarrels, being the subject of frequent satire.
[64] Thomas Galloway (1796-1851),
who was professor of mathematics at Sandhurst for a time, and was later
the actuary of the Amicable Life Assurance Company of London. In the
latter capacity he naturally came to be associated with De Morgan.
[65] Giordano Bruno was born near
Naples about 1550. He left the Dominican order to take up Calvinism, and
among his publications was L'expulsion de la bête triomphante. He
taught philosophy at Paris and Wittenberg, and some of his works were
published in England in 1583-86. Whether or not he was roasted alive "for
the maintenance and defence of the holy Church," as De Morgan states,
depends upon one's religious point of view. At any rate, he was roasted
as a heretic.
[66] Referring to part of his
Discours de la méthode, Leyden, 1637.
[67] Bartholomew Legate, who was
born in Essex about 1575. He denied the divinity of Christ and was the
last heretic burned at Smithfield.
[68] Edward Wightman, born probably
in Staffordshire. He was anti-Trinitarian, and claimed to be the Messiah.
He was the last man burned for heresy in England.
[69] Gaspar Schopp, born at
Neumarck in 1576, died at Padua in 1649; grammarian, philologist, and
satirist.
[70] Konrad Ritterhusius, born at
Brunswick in 1560; died at Altdorf in 1613. He was a jurist of some
power.
[71] Johann Jakob Brucker, born at
Augsburg in 1696, died there in 1770. He wrote on the history of
philosophy (1731-36, and 1742-44).
[72] Daniel Georg Morhof, born at
Wismar in 1639, died at Lübeck in 1691. He was rector of the University
of Kiel, and professor of eloquence, poetry, and history.
[73] In the Histoire des
Sciences Mathématiques, vol. IV, note X, pp. 416-435 of the 1841
edition.
[74] Colenso (1814-1883),
missionary bishop of Natal, was one of the leaders of his day in the
field of higher biblical criticism. De Morgan must have admired his
mathematical works, which were not without merit.
[75] Samuel Roffey Maitland, born
at London in 1792; died at Gloucester in 1866. He was an excellent
linguist and a critical student of the Bible. He became librarian at
Lambeth in 1838.
[76] Archbishop Howley (1766-1848)
was a thorough Tory. He was one of the opponents of the Roman Catholic
Relief bill, the Reform bill, and the Jewish Civil Disabilities Relief
bill.
[77] We have, in America at least,
almost forgotten the great stir made by Edward B. Pusey (1800-1882) in
the great Oxford movement in the middle of the nineteenth century. He was
professor of Hebrew at Oxford, and canon of Christ Church.
[78] That is, his Magia
universalis naturae et artis sive recondita naturalium et artificialium
rerum scientia, Würzburg, 1657, 4to, with editions at Bamberg in
1671, and at Frankfort in 1677. Gaspard Schott (Königshofen 1608,
Würzburg 1666) was a physicist and mathematician, devoting most of his
attention to the curiosities of his sciences. His type of mind must have
appealed to De Morgan.
[79] Salicetti Quadratura
circuli nova, perspicua, expedita, veraque tum naturalis, tum
geometrica, etc., 1608.—Consideratio nova in opusculum
Archimedis de circuli dimensione, etc., 1609.
[80] Melchior Adam, who died at
Heidelberg in 1622, wrote a collection of biographies which was published
at Heidelberg and Frankfort from 1615 to 1620.
[81] Born at Baden in 1524; died at
Basel in 1583. The Erastians were related to the Zwinglians, and opposed
all power of excommunication and the infliction of penalties by a
church.
[82] See Acts xii. 20.
[83] Theodore de Bèse, a French
theologian; born at Vezelay, in Burgundy, in 1519; died at Geneva, in
1605.
[84] Dr. Robert Lee (1804-1868) had
some celebrity in De Morgan's time through his attempt to introduce music
and written prayers into the service of the Scotch Presbyterian
church.
[85] Born at Veringen,
Hohenzollern, in 1512; died at Röteln in 1564.
[86] Born at Kinnairdie,
Bannfshire, in 1661; died at London in 1708. His Astronomiae Physicae
et Geometriae Elementa, Oxford, 1702, was an influential work.
[87] The title was carelessly
copied by De Morgan, not an unusual thing in his case. The original
reads: A Plaine Discovery, of the whole Revelation of S. Iohn: set downe
in two treatises ... set foorth by John Napier L. of Marchiston ...
whereunto are annexed, certaine Oracles of Sibylla ... London ...
1611.
[88] I have not seen the first
edition, but it seems to have appeared in Edinburgh, in 1593, with a
second edition there in 1594. The 1611 edition was the third.
[89] It seems rather certain that
Napier felt his theological work of greater importance than that in
logarithms. He was born at Merchiston, near (now a part of) Edinburgh, in
1550, and died there in 1617, three years after the appearance of his
Mirifici logarithmorum canonis descriptio.
[90] Followed, in the third
edition, from which he quotes, by a comma.
[91] There was an edition published
at Stettin in 1633. An English translation by P. F. Mottelay appeared at
London in 1893. Gilbert (1540-1603) was physician to Queen Elizabeth and
President of the College of Physicians at London. His De Magnete
was the first noteworthy treatise on physics printed in England. He
treated of the earth as a spherical magnet and suggested the variation
and declination of the needle as a means of finding latitude at sea.
[92] The title says "ab authoris
fratre collectum," although it was edited by J. Gruterus.
[93] Porta was born at Naples in
1550 and died there in 1615. He studied the subject of lenses and the
theory of sight, did some work in hydraulics and agriculture, and was
well known as an astrologer. His Magiae naturalis libri XX was
published at Naples in 1589. The above title should read
curvilineorum.
[94] Cataldi was born in 1548 and
died at Bologna in 1626. He was professor of mathematics at Perugia,
Florence, and Bologna, and is known in mathematics chiefly for his work
in continued fractions. He was one of the scholarly men of his day.
[95] Georg Joachim Rheticus was
born at Feldkirch in 1514 and died at Caschau, Hungary, in 1576. He was
one of the most prominent pupils of Copernicus, his Narratio de libris
revolutionum Copernici (Dantzig, 1540) having done much to make the
theory of his master known.
[96] Henry Briggs, who did so much
to make logarithms known, and who used the base 10, was born at Warley
Wood, in Yorkshire, in 1560, and died at Oxford in 1630. He was Savilian
professor of mathematics at Oxford, and his grave may still be seen
there.
[97] He lived at "Reggio nella
Emilia" in the 16th and 17th centuries. His Regola e modo facilissimo
di quadrare il cerchio was published at Reggio in 1609.
[98] Christoph Klau (Clavius) was
born at Bamberg in 1537, and died at Rome in 1612. He was a Jesuit priest
and taught mathematics in the Jesuit College at Rome. He wrote a number
of works on mathematics, including excellent text-books on arithmetic and
algebra.
[99] Christopher Gruenberger, or
Grienberger, was born at Halle in Tyrol in 1561, and died at Rome in
1636. He was, like Clavius, a Jesuit and a mathematician, and he wrote a
little upon the subject of projections. His Prospectiva nova
coelestis appeared at Rome in 1612.
[100] The name should, of course,
be Lansbergii in the genitive, and is so in the original title. Philippus
Lansbergius was born at Ghent in 1560, and died at Middelburg in 1632. He
was a Protestant theologian, and was also a physician and astronomer. He
was a well-known supporter of Galileo and Copernicus. His
Commentationes in motum terrae diurnum et annuum appeared at
Middelburg in 1630 and did much to help the new theory.
[101] I have never seen the work.
It is rare.
[102] The African explorer, born
in Somersetshire in 1827, died at Bath in 1864. He was the first European
to cross Central Africa from north to south. He investigated the sources
of the Nile.
[103] Prester (Presbyter, priest)
John, the legendary Christian king whose realm, in the Middle Ages, was
placed both in Asia and in Africa, is first mentioned in the chronicles
of Otto of Freisingen in the 12th century. In the 14th century his
kingdom was supposed to be Abyssinia.
[104] "It is a profane and
barbarous nation, dirty and slovenly, who eat their meat half raw and
drink mare's milk, and who use table-cloths and napkins only to wipe
their hands and mouths."
[105] "The great Prester John,
who is the fourth in rank, is emperor of Ethiopia and of the Abyssinians,
and boasts of his descent from the race of David, as having descended
from the Queen of Sheba, Queen of Ethiopia. She, having gone to Jerusalem
to see the wisdom of Solomon, about the year of the world 2952, returned
pregnant with a son whom they called Moylech, from whom they claim
descent in a direct line. And so he glories in being the most ancient
monarch in the world, saying that his empire has endured for more than
three thousand years, which no other empire is able to assert. He also
puts into his titles the following: 'We, the sovereign in my realms,
uniquely beloved of God, pillar of the faith, sprung from the race of
Judah, etc.' The boundaries of this empire touch the Red Sea and the
mountains of Azuma on the east, and on the western side it is bordered by
the River Nile which separates it from Nubia. To the north lies Egypt,
and to the south the kingdoms of Congo and Mozambique. It extends forty
degrees in length, or one thousand twenty-five leagues, from Congo or
Mozambique on the south to Egypt on the north; and in width it reaches
from the Nile on the west to the mountains of Azuma on the east, seven
hundred twenty-five leagues, or twenty-nine degrees. This empire contains
thirty large provinces, namely Medra, Gaga, Alchy, Cedalon, Mantro,
Finazam, Barnaquez, Ambiam, Fungy, Angoté, Cigremaon, Gorga, Cafatez,
Zastanla, Zeth, Barly, Belangana, Tygra, Gorgany, Barganaza, d'Ancut,
Dargaly, Ambiacatina, Caracogly, Amara, Maon (sic), Guegiera,
Bally, Dobora, and Macheda. All of these provinces are situated directly
under the equinoctial line between the tropics of Capricorn and Cancer;
but they are two hundred fifty leagues nearer our tropic than the other.
The name of Prester John signifies Great Lord, and is not Priest
[Presbyter] as many think. He has always been a Christian, but often
schismatic. At the present time he is a Catholic and recognizes the Pope
as sovereign pontiff. I met one of his bishops in Jerusalem, and often
conversed with him through the medium of our guide. He was of grave and
serious bearing, pleasant of speech, but wonderfully subtle in everything
he said. He took great delight in what I had to relate concerning our
beautiful ceremonies and the dignity of our prelates in their pontifical
vestments. As to other matters I will only say that the Ethiopian is
joyous and merry, not at all like the Tartar in the matter of filth, nor
like the wretched Arab. They are refined and subtle, trusting no one,
wonderfully suspicious, and very devout. They are not at all black as is
commonly supposed, by which I refer to those who do not live under the
equator or too near to it, for these are Moors as we shall see."
With respect to this translation it should be said that the original
forms of the proper names have been preserved, although they are not
those found in modern works. It should also be stated that the meaning of
Prester is not the one that was generally accepted by scholars at the
time the work was written, nor is it the one accepted to-day. There seems
to be no doubt that the word is derived from Presbyter as stated in note
103 on page 71, since the
above-mentioned chronicles of Otto, bishop of Freisingen about the middle
of the twelfth century, states this fact clearly. Otto received his
information from the bishop of Gabala (the Syrian Jibal) who told him the
story of John, rex et sacerdos, or Presbyter John as he liked to
be called. He goes on to say "Should it be asked why, with all this power
and splendor, he calls himself merely 'presbyter,' this is because of his
humility, and because it was not fitting for one whose server was a
primate and king, whose butler an archbishop and king, whose chamberlain
a bishop and king, whose master of the horse an archimandrite and king,
whose chief cook an abbot and king, to be called by such titles as
these."
[106] Thomas Fienus (Fyens) was
born at Antwerp in 1567 and died in 1631. He was professor of medicine at
Louvain. Besides the editions mentioned below, his De cometis anni
1618 appeared at Leipsic in 1656. He also wrote a Disputatio an
coelum moveatur et terra quiescat, which appeared at Antwerp in 1619,
and again at Leipsic in 1656.
[107] Libertus Fromondus (1587-c
1653), a Belgian theologian, dean of the College Church at Harcourt, and
professor at Louvain. The name also appears as Froidmont and
Froimont.
[108] L. Fromondi ...
meteorologicorum libri sex.... Cui accessit T. Fieni et L. Fromondi
dissertationes de cometa anni 1618.... This is from the 1670 edition.
The 1619 edition was published at Antwerp. The Meteorologicorum libri
VI, appeared at Antwerp in 1627. He also wrote Anti-Aristarchus
sive orbis terrae immobilis liber unicus (Antwerp, 1631);
Labyrrinthus sive de compositione continui liber unus, Philosophis,
Mathematicis, Theologis utilis et jucundus (Antwerp, 1631) and
Vesta sive Anti-Aristarchi vindex adversus Jac. Lansbergium (Philippi
filium) et copernicanos (Antwerp, 1634).
[109] Snell was born at Leyden in
1591, and died there in 1626. He studied under Tycho Brahe and Kepler,
and is known for Snell's law of the refraction of light. He was the first
to determine the size of the earth by measuring the arc of a meridian
with any fair degree of accuracy. The title should read: Willebrordi
Snellii R. F. Cyclometricus, de circuli dimensione secundum Logistarum
abacos, et ad Mechanicem accuratissima....
[110] Bacon was born at York
House, London, in 1561, and died near Highgate, London, in 1626. His
Novum Organum Scientiarum or New Method of employing the reasoning
faculties in the pursuits of Truth appeared at London in 1620. He had
previously published a work entitled Of the Proficience and
Advancement of Learning, divine and humane (London, 1605), which
again appeared in 1621. His De augmentis scientiarum Libri IX
appeared at Paris in 1624, and his Historia naturalis et
experimentalis de ventis at Leyden in 1638. He was successively
solicitor general, attorney general, lord chancellor (1619), Baron
Verulam and Viscount St. Albans. He was deprived of office and was
imprisoned in the Tower of London in 1621, but was later pardoned.
[111] The Greek form,
Organon, is sometimes used.
[112] James Spedding (1808-1881),
fellow of Cambridge, who devoted his life to his edition of Bacon.
[113] R. Leslie Ellis
(1817-1859), editor of the Cambridge Mathematical Journal. He also
wrote on Roman aqueducts, on Boole's Laws of Thought, and on the
formation of a Chinese dictionary.
[114] Douglas Derion Heath
(1811-1897), a classical and mathematical scholar.
[115] There have been numerous
editions of Bacon's complete works, including the following: Frankfort,
1665; London, 1730, 1740, 1764, 1765, 1778, 1803, 1807, 1818, 1819, 1824,
1825-36, 1857-74, 1877. The edition to which De Morgan refers is that of
1857-74, 14 vols., of which five were apparently out at the time he
wrote. There were also French editions in 1800 and 1835.
[116] So in the original for
Tycho Brahe.
[117] In general these men acted
before Baron wrote, or at any rate, before he wrote the Novum
Organum, but the statement must not be taken too literally. The dates
are as follows: Copernicus, 1473-1543; Tycho Brahe, 1546-1601; Gilbert,
1540-1603; Kepler, 1571-1630; Galileo, 1564-1642; Harvey, 1578-1657. For
example, Harvey's Exercitatio Anatomica de Motu Cordis et
Sanguinis did not appear until 1628, and his Exercitationes de
Generatione until 1651.
[118] Robert Hooke (1635-1703)
studied under Robert Boyle at Oxford. He was "Curator of Experiments" to
the Royal Society and its secretary, and was professor of geometry at
Gresham College, London. It is true that he was "very little of a
mathematician" although he wrote on the motion of the earth (1674), on
helioscopes and other instruments (1675), on the rotation of Jupiter
(1666), and on barometers and sails.
[119] The son of the Sir William
mentioned below. He was born in 1792 and died in 1871. He wrote a
treatise on light (1831) and one on astronomy (1836), and established an
observatory at the Cape of Good Hope where he made observations during
1834-1838, publishing them in 1847. On his return to England he was
knighted, and in 1848 was made president of the Royal Society. The title
of the work to which reference is made is: A preliminary discourse on
the Study of Natural Philosophy. It appeared at London in 1831.
[120] Sir William was horn at
Hanover in 1738 and died at Slough, near Windsor in 1822. He discovered
the planet Uranus and six satellites, besides two satellites of Saturn.
He was knighted by George III.
[121] This was the work of 1836.
He also published a work entitled Outlines of Astronomy in
1849.
[122] While Newton does not tell
the story, he refers in the Principia (1714 edition, p. 293) to
the accident caused by his cat.
[123] Marino Ghetaldi
(1566-1627), whose Promotus Archimedes appeared at Rome in 1603,
Nonnullae propositiones de parabola at Rome in 1603. and
Apollonius redivivus at Venice in 1607. He was a nobleman and was
ambassador from Venice to Rome.
[124] Simon Stevin (born at
Bruges, 1548; died at the Hague, 1620). He was an engineer and a soldier,
and his La Disme (1585) was the first separate treatise on the
decimal fraction. The contribution referred to above is probably that on
the center of gravity of three bodies (1586).
[125] Habakuk Guldin (1577-1643),
who took the name Paul on his conversion to Catholicism. He became a
Jesuit, and was professor of mathematics at Vienna and later at Gratz. In
his Centrobaryca seu de centro gravitatis trium specierum quantitatis
continuae (1635), of the edition of 1641, appears the Pappus rule for
the volume of a solid formed by the revolution of a plane figure about an
axis, often spoken of as Guldin's Theorem.
[126] Edward Wright was born at
Graveston, Norfolkshire, in 1560, and died at London in 1615. He was a
fellow of Caius College, Cambridge, and in his work entitled The
correction of certain errors in Navigation (1599) he gives the
principle of Mercator's projection. He translated the Portuum
investigandorum ratio of Stevin in 1599.
[127] De Morgan never wrote a
more suggestive sentence. Its message is not for his generation
alone.
[128] The eminent French
physicist, Jean Baptiste Biot (1779-1862), professor in the Collège de
France. His work Sur les observatoires météorologiques appeared in
1855.
[129] George Biddell Airy
(1801-1892), professor of astronomy and physics at Cambridge, and
afterwards director of the Observatory at Greenwich.
[130] De Morgan would have
rejoiced in the rôle played by Intuition in the mathematics of to-day,
notably among the followers of Professor Klein.
[131] Colburn was the best known
of the calculating boys produced in America. He was born at Cabot,
Vermont, in 1804, and died at Norwich, Vermont, in 1840. Having shown
remarkable skill in numbers as early as 1810, he was taken to London in
1812, whence he toured through Great Britain and to Paris. The Earl of
Bristol placed him in Westminster School (1816-1819). On his return to
America he became a preacher, and later a teacher of languages.
[132] The history of calculating
boys is interesting. Mathieu le Coc (about 1664), a boy of Lorraine,
could extract cube roots at sight at the age of eight. Tom Fuller, a
Virginian slave of the eighteenth century, although illiterate, gave the
number of seconds in 7 years 17 days 12 hours after only a minute and a
half of thought. Jedediah Buxton, an Englishman of the eighteenth
century, was studied by the Royal Society because of his remarkable
powers. Ampère, the physicist, made long calculations with pebbles at the
age of four. Gauss, one of the few infant prodigies to become an adult
prodigy, corrected his father's payroll at the age of three. One of the
most remarkable of the French calculating boys was Henri Mondeux. He was
investigated by Arago, Sturm, Cauchy, and Liouville, for the Académie des
Sciences, and a report was written by Cauchy. His specialty was the
solution of algebraic problems mentally. He seems to have calculated
squares and cubes by a binomial formula of his own invention. He died in
obscurity, but was the subject of a Biographie by Jacoby (1846).
George P. Bidder, the Scotch engineer (1806-1878), was exhibited as an
arithmetical prodigy at the age of ten, and did not attend school until
he was twelve. Of the recent cases two deserve special mention, Inaudi
and Diamandi. Jacques Inaudi (born in 1867) was investigated for the
Académie in 1892 by a commission including Poincaré, Charcot, and Binet.
(See the Revue des Deux Mondes, June 15, 1892, and the laboratory
bulletins of the Sorbonne). He has frequently exhibited his remarkable
powers in America. Périclès Diamandi was investigated by the same
commission in 1893. See Alfred Binet, Psychologie des Grands
Calculateurs et Joueurs d'Echecs, Paris, 1894.
[133] John Flamsteed's
(1646-1719) "old white house" was the first Greenwich observatory. He was
the Astronomer Royal and first head of this observatory.
[134] It seems a pity that De
Morgan should not have lived to lash those of our time who are demanding
only the immediately practical in mathematics. His satire would have been
worth the reading against those who seek to stifle the science they
pretend to foster.
[135] Ismael Bouillaud, or
Boulliau, was born in 1605 and died at Paris in 1694. He was well known
as an astronomer, mathematician, and jurist. He lived with De Thou at
Paris, and accompanied him to Holland. He traveled extensively, and was
versed in the astronomical work of the Persians and Arabs. It was in his
Astronomia philolaica, opus novum (Paris, 1645) that he attacked
Kepler's laws. His tables were shown to be erroneous by the fact that the
solar eclipse did not take place as predicted by him in 1645.
[136] As it did, until 1892, when
Airy had reached the ripe age of ninety-one.
[137] Didaci a Stunica ... In
Job commentaria appeared at Toledo in 1584.
[138] "The false Pythagorean
doctrine, absolutely opposed to the Holy Scriptures, concerning the
mobility of the earth and the immobility of the sun."
[139] Paolo Antonio Foscarini
(1580-1616), who taught theology and philosophy at Naples and Messina,
was one of the first to champion the theories of Copernicus. This was in
his Lettera sopra l'opinione de' Pittagorici e del Copernico, della
mobilità della Terra e stabilità del Sole, e il nuovo pittagorico sistema
del mondo, 4to, Naples, 1615. The condemnation of the Congregation
was published in the following spring, and in the year of Foscarini's
death at the early age of thirty-six.
[140] "To be wholly prohibited
and condemned," because "it seeks to show that the aforesaid doctrine is
consonant with truth and is not opposed to the Holy Scriptures."
[141] "As repugnant to the Holy
Scriptures and to its true and Catholic interpretation (which in a
Christian man cannot be tolerated in the least), he does not hesitate to
treat (of his subject) 'by hypothesis', but he even adds 'as
most true'!"
[142] "To the places in which he
discusses not by hypothesis but by making assertions concerning the
position and motion of the earth."
[143] "Copernicus. If by
chance there shall be vain talkers who, although ignorant of all
mathematics, yet taking it upon themselves to sit in judgment upon the
subject on account of a certain passage of Scripture badly distorted for
their purposes, shall have dared to criticize and censure this teaching
of mine, I pay no attention to them, even to the extent of despising
their judgment as rash. For it is not unknown that Lactantius, a writer
of prominence in other lines although but little versed in mathematics,
spoke very childishly about the form of the earth when he ridiculed those
who declared that it was spherical. Hence it should not seem strange to
the learned if some shall look upon us in the same way. Mathematics is
written for mathematicians, to whom these labors of ours will seem, if I
mistake not, to add something even to the republic of the Church....
Emend. Here strike out everything from 'if by chance' to the words
'these labors of ours,' and adapt it thus: 'But these labors of
ours.'"
[144] "Copernicus. However
if we consider the matter more carefully it will be seen that the
investigation is not yet completed, and therefore ought by no means to be
condemned. Emend. However, if we consider the matter more
carefully it is of no consequence whether we regard the earth as existing
in the center of the universe or outside of the center, so far as the
solution of the phenomena of celestial movements is concerned."
[145] "The whole of this chapter
may be cut out, since it avowedly treats of the earth's motion, while it
refutes the reasons of the ancients proving its immobility. Nevertheless,
since it seems to speak problematically, in order that it may satisfy the
learned and keep intact the sequence and unity of the book let it be
emended as below."
[146] "Copernicus.
Therefore why do we still hesitate to concede to it motion which is by
nature consistent with its form, the more so because the whole universe
is moving, whose end is not and cannot be known, and not confess that
there is in the sky an appearance of daily revolution, while on the earth
there is the truth of it? And in like manner these things are as if
Virgil's Æneas should say, 'We are borne from the harbor' ...
Emend. Hence I cannot concede motion to this form, the more so
because the universe would fall, whose end is not and cannot be known,
and what appears in the heavens is just as if ..."
[147] "Copernicus. I also
add that it would seem very absurd that motion should be ascribed to that
which contains and locates, and not rather to that which is contained and
located, that is the earth. Emend. I also add that it is not more
difficult to ascribe motion to the contained and located, which is the
earth, than to that which contains it."
[148] "Copernicus. You
see, therefore, that from all these things the motion of the earth is
more probable than its immobility, especially in the daily revolution
which is as it were a particular property of it. Emend. Omit from
'You see' to the end of the chapter."
[149] "Copernicus.
Therefore, since there is nothing to hinder the motion of the earth, it
seems to me that we should consider whether it has several motions, to
the end that it may be looked upon as one of the moving stars.
Emend. Therefore, since I have assumed that the earth moves, it
seems to me that we should consider whether it has several motions."
[150] "Copernicus. We are
not ashamed to acknowledge ... that this is preferably verified in the
motion of the earth. Emend. We are not ashamed to assume ... that
this is consequently verified in the motion."
[151] "Copernicus. So
divine is surely this work of the Best and Greatest. Emend. Strike
out these last words."
[152] This should be Cap. 11,
lib. i, p. 10.
[153] "Copernicus.
Demonstration of the threefold motion of the earth. Emend. On the
hypothesis of the threefold motion of the earth and its
demonstration."
[154] This should be Cap. 20,
lib. iv, p. 122.
[155] "Copernicus.
Concerning the size of these three stars, the sun, the moon and the
earth. Emend. Strike out the words 'these three stars,' because
the earth is not a star as Copernicus would make it."
[156] He seems to speak
problematically in order to satisfy the learned.
[157] One of the Church Fathers,
born about 250 A.D., and died about 330, probably at Trèves. He wrote
Divinarum Institutionum Libri VII. and other controversial and
didactic works against the learning and philosophy of the Greeks.
[158] Giovanni Battista Riccioli
(1598-1671) taught philosophy and theology at Parma and Bologna, and was
later professor of astronomy. His Almagestum novum appeared in
1651, and his Argomento fisico-matematico contro il moto diurno della
terra in 1668.
[159] He was a native of
Arlington, Sussex, and a pensioner of Christ's College, Cambridge. In
1603 he became a master of arts at Oxford.
[160] Straying, i.e., from the
right way.
[161] "Private subjects may, in
the presence of danger, defend themselves or their families against a
monarch as against any malefactor, if the monarch assaults them like a
bandit or a ravisher, and provided they are unable to summon the usual
protection and cannot in any way escape the danger."
[162] Daniel Neal (1678-1743), an
independent minister, wrote a History of the Puritans that
appeared in 1732. The account may be found in the New York edition of
1843-44, vol. I, p. 271.
[163] Anthony Wood (1632-1695),
whose Historia et Antiquitates Universitatis Oxoniensis (1674) and
Athenae Oxoniensis (1691) are among the classics on Oxford.
[164] Part of the title, not here
quoted, shows the nature of the work more clearly: "liber unicus, in quo
decretum S. Congregationis S. R. E. Cardinal. an. 1616, adversus
Pythagorico-Copernicanos editum defenditur."
[165] This was John Elliot
Drinkwater Bethune (1801-1851), the statesman who did so much for
legislative and educational reform in India. His father, John Drinkwater
Bethune, wrote a history of the siege of Gibraltar.
[166] The article referred to is
about thirty years old; since it appeared another has been given
(Dubl. Rev., Sept. 1865) which is of much greater depth. In it
will also be found the Roman view of Bishop Virgil (ante, p.
32).—A. De M.
[167] Jean Baptiste Morin
(1583-1656), in his younger days physician to the Bishop of Boulogne and
the Duke of Luxemburg, became in 1630 professor of mathematics at the
Collège Royale. His chief contribution to the problem of the
determination of longitude is his Longitudinum terrestrium et
coelestium nova et hactenus optata scientia (1634). He also wrote
against Copernicus in his Famosi problematis de telluris motu vel
quiete hactenus optata solutio (1631), and against Lansberg in his
Responsio pro telluris quiete (1634).
[168] The work appeared at Leyden
in 1626, at Amsterdam in 1634, at Copenhagen in 1640 and again at Leyden
in 1650. The title of the 1640 edition is Arithmeticae Libri II et
Geometriae Libri VI. The work on which it is based is the
Arithmeticae et Geometriae Practica, which appeared in 1611.
[169] The father's name was
Adriaan, and Lalande says that it was Montucla who first made the mistake
of calling him Peter, thinking that the initials P. M. stood for Petrus
Metius, when in reality they stood for piae memoriae! The ratio
355/113 was known in China hundreds of years before his time. See note 55, page 52.
[170] Adrian Metius (1571-1635)
was professor of medicine at the University of Franeker. His work was,
however, in the domain of astronomy, and in this domain he published
several treatises.
[171] The first edition was
entitled: The Discovery of a World in the Moone. Or, a Discourse
Tending to prove that 'tis probable there may be another habitable World
in that Planet. 1638, 8vo. The fourth edition appeared in 1684. John
Wilkins (1614-1672) was Warden of Wadham College, Oxford; master of
Trinity, Cambridge; and, later, Bishop of Chester. He was influential in
founding the Royal Society.
[172] The first edition was
entitled: C. Hugenii Κοσμοθεωρος,
sive de Terris coelestibus, earumque ornatu, conjecturae, The
Hague, 1698, 4to. There were several editions. It was also translated
into French (1718), and there was another English edition (1722).
Huyghens (1629-1695) was one of the best mathematical physicists of his
time.
[173] It is hardly necessary to
say that science has made enormous advance in the chemistry of the
universe since these words were written.
[174] William Whewell (1794-1866)
is best known through his History of the Inductive Sciences (1837)
and Philosophy of the Inductive Sciences (1840).
[175] Thomas Chalmers
(1780-1847), the celebrated Scotch preacher. These discourses were
delivered while he was minister in a large parish in the poorest part of
Glasgow, and in them he attempted to bring science into harmony with the
Bible. He was afterwards professor of moral philosophy at St. Andrew's
(1823-28), and professor of theology at Edinburgh (1828). He became the
leader of a schism from the Scotch Presbyterian Church,—the Free
Church.
[176] That is, in Robert Watt's
(1774-1819) Bibliotheca Britannica (posthumous, 1824). Nor is it
given in the Dictionary of National Biography.
[177] The late Greek satirist and
poet, c. 120-c. 200 A.D.
[178] François Rabelais (c.
1490-1553) the humorist who created Pantagruel (1533) and Gargantua
(1532). His work as a physician and as editor of the works of Galen and
Hippocrates is less popularly known.
[179] Francis Godwin (1562-1633)
bishop of Llandaff and Hereford. Besides some valuable historical works
he wrote The Man in the Moone, or a Discourse of a voyage thither by
Domingo Gonsales, the Speed Messenger of London, 1638.
[180] Bernard Le Bovier de
Fontenelle (1657-1757), historian, critic, mathematician, Secretary of
the Académie des Sciences, and member of the Académie Française. His
Entretien sur la pluralité des mondes appeared at Paris in
1686.
[181] Athanasius Kircher
(1602-1680), Jesuit, professor of mathematics and philosophy, and later
of Hebrew and Syriac, at Wurzburg; still later professor of mathematics
and Hebrew at Rome. He wrote several works on physics. His collection of
mathematical instruments and other antiquities became the basis of the
Kircherian Museum at Rome.
[182] "Both belief and non-belief
are dangerous. Hippolitus died because his stepmother was believed. Troy
fell because Cassandra was not believed. Therefore the truth should be
investigated long before foolish opinion can properly judge." (Prove =
probe?).
[183] Jacobus Grandamicus
(Jacques Grandami) was born at Nantes in 1588 and died at Paris in 1672.
He was professor of theology and philosophy in the Jesuit colleges at
Rennes, Tours, Rouen, and other places. He wrote several works on
astronomy.
[184] "And I, if I be lifted up
from the earth, will draw all men unto me." John xii. 32.
[185] Andrea Argoli (1568-1657)
wrote a number of works on astronomy, and computed ephemerides from 1621
to 1700.
[186] So in the original edition
of the Budget. It is Johannem Pellum in the original title. John
Pell (1610 or 1611-1685) studied at Cambridge and Oxford, and was
professor of mathematics at Amsterdam (1643-46) and Breda (1646-52). He
left many manuscripts but published little. His name attaches by accident
to an interesting equation recently studied with care by Dr. E. E.
Whitford (New York, 1912).
[187] Christianus Longomontanus
(Christen Longberg or Lumborg) was born in 1569 at Longberg, Jutland, and
died in 1647 at Copenhagen. He was an assistant of Tycho Brahe and
accepted the diurnal while denying the orbital motion of the earth. His
Cyclometria e lunulis reciproce demonstrata appeared in 1612 under
the name of Christen Severin, the latter being his family name. He wrote
several other works on the quadrature problem, and some treatises on
astronomy.
[188] The names are really pretty
well known. Giles Persone de Roberval was born at Roberval near Beauvais
in 1602, and died at Paris in 1675. He was professor of philosophy at the
Collège Gervais at Paris, and later at the Collège Royal. He claimed to
have discovered the theory of indivisibles before Cavalieri, and his work
is set forth in his Traité des indivisibles which appeared
posthumously in 1693.
Hobbes (1588-1679), the political and social philosopher, lived a good
part of his time (1610-41) in France where he was tutor to several young
noblemen, including the Cavendishes. His Leviathan (1651) is said
to have influenced Spinoza, Leibnitz, and Rousseau. His Quadratura
circuli, cubatio sphaerae, duplicatio cubi ... (London, 1669),
Rosetum geometricum ... (London, 1671), and Lux Mathematica,
censura doctrinae Wallisianae contra Rosetum Hobbesii (London, 1674)
are entirely forgotten to-day. (See a further note, infra.)
Pierre de Carcavi, a native of Lyons, died at Paris in 1684. He was a
member of parliament, royal librarian, and member of the Académie des
Sciences. His attempt to prove the impossibility of the quadrature
appeared in 1645. He was a frequent correspondent of Descartes.
Cavendish (1591-1654) was Sir (not Lord) Charles. He was, like De
Morgan himself, a bibliophile in the domain of mathematics. His life was
one of struggle, his term as member of parliament under Charles I being
followed by gallant service in the royal army. After the war he sought
refuge on the continent where he met most of the mathematicians of his
day. He left a number of manuscripts on mathematics, which his widow
promptly disposed of for waste paper. If De Morgan's manuscripts had been
so treated we should not have had his revision of his Budget of
Paradoxes.
Marin Mersenne (1588-1648), a minorite, living in the cloisters at
Nevers and Paris, was one of the greatest Franciscan scholars. He edited
Euclid, Apollonius, Archimedes, Theodosius, and Menelaus (Paris, 1626),
translated the Mechanics of Galileo into French (1634), wrote
Harmonicorum Libri XII (1636), and Cogitata
physico-mathematica (1644), and taught theology and philosophy at
Nevers.
Johann Adolph Tasse (Tassius) was born in 1585 and died at Hamburg in
1654. He was professor of mathematics in the Gymnasium at Hamburg, and
wrote numerous works on astronomy, chronology, statics, and elementary
mathematics.
Johann Ludwig, Baron von Wolzogen, seems to have been one of the early
unitarians, called Fratres Polonorum because they took refuge in
Poland. Some of his works appear in the Bibliotheca Fratrum
Polonorum (Amsterdam, 1656). I find no one by the name who was
contributing to mathematics at this time.
Descartes is too well known to need mention in this connection.
Bonaventura Cavalieri (1598-1647) was a Jesuit, a pupil of Galileo,
and professor of mathematics at Bologna. His greatest work, Geometria
indivisibilibus continuorum nova quadam ratione promota, in which he
makes a noteworthy step towards the calculus, appeared in 1635.
Jacob (Jacques) Golius was born at the Hague in 1596 and died at
Leyden in 1667. His travels in Morocco and Asia Minor (1622-1629) gave
him such knowledge of Arabic that he became professor of that language at
Leyden. After Snell's death he became professor of mathematics there. He
translated Arabic works on mathematics and astronomy into Latin.
[189] It would be interesting to
follow up these rumors, beginning perhaps with the tomb of Archimedes.
The Ludolph van Ceulen story is very likely a myth. The one about Fagnano
may be such. The Bernoulli tomb does have the spiral, however (such as it
is), as any one may see in the cloisters at Basel to-day.
[190] Collins (1625-1683) was
secretary of the Royal Society, and was "a kind of register of all new
improvements in mathematics." His office brought him into correspondence
with all of the English scientists, and he was influential in the
publication of various important works, including Branker's translation
of the algebra by Rhonius, with notes by Pell, which was the first work
to contain the present English-American symbol of division. He also
helped in the publication of editions of Archimedes and Apollonius, of
Kersey's Algebra, and of the works of Wallis. His profession was that of
accountant and civil engineer, and he wrote three unimportant works on
mathematics (one published posthumously, and the others in 1652 and
1658).
Heinrich Christian Schumacher (1780-1850) was professor of astronomy
at Copenhagen and director of the observatory at Altona. His translation
of Carnot's Géométrie de position (1807) brought him into personal
relations with Gauss, and the friendship was helpful to Schumacher. He
was a member of many learned societies and had a large circle of
acquaintances. He published numerous monographs and works on
astronomy.
Gassendi (1592-1655) might well have been included by De Morgan in the
group, since he knew and was a friend of most of the important
mathematicians of his day. Like Mersenne, he was a minorite, but he was a
friend of Galileo and Kepler, and wrote a work under the title
Institutio astronomica, juxta hypotheses Copernici, Tychonis-Brahaei
et Ptolemaei (1645). He taught philosophy at Aix, and was later
professor of mathematics at the College Royal at Paris.
Burnet is the Bishop Gilbert Burnet (1643-1715) who was so strongly
anti-Romanistic that he left England during the reign of James II and
joined the ranks of the Prince of Orange. William made him bishop of
Salisbury.
[191] There is some substantial
basis for De Morgan's doubts as to the connection of that
mirandula of his age, Sir Kenelm Digby (1603-1665), with the
famous poudre de sympathie. It is true that he was just the one to
prepare such a powder. A dilletante in everything,—learning, war,
diplomacy, religion, letters, and science—he was the one to exploit
a fraud of this nature. He was an astrologer, an alchemist, and a
fabricator of tales, and well did Henry Stubbes characterize him as "the
very Pliny of our age for lying." He first speaks of the powder in a
lecture given at Montpellier in 1658, and in the same year he published
the address at Paris under the title: Discours fait en une célèbre
assemblée par le chevalier Digby .... touchant la guérison de playes par
la poudre de sympathie. The London edition referred to by De Morgan
also came out in 1658, and several editions followed it in England,
France and Germany. But Nathaniel Highmore in his History of
Generation (1651) referred to the concoction as "Talbot's Powder"
some years before Digby took it up. The basis seems to have been vitriol,
and it was claimed that it would heal a wound by simply being applied to
a bandage taken from it.
[192] This work by Thomas Birch
(1705-1766) came out in 1756-57. Birch was a voluminous writer on English
history. He was a friend of Dr. Johnson and of Walpole, and he wrote a
life of Robert Boyle.
[193] We know so much about John
Evelyn (1620-1706) through the diary which he began at the age of eleven,
that we forget his works on navigation and architecture.
[194] I suppose this was the
seventh Earl of Shrewsbury (1553-1616).
[195] This is interesting in view
of the modern aseptic practice of surgery and the antiseptic treatment of
wounds inaugurated by the late Lord Lister.
[196] Perhaps De Morgan had not
heard the bon mot of Dr. Holmes: "I firmly believe that if the
whole materia medica could be sunk to the bottom of the sea, it
would be all the better for mankind and all the worse for the
fishes."
[197] The full title is worth
giving, because it shows the mathematical interests of Hobbes, and the
nature of the six dialogues: Examinatio et emendatio mathematicae
hodiernae qualis explicatur in libris Johannis Wallisii geometriae
professoris Saviliani in Academia Oxoniensi: distributa in sex dialogos
(1. De mathematicae origine ...; 2. De principiis traditis ab Euclide; 3.
De demonstratione operationum arithmeticarum ...; 4. De rationibus; 5. De
angula contactus, de sectionibus coni, et arithmetica infinitorum; 6.
Dimensio circuli tribus methodis demonstrata ... item cycloidis verae
descriptio et proprietates aliquot.) Londini, 1660 (not 1666). For a
full discussion of the controversy over the circle, see George Croom
Robertson's biography of Hobbes in the eleventh edition of the
Encyclopaedia Britannica.
[198] This is his
Animadversions upon Mr. Hobbes' late book De principiis et
ratiocinatione geometrarum, 1666, or his Hobbianae quadraturae
circuli, cubationis sphaerae et duplicationis cubi confutatio, also
of 1669.
[199] This is the work of 1669
referred to above.
[200] Gregoire de St. Vincent
(1584-1667) published his Opus geometricum quadraturae circuli et
sectionum coni at Antwerp in 1647.
[201] This appears in J.
Scaligeri cyclometrica elementa duo, Lugduni Batav., 1594.
[202] Adriaen van Roomen
(1561-1615) gave the value of π to sixteen
decimal places in his Ideae mathematicae pars prima (1593), and
wrote his In Archimedis circuli dimensionem expositio &
analysis in 1597.
[203] Kästner. See note 30 on page 43.
[204] Bentley (1662-1742) might
have done it, for as the head of Trinity College, Cambridge, and a
follower of Newton, he knew some mathematics. Erasmus (1466-1536) lived a
little too early to attempt it, although his brilliant satire might have
been used to good advantage against those who did try.
[205] "In grammar, to give the
winds to the ships and to give the ships to the winds mean the same
thing. But in geometry it is one thing to assume the circle BCD not
greater than thirty-six segments BCDF, and another (to assume) the
thirty-six segments BCDF not greater than the circle. The one assumption
is true, the other false."
[206] The Greek scholar
(1559-1614) who edited a Greek and Latin edition of Aristotle in
1590.
[207] Jacques Auguste de Thou
(1553-1617), the historian and statesman.
[208] "To value Scaliger higher
even when wrong, than the multitude when right."
[209] "I would rather err with
Scaliger than be right with Clavius."
[210] "The perimeter of the
dodecagon to be inscribed in a circle is greater than the perimeter of
the circle. And the more sides a polygon to be inscribed in a circle
successively has, so much the greater will the perimeter of the polygon
be than the perimeter of the circle."
[211] De Morgan took, perhaps,
the more delight in speaking thus of Sir William Hamilton (1788-1856)
because of a spirited controversy that they had in 1847 over the theory
of logic. Possibly, too, Sir William's low opinion of mathematics had its
influence.
[212] Edwards (1699-1757) wrote
The canons of criticism (1747) in which he gave a scathing
burlesque on Warburton's Shakespeare. It went through six editions.
[213] Antoine Teissier (born in
1632) published his Eloges des hommes savants, tirés de l'histoire de
M. de Thou in 1683.
[214] "He boasted without reason
of having found the quadrature of the circle. The glory of this admirable
discovery was reserved for Joseph Scaliger, as Scévole de St. Marthe has
written."
[215] Natural and political
observations mentioned in the following Index, and made upon the Bills of
Mortality.... With reference to the government, religion, trade, growth,
ayre, and diseases of the said city. London, 1662, 4to. The book went
through several editions.
[216] Ne sutor ultra
crepidam, "Let the cobbler stick to his last," as we now say.
[217] The author (1632-1695) of
the Historia et Antiquitates Universitatis Oxoniensis (1674). See
note 163, page 98.
[218] The mathematical guild owes
Samuel Pepys (1633-1703) for something besides his famous diary
(1659-1669). Not only was he president of the Royal Society (1684), but
he was interested in establishing Sir William Boreman's mathematical
school at Greenwich.
[219] John Graunt (1620-1674) was
a draper by trade, and was a member of the Common Council of London until
he lost office by turning Romanist. Although a shopkeeper, he was elected
to the Royal Society on the special recommendation of Charles II. Petty
edited the fifth edition of his work, adding much to its size and value,
and this may be the basis of Burnet's account of the authorship.
[220] Petty (1623-1687) was a
mathematician and economist, and a friend of Pell and Sir Charles
Cavendish. His survey of Ireland, made for Cromwell, was one of the first
to be made on a large scale in a scientific manner. He was one of the
founders of the Royal Society.
[221] The story probably arose
from Graunt's recent conversion to the Roman Catholic faith.
[222] He was born in 1627 and
died in 1704. He published a series of ephemerides, beginning in 1659. He
was imprisoned in 1679, at the time of the "Popish Plot," and again for
treason in 1690. His important astrological works are the Animal
Cornatum, or the Horn'd Beast (1654) and The Nativity of the late
King Charls (1659).
[223] Isaac D'Israeli
(1766-1848), in his Curiosities of Literature (1791), speaking of
Lilly, says: "I shall observe of this egregious astronomer, that there is
in this work, so much artless narrative, and at the same time so much
palpable imposture, that it is difficult to know when he is speaking what
he really believes to be the truth." He goes on to say that Lilly relates
that "those adepts whose characters he has drawn were the lowest
miscreants of the town. Most of them had taken the air in the pillory,
and others had conjured themselves up to the gallows. This seems a true
statement of facts."
[224] It is difficult to estimate
William Lilly (1602-1681) fairly. His Merlini Anglici ephemeris,
issued annually from 1642 to 1681, brought him a great deal of money. Sir
George Wharton (1617-1681) also published an almanac annually from 1641
to 1666. He tried to expose John Booker (1603-1677) by a work entitled
Mercurio-Coelicio-Mastix; or, an Anti-caveat to all such, as have
(heretofore) had the misfortune to be Cheated and Deluded by that Grand
and Traiterous Impostor of this Rebellious Age, John Booker, 1644.
Booker was "licenser of mathematical [astrological] publications," and as
such he had quarrels with Lilly, Wharton, and others.
[225] See note 171 on page 100.
[226] This is the Ars
Signorum, vulgo character universalis et lingua philosophica, that
appeared at London in 1661, 8vo. George Dalgarno anticipated modern
methods in the teaching of the deaf and dumb.
[227] See note 200 on page 110.
[228] If the hyperbola is
referred to the asymptotes as axes, the area between two ordinates
(x = a, x = b) is the difference of the
logarithms of a and b to the base e. E.g., in the
case of the hyperbola xy = 1, the area between x = a
and x = 1 is log a.
[229] "On ne peut lui refuser la
justice de remarquer que personne avant lui ne s'est porté dans cette
recherche avec autant de génie, & même, si nous en exceptons son
objet principal, avec autant de succès." Quadrature du Cercle, p.
66.
[230] The title proceeds: Seu
duae mediae proportionales inter extremas datas per circulum et per
infinitas hyperbolas, vel ellipses et per quamlibet exhibitae....
René Francois, Baron de Sluse (1622-1685) was canon and chancellor of
Liège, and a member of the Royal Society. He also published a work on
tangents (1672). The word mesolabium is from the Greek μεσολάβιον
or μεσόλαβον,
an instrument invented by Eratosthenes for finding two mean
proportionals.
[231] The full title has some
interest: Vera circuli et hyperbolae quadratura cui accedit geometriae
pars universalis inserviens quantitatum curvarum transmutationi et
mensurae. Authore Jacobo Gregorio Abredonensi Scoto ... Patavii,
1667. That is, James Gregory (1638-1675) of Aberdeen (he was really born
near but not in the city), a good Scot, was publishing his work down in
Padua. The reason was that he had been studying in Italy, and that this
was a product of his youth. He had already (1663) published his Optica
promota, and it is not remarkable that his brilliancy brought him a
wide circle of friends on the continent and the offer of a pension from
Louis XIV. He became professor of mathematics at St Andrews and later at
Edinburgh, and invented the first successful reflecting telescope. The
distinctive feature of his Vera quadratura is his use of an
infinite converging series, a plan that Archimedes used with the
parabola.
[232] Jean de Beaulieu wrote
several works on mathematics, including La lumière de
l'arithmétique (n.d.), La lumière des mathématiques (1673),
Nouvelle invention d'arithmétique (1677), and some mathematical
tables.
[233] A just estimate. There were
several works published by Gérard Desargues (1593-1661), of which the
greatest was the Brouillon Proiect (Paris, 1639). There is an
excellent edition of the Œuvres de Desargues by M. Poudra,
Paris, 1864.
[234] "A certain M. de Beaugrand,
a mathematician, very badly treated by Descartes, and, as it appears,
rightly so."
[235] This is a very old
approximation for π. One of the latest
pretended geometric proofs resulting in this value appeared in New York
in 1910, entitled Quadrimetry (privately printed).
[236] "Copernicus, a German, made
himself no less illustrious by his learned writings; and we might say of
him that he stood alone and unique in the strength of his problems, if
his excessive presumption had not led him to set forth in this science a
proposition so absurd that it is contrary to faith and reason, namely
that the circumference of a circle is fixed and immovable while the
center is movable: on which geometrical principle he has declared in his
astrological treatise that the sun is fixed and the earth is in
motion."
[237] So in the original.
[238] Franciscus Maurolycus
(1494-1575) was really the best mathematician produced by Sicily for a
long period. He made Latin translations of Theodosius, Menelaus, Euclid,
Apollonius, and Archimedes, and wrote on cosmography and other
mathematical subjects.
[239] "Nicolaus Copernicus is
also tolerated who asserted that the sun is fixed and that the earth
whirls about it; and he rather deserves a whip or a lash than a
reproof."
[240] "Algebra is the curious
science of scholars, and particularly for a general of an army, or a
captain, in order quickly to draw up an army in battle array and to
number the musketeers and pikemen who compose it, without the figures of
arithmetic. This science has five special figures of this kind: P means
plus in commerce and pikemen in the army; M means
minus, and musketeer in the art of war;... R signifies
root in the measurement of a cube, and rank in the
army; Q means square (French quarè, as then spelled) in
both cases; C means cube in mensuration, and cavalry in
arranging batallions and squadrons. As for the operations of this
science, they are as follows: to add a plus and a plus, the
sum will be plus; to add minus with plus, take the
less from the greater and the remainder will be the sum required or the
number to be found. I say this only in passing, for the benefit of those
who are wholly ignorant of it."
[241] He refers to the Joannis
de Beaugrand ... Geostatice, seu de vario pondere gravium secundum varia
a terrae (centro) intervalla dissertatio mathematica, Paris, 1636.
Pascal relates that de Beaugrand sent all of Roberval's theorems on the
cycloid and Fermat's on maxima and minima to Galileo in 1638, pretending
that they were his own.
[242] More (1614-1687) was a
theologian, a fellow of Christ College, Cambridge, and a Christian
Platonist.
[243] Matthew Hale (1609-1676)
the famous jurist, wrote a number of tracts on scientific, moral, and
religious subjects. These were collected and published in 1805.
[244] They might have been
attributed to many a worse man than Dr. Hales (1677-1761), who was a
member of the Royal Society and of the Paris Academy, and whose scheme
for the ventilation of prisons reduced the mortality at the Savoy prison
from one hundred to only four a year. The book to which reference is made
is Vegetable Staticks or an Account of some statical experiments on
the sap in Vegetables, 1727.
[245] Pleas of the Crown; or a
Methodical Summary of the Principal Matters relating to the subject,
1678.
[246] Thomae Streete
Astronomia Carolina, a new theory of the celestial motions, 1661. It
also appeared at Nuremberg in 1705, and at London in 1710 and 1716
(Halley's editions). He wrote other works on astronomy.
[247] This was the Sir Thomas
Street (1626-1696) who passed sentence of death on a Roman Catholic
priest for saying mass. The priest was reprieved by the king, but in the
light of the present day one would think the justice more in need of
pardon. He took part in the trial of the Rye House Conspirators in
1683.
[248] Edmund Halley (1656-1742),
who succeeded Wallis (1703) as Savilian professor of mathematics at
Oxford, and Flamsteed (1720) as head of the Greenwich observatory. It is
of interest to note that he was instrumental in getting Newton's
Principia printed.
[249] Shepherd (born in 1760) was
one of the most famous lawyers of his day. He was knighted in 1814 and
became Attorney General in 1817.
[250] This was William Hone
(1780-1842), a book publisher, who wrote satires against the government,
and who was tried three times because of his parodies on the catechism,
creed, and litany (illustrated by Cruikshank). He was acquitted on all of
the charges.
[251] Valentinus was a
Benedictine monk and was still living at Erfurt in 1413. His Currus
triumphalis antimonii appeared in 1624. Synesius was Bishop of
Ptolemaide, who died about 430. His works were printed at Paris in 1605.
Theodor Kirckring (1640-1693) was a fellow-student of Spinoza's. Besides
the commentary on Valentine he left several works on anatomy. His
commentary appeared at Amsterdam in 1671. There were several editions of
the Chariot.
[252] The chief difficulty with
this curious "monk-bane" etymology is its absurdity. The real origin of
the word has given etymologists a good deal of trouble.
[253] Robert Boyle (1627-1691),
son of "the Great Earl" (of Cork). Perhaps his best-known discovery is
the law concerning the volume of gases.
[254] The real name of Eirenaeus
Philalethes (born in 1622) is unknown. It may have been Childe. He
claimed to have discovered the philosopher's stone in 1645. His tract in
this work is The Secret of the Immortal Liquor Alkahest or
Ignis-Aqua. See note 260, infra.
[255] Johann Baptist van Helmont,
Herr von Merode, Royenborg etc. (1577-1644). His chemical discoveries
appeared in his Ortus medicinae (1648), which went through many
editions.
[256] De Morgan should have
written up Francis Anthony (1550-1623), whose Panacea aurea sive
tractatus duo de auro potabili (Hamburg, 1619) described a panacea
that he gave for every ill. He was repeatedly imprisoned for practicing
medicine without a license from the Royal College of Physicians.
[257] Bernardus Trevisanus
(1406-1490), who traveled even through Barbary, Egypt, Palestine, and
Persia in search of the philosopher's stone. He wrote several works on
alchemy,—De Chemica (1567), De Chemico Miraculo
(1583), Traité de la nature de l'oeuf des philosophes (1659),
etc., all published long after his death.
[258] George Ripley (1415-1490)
was an Augustinian monk, later a chamberlain of Innocent VIII, and still
later a Carmelite monk. His Liber de mercuris philosophico and
other tracts first appeared in Opuscula quaedam chymica
(Frankfort, 1614).
[259] Besides the Opus
majus, and other of the better known works of this celebrated
Franciscan (1214-1294), there are numerous tracts on alchemy that
appeared in the Thesaurus chymicus (Frankfort, 1603).
[260] George Starkey (1606-1665
or 1666) has special interest for American readers. He seems to have been
born in the Bermudas and to have obtained the bachelor's degree in
England. He then went to America and in 1646 obtained the master's degree
at Harvard, apparently under the name of Stirk. He met Eirenaeus
Philalethes (see note 254 above) in America and
learned alchemy from him. Returning to England, he sold quack medicines
there, and died in 1666 from the plague after dissecting a patient who
had died of the disease. Among his works was the Liquor Alcahest, or a
Discourse of that Immortal Dissolvent of Paracelsus and Helmont,
which appeared (1675) some nine years after his death.
[261] Platt (1552-1611) was the
son of a London brewer. Although he left a manuscript on alchemy, and
wrote a book entitled Delights for Ladies to adorne their Persons
(1607), he was knighted for some serious work on the chemistry of
agriculture, fertilizing, brewing, and the preserving of foods, published
in The Jewell House of Art and Nature (1594).
[262] "Those who wish to call a
man a liar and deceiver speak of him a writer of almanacs; but those who
(would call him) a scoundrel and an imposter (speak of him as) a
chemist."
[263] "Trust your barque to the
winds but not your body to a chemist; any breeze is safer than the faith
of a chemist."
[264] Probably the Jesuit, Père
Claude François Menestrier (1631-1705), a well known historian.
[265] The author was Christopher
Nesse (1621-1705), a belligerent Calvinist, who wrote many controversial
works and succeeded in getting excommunicated four times. One of his most
virulent works was A Protestant Antidote against the Poison of
Popery.
[266] John Case (c. 1660-1700)
was a famous astrologer and physician. He succeeded to Lilly's practice
in London. In a darkened room, wherein he kept an array of mystical
apparatus, he pretended to show the credulous the ghosts of their
departed relatives. Besides his astrological works he wrote one serious
treatise, the Compendium Anatomicum nova methodo institutum
(1695), in which he defends Harvey's theories of embryology.
[267] Marcelis (1636-after 1714)
was a soap maker of Amsterdam. It is to be hoped that he made better soap
than values of π.
[268] John Craig (died in 1731)
was a Scotchman, but most of his life was spent at Cambridge reading and
writing on mathematics. He endeavored to introduce the Leibnitz
differential calculus into England. His mathematical works include the
Methodus Figurarum ... Quadraturas determinandi (1685),
Tractatus ... de Figurarum Curvilinearum Quadraturis et locis
Geometricis (1693), and De Calculo Fluentium libri duo
(1718).
[269] As is well known, this
subject owes much to the Bernoullis. Craig's works on the calculus
brought him into controversy with them. He also wrote on other subjects
in which they were interested, as in his memoir On the Curve of the
quickest descent (1700), On the Solid of least resistance
(1700), and the Solution of Bernoulli's problem on Curves
(1704).
[270] This is Samuel Lee
(1783-1852), the young prodigy in languages. He was apprenticed to a
carpenter at twelve and learned Greek while working at the trade. Before
he was twenty-five he knew Hebrew, Chaldee, Syriac, Samaritan, Persian,
and Hindustani. He later became Regius professor of Hebrew at
Cambridge.
[271] "Where the devil, Master
Ludovico, did you pick up such a collection?"
[272] Lord William Brounker (c.
1620-1684), the first president of the Royal Society, is best known in
mathematics for his contributions to continued fractions.
[273] Horace Walpole (1717-1797)
published his Catalogue of the Royal and Noble Authors of England
in 1758. Since his time a number of worthy names in the domain of science
in general and of mathematics in particular might be added from the
peerage of England.
[274] It was written by Charles
Hayes (1678-1760), a mathematician and scholar of no mean attainments. He
travelled extensively, and was deputy governor of the Royal African
Company. His Treatise on Fluxions (London, 1704) was the first
work in English to explain Newton's calculus. He wrote a work entitled
The Moon (1723) to prove that our satellite shines by its own as
well as by reflected light. His Chronographia Asiatica &
Aegyptica (1758) gives the results of his travels.
[275] Publick in the
original.
[276] Whiston (1667-1752)
succeeded Newton as Lucasian professor of mathematics at Cambridge. In
1710 he turned Arian and was expelled from the university. His work on
Primitive Christianity appeared the following year. He wrote many
works on astronomy and religion.
[277] Ditton (1675-1715) was, on
Newton's recommendation, made Head of the mathematical school at Christ's
Hospital, London. He wrote a work on fluxions (1706). His idea for
finding longitude at sea was to place stations in the Atlantic to fire
off bombs at regular intervals, the time between the sound and the flash
giving the distance. He also corresponded with Huyghens concerning the
use of chronometers for the purpose.
[278] This was John Arbuthnot (c.
1658-1735), the mathematician, physician and wit. He was intimate with
Pope and Swift, and was Royal physician to Queen Anne. Besides various
satires he published a translation of Huyghens's work on probabilities
(1692) and a well-known treatise on ancient coins, weights, and measures
(1727).
[279] Greene (1678-1730) was a
very eccentric individual and was generally ridiculed by his
contemporaries. In his will he directed that his body be dissected and
his skeleton hung in the library of King's College, Cambridge.
Unfortunately for his fame, this wish was never carried out.
[280] This was the historian,
Robert Sanderson (1660-1741), who spent most of his life at
Cambridge.
[281] I presume this was William
Jones (1675-1749) the friend of Newton and Halley, vice-president of the
Royal Society, in whose Synopsis Palmariorum Matheseos (1706) the
symbol π is first used for the circle
ratio.
[282] This was the Geometrica
solidorum, sive materiae, seu de varia compositione, progressione,
rationeque velocitatum, Cambridge, 1712. The work was parodied in
A Taste of Philosophical Fanaticism ... by a gentleman of the
University of Gratz.
[283] The antiquary and scientist
(1690-1754), president of the Royal Society, member of the Académie,
friend of Newton, and authority on numismatics.
[284] She was Catherine Barton,
Newton's step-niece. She married John Conduitt, master of the mint, who
collected materials for a life of Newton.
A propos of Mrs. Conduitt's life of her illustrious uncle, Sir
George Greenhill tells a very good story on Poincaré, the well-known
French mathematician. At an address given by the latter at the
International Congress of Mathematicians held in Rome in 1908 he spoke of
the story of Newton and the apple as a mere fable. After the address Sir
George asked him why he had done so, saying that the story was first
published by Voltaire, who had heard it from Newton's niece, Mrs.
Conduitt. Poincaré looked blank and said, "Newton, et la nièce de Newton,
et Voltaire,—non! je ne vous comprends pas!" He had thought Sir
George meant Professor Volterra of Rome, whose name in French is
Voltaire, and who could not possibly have known a niece of Newton without
bridging a century or so.
[285] This was the Edmund Turnor
(1755-1829) who wrote the Collections for the Town and Soke of
Grantham, containing authentic Memoirs of Sir Isaac Newton, from Lord
Portsmouth's Manuscripts, London, 1806.
[286] It may be recalled to mind
that Sir David (1781-1868) wrote a life of Newton (1855).
[287] "They are in the country.
We rejoice."
[288] "I am here, chatterbox,
suck!"
[289] "I have been graduated! I
decline!"
[290] Giovanni Castiglioni
(Castillon, Castiglione), was born at Castiglione, in Tuscany, in 1708,
and died at Berlin in 1791. He was professor of mathematics at Utrecht
and at Berlin. He wrote on De Moivre's equations (1762), Cardan's rule
(1783), and Euclid's treatment of parallels (1788-89).
[291] This was the Isaaci
Newtoni, equitis aurati, opuscula mathematica, philosophica et
philologica, Lausannae & Genevae, 1744.
[292] At London, 4to.
[293] "All the English attribute
it to Newton."
[294] Stephen Peter Rigaud
(1774-1839), Savilian professor of geometry at Oxford (1810-27) and later
professor of astronomy and head of the Radcliffe Observatory. He wrote
An historical Essay on first publication of Sir Isaac Newton's
Principia, Oxford, 1838, and a two-volume work entitled
Correspondence of Scientific Men of the 17th Century, 1841.
[295] It is no longer considered
by scholars as the work of Newton.
[296] J. Edleston, the author of
the Correspondence of Sir Isaac Newton and Professor Cotes,
London, 1850.
[297] Palmer (1601-1647) was
Master of Queen's College, Cambridge, a Puritan but not a separatist. His
work, The Characters of a believing Christian, in Paradoxes and
seeming contradictions, appeared in 1645.
[298] Grosart (1827-1899) was a
Presbyterian clergyman. He was a great bibliophile, and issued numerous
reprints of rare books.
[299] This was the year after
Palmer's death. The title was, The Remaines of ... Francis Lord
Verulam....; being Essays and severall Letters to severall great
personages, and other pieces of various and high concernment not
heretofore published, London, 1648, 4to.
[300] Shaw (1694-1763) was
physician extraordinary to George II. He wrote on chemistry and medicine,
and his edition of the Philosophical Works of Francis Bacon
appeared at London in 1733.
[301] John Locke (1632-1704), the
philosopher. This particular work appeared in 1695. There was an edition
in 1834 (vol. 25 of the Sacred Classics) and one in 1836 (vol. 2
of the Christian Library).
[302] I use the word
Socinian because it was so much used in Locke's time: it is used
in our own day by the small fry, the unlearned clergy and their immediate
followers, as a term of reproach for all Unitarians. I suspect
they have a kind of liking for the word; it sounds like so
sinful. The learned clergy and the higher laity know better: they
know that the bulk of the modern Unitarians go farther than Socinus, and
are not correctly named as his followers. The Unitarians themselves
neither desire nor deserve a name which puts them one point nearer to
orthodoxy than they put themselves. That point is the doctrine that
direct prayer to Jesus Christ is lawful and desirable: this Socinus held,
and the modern Unitarians do not hold. Socinus, in treating the subject
in his own Institutio, an imperfect catechism which he left, lays
much more stress on John xiv. 13 than on xv. 16 and xvi. 23. He is not
disinclined to think that Patrem should be in the first citation,
where some put it; but he says that to ask the Father in the name of the
Son is nothing but praying to the Son in prayer to the Father. He labors
the point with obvious wish to secure a conclusive sanction. In the
Racovian Catechism, of which Faustus Socinus probably drew the first
sketch, a clearer light is arrived at. The translation says: "But wherein
consists the divine honor due to Christ? In adoration likewise and
invocation. For we ought at all times to adore Christ, and may in our
necessities address our prayers to him as often as we please; and there
are many reasons to induce us to do this freely." There are some who like
accuracy, even in aspersion—A. De M.
Socinus, or Fausto Paolo Sozzini (1539-1604), was an antitrinitarian
who believed in prayer and homage to Christ. Leaving Italy after his
views became known, he repaired to Basel, but his opinions were too
extreme even for the Calvinists. He then tried Transylvania, attempting
to convert to his views the antitrinitarian Bishop Dávid. The only result
of his efforts was the imprisonment of Dávid and his own flight to
Poland, in which country he spent the rest of his life (1579-1604). His
complete works appeared first at Amsterdam in 1668, in the Bibliotheca
Fratres Polonorum. The Racovian Catechism (1605) appeared
after his death, but it seems to have been planned by him.
[303] "As much of faith as is
necessary to salvation is contained in this article, Jesus is the
Christ."
[304] Edwards (1637-1716) was a
Cambridge fellow, strongly Calvinistic. He published many theological
works, attacking the Arminians and Socinians. Locke and Whiston were
special objects of attack.
[305] Sir I. Newton's views on
points of Trinitarian Doctrine; his Articles of Faith, and the General
Coincidence of his Opinions with those of J. Locke; a Selection of
Authorities, with Observations, London, 1856.
[306] A Confession of the
Faith, Bristol, 1752, 8vo.
[307] This was really very
strange, because Laud (1573-1644), while he was Archbishop of Canterbury,
forced a good deal of High Church ritual on the Puritan clergy, and even
wished to compel the use of a prayer book in Scotland. It was this
intolerance that led to his impeachment and execution.
[308] The name is Jonchère. He
was a man of some merit, proposing (1718) an important canal in Burgundy,
and publishing a work on the Découverte des longitudes estimées
généralement impossible à trouver, 1734 (or 1735).
[309] Locke invented a kind of an
instrument for finding longitude, and it is described in the appendix,
but I can find nothing about the man. There was published some years
later (London, 1751) another work of his, A new Problem to discover
the longitude at sea.
[310] Baxter, concerning whom I
know merely that he was a schoolmaster, starts with the assumption of
this value, and deduces from it some fourteen properties relating to the
circle.
[311] John, who died in 1780, was
a well-known character in his way. He was a bookseller on Fleet Street,
and his shop was a general rendezvous for the literary men of his time.
He wrote the Memoirs of the Life and Writings of Mr. William
Whiston (1749, with another edition in 1753). He was one of the first
to issue regular catalogues of books with prices affixed.
[312] The name appears both as
Hulls and as Hull. He was born in Gloucestershire in 1699. In 1754 he
published The Art of Measuring made Easy by the help of a new Sliding
Scale.
[313] Thomas Newcomen (1663-1729)
invented the first practical steam engine about 1710. It was of about
five and a half horse power, and was used for pumping water from coal
mines. Savery had described such an engine in 1702, but Newcomen improved
upon it and made it practical.
[314] The well-known benefactor
of art (1787-1863).
[315] The tract was again
reprinted in 1860.
[316] Hulls made his experiment
on the Avon, at Evesham, in 1737, having patented his machine in 1736. He
had a Newcomen engine connected with six paddles. This was placed in the
front of a small tow boat. The experiment was a failure.
[317] William Symington
(1763-1831). In 1786 he constructed a working model of a steam road carriage. The
machinery was applied to a small boat in 1788, and with such success as
to be tried on a larger boat in 1789. The machinery was clumsy, however,
and in 1801 he took out a new patent for the style of engine still used
on paddle wheel steamers. This engine was successfully used in 1802, on
the Charlotte Dundas. Fulton (1765-1815) was on board, and so impressed
Robert Livingston with the idea that the latter furnished the money to
build the Clermont (1807), the beginning of successful river
navigation.
[318] Louis Bertrand Castel
(1688-1757), most of whose life was spent in trying to perfect his
Clavecin oculaire, an instrument on the order of the harpsichord,
intended to produce melodies and harmonies of color. He also wrote
L'Optique des couleurs (1740) and Sur le fond de la Musique
(1754).
[319] Dr. Robinson (1680-1754)
was professor of physic at Trinity College, Dublin, and three times
president of King and Queen's College of Physicians. In his Treatise
on the Animal Economy (1732-3, with a third edition in 1738) he
anticipated the discoveries of Lavoisier and Priestley on the nature of
oxygen.
[320] There was another edition,
published at London in 1747, 8vo.
[321] The author seems to have
shot his only bolt in this work. I can find nothing about him.
[322] Quod Deus sit, mundusque
ab ipso creatus fuerit in tempore, ejusque providentia gubernetur.
Selecta aliquot theoremata adversos atheos, etc., Paris, 1635,
4to.
[323] The British Museum
Catalogue mentions a copy of 1740, but this is possibly a misprint.
[324] This was Johann II
(1710-1790), son of Johann I, who succeeded his father as professor of
mathematics at Basel.
[325] Samuel Koenig (1712-1757),
who studied under Johann Bernoulli I. He became professor of mathematics
at Franeker (1747) and professor of philosophy at the Hague (1749).
[326] "In accordance with the
hypotheses laid down in this memoir it is so evident that t must =
34, y = 1, and z = 1, that there is no need of proof or
authority for it to be recognized by every one."
[327] "I subscribe to the
judgment of Mr. Bernoulli as a result of these hypotheses."
[328] "It clearly appears from my
present analysis and demonstration that they have already recognized and
perfectly agreed to the fact that the quadrature of the circle is
mathematically demonstrated."
[329] Dr. Knight (died in 1772)
made some worthy contributions to the literature of the mariner's
compass. As De Morgan states, he was librarian of the British Museum.
[330] Sir Anthony Panizzi
(1797-1879) fled from Italy under sentence of death (1822). He became
assistant (1831) and chief (1856) librarian of the British Museum, and
was knighted in 1869. He began the catalogue of printed books of the
Museum.
[331] Wright (1711-1786) was a
physicist. He was offered the professorship of mathematics at the
Imperial Academy of St. Petersburg but declined to accept it. This work
is devoted chiefly to the theory of the Milky Way, the via lactea
as he calls it after the manner of the older writers.
[332] Troughton (1753-1835) was
one of the world's greatest instrument makers. He was apprenticed to his
brother John, and the two succeeded (1770) Wright and Cole in Fleet
Street. Airy called his method of graduating circles the greatest
improvement ever made in instrument making. He constructed (1800) the
first modern transit circle, and his instruments were used in many of the
chief observatories of the world.
[333] William Simms (1793-1860)
was taken into partnership by Troughton (1826) after the death of the
latter's brother. The firm manufactured some well-known instruments.
[334] This was George Horne
(1730-1792), fellow of Magdalen College, Oxford, vice-Chancellor of the
University (1776), Dean of Canterbury (1781), and Bishop of Norwich
(1790). He was a great satirist, but most of his pamphlets against men
like Adam Smith, Swedenborg, and Hume, were anonymous, as in the case of
this one against Newton. He was so liberal in his attitude towards the
Methodists that he would not have John Wesley forbidden to preach in his
diocese. He was twenty-one when this tract appeared.
[335] Martin (1704-1782) was by
no means "old Benjamin Martin" when Horne wrote this pamphlet in 1749. In
fact he was then only forty-five. He was a physicist and a well-known
writer on scientific instruments. He also wrote Philosophia Britannica
or a new and comprehensive system of the Newtonian Philosophy
(1759).
[336] Jean Théophile Desaguliers,
or Des Aguliers (1683-1744) was the son of a Protestant who left France
after the revocation of the Edict of Nantes. He became professor of
physics at Oxford, and afterwards gave lectures in London. Later he
became chaplain to the Prince of Wales. He published several works on
physics.
[337] Charles Hutton (1737-1823),
professor of mathematics at Woolwich (1772-1807). His Mathematical
Tables (1785) and Mathematical and Philosophical Dictionary
(1795-1796) are well known.
[338] James Epps (1773-1839)
contributed a number of memoirs on the use and corrections of
instruments. He was assistant secretary of the Astronomical Society.
[339] John Hutchinson (1674-1737)
was one of the first to try to reconcile the new science of geology with
Genesis. He denied the Newtonian hypothesis as dangerous to religion, and
because it necessitated a vacuum. He was a mystic in his interpretation
of the Scriptures, and created a sect that went under the name of
Hutchinsonians.
[340] John Rowning, a
Lincolnshire rector, died in 1771. He wrote on physics, and published a
memoir on A machine for finding the roots of equations universally
(1770).
[341] It is always difficult to
sanction this spelling of the name of this Jesuit father who is so often
mentioned in the analytic treatment of conics. He was born in Ragusa in
1711, and the original spelling was Ruđer Josip
Bošković. When he went to live in Italy, as professor of
mathematics at Rome (1740) and at Pavia, the name was spelled Ruggiero
Giuseppe Boscovich, although Boscovicci would seem to a foreigner more
natural. His astronomical work was notable, and in his De maculis
solaribus (1736) there is the first determination of the equator of a
planet by observing the motion of spots on its surface. Boscovich came
near having some contact with America, for he was delegated to observe in
California the transit of Venus in 1755, being prevented by the
dissolution of his order just at that time. He died in 1787, at
Milan.
[342] James Granger (1723-1776)
who wrote the Biographical History of England, London, 1769. His
collection of prints was remarkable, numbering some fourteen
thousand.
[343] He was curator of
experiments for the Royal Society. He wrote a large number of books and
monographs on physics. He died about 1713.
[344] Lee seems to have made no
impression on biographers.
[345] This work appeared at
London in 1852.
[346] Of course this is no longer
true. The most scholarly work to-day is that of Rudio, Archimedes,
Huygens, Lambert, Legendre, vier Abhandlungen über die Kreismessung ...
mit einer Uebersicht über die Geschichte des Problems von der Quadratur
des Zirkels, von den ältesten Zeiten bis auf unsere Tage, Leipsic,
1892.
[347] Joseph Jérome le François
de Lalande (1732-1807), professor of astronomy in the Collège de France
(1753) and director of the Paris Observatory (1761). His writings on
astronomy and his Bibliographie astronomique, avec l'histoire de
l'astronomie depuis 1781 jusqu'en 1802 (Paris, 1803) are well
known.
[348] De Morgan refers to his
Histoire de l'Astronomie au 18e siècle, which appeared in 1827,
five years after Delambre's death. Jean Baptiste Joseph Delambre
(1749-1822) was a pupil of and a collaborator with Lalande, following his
master as professor of astronomy in the Collège de France. His work on
the measurements for the metric system is well known, and his four
histories of astronomy, ancienne (1817), au moyen âge
(1819), moderne (1821), and au 18e siècle (posthumous,
1827) are highly esteemed.
[349] Jean-Joseph Rive
(1730-1792), a priest who left his cure under grave charges, and a
quarrelsome character. His attack on Montucla was a case of the pot
calling the kettle black; for while he was a brilliant writer he was a
careless bibliographer.
[350] Isaac Barrow (1630-1677)
was quite as well known as a theologian as he was from his Lucasian
professorship of mathematics at Cambridge.
[351] "Besides we can see by this
that Barrow was a poor philosopher; for he believed in the immortality of
the soul and in a Divinity other than universal nature."
[352] The Récréations
mathématiques et physiques (Paris, 1694) of Jacques Ozanam
(1640-1717) is a work that is still highly esteemed. Among various other
works he wrote a Dictionnaire mathématique ou Idée générale des
mathématiques (1690) that was not without merit. The
Récréations went through numerous editions (Paris, 1694, 1696,
1741, 1750, 1770, 1778, and the Montucla edition of 1790; London, 1708,
the Montucla-Hutton edition of 1803 and the Riddle edition of 1840;
Dublin, 1790).
[353] Hendryk van Etten, the
nom de plume of Jean Leurechon (1591-1670), rector of the Jesuit
college at Bar, and professor of philosophy and mathematics. He wrote on
astronomy (1619) and horology (1616), and is known for his Selecta
Propositiones in tota sparsim mathematica pulcherrime propositae in
solemni festo SS. Ignatii et Francesci Xaverii, 1622. The book to
which De Morgan refers is his Récréation mathématicque, composée de
plusieurs problèmes plaisants et facetieux, Lyons, 1627, with an
edition at Pont-à-Mousson, 1629. There were English editions published at
London in 1633, 1653, and 1674, and Dutch editions in 1662 and 1672.
I do not understand how De Morgan happened to miss owning the work by
Claude Gaspar Bachet de Meziriac (1581-1638), Problèmes plaisans et
délectables, which appeared at Lyons in 1612, 8vo, with a second
edition in 1624. There was a fifth edition published at Paris in
1884.
[354] His title page closes with
"Paris, Chez Ch. Ant. Jombert.... M DCC LIV."
This was Charles-Antoine Jombert (1712-1784), a printer and bookseller
with some taste for painting and architecture. He wrote several works and
edited a number of early treatises.
[355] The late Professor Newcomb
made the matter plain even to the non-mathematical mind, when he said
that "ten decimal places are sufficient to give the circumference of the
earth to the fraction of an inch, and thirty decimal places would give
the circumference of the whole visible universe to a quantity
imperceptible with the most powerful microscope."
[356] Antinewtonianismi pars
prima, in qua Newtoni de coloribus systema ex propriis principiis
geometrice evertitur, et nova de coloribus theoria luculentissimis
experimentis demonstrantur.... Naples, 1754; pars secunda,
Naples, 1756.
[357] Celestino Cominale
(1722-1785) was professor of medicine at the University of Naples.
[358] The work appeared in the
years from 1844 to 1849.
[359] There was a Vienna edition
in 1758, 4to, and another in 1759, 4to. This edition is described on the
title page as Editio Veneta prima ipso auctore praesente, et
corrigente.
[360] The first edition was
entitled De solis ac lunae defectibus libri V. P. Rogerii Josephi
Boscovich ... cum ejusdem auctoris adnotationibus, London, 1760. It
also appeared in Venice in 1761, and in French translation by the Abbé de
Baruel in 1779, and was a work of considerable influence.
[361] Paulian (1722-1802) was
professor of physics at the Jesuit college at Avignon. He wrote several
works, the most popular of which, the Dictionnaire de physique
(Avignon, 1761), went through nine editions by 1789.
[362] This is correct.
[363] Probably referring to the
fact that Hill (1795-1879), who had done so much for postal reform, was
secretary to the postmaster general (1846), and his name was a synonym
for the post office directory.
[364] Richard Lovett (1692-1780)
was a good deal of a charlatan. He claimed to have studied electrical
phenomena, and in 1758 advertised that he could effect marvelous cures,
especially of sore throat, by means of electricity. Before publishing the
works mentioned by De Morgan he had issued others of similar character,
including The Subtile Medium proved (London, 1756) and The
Reviewers Reviewed (London, 1760).
[365] Jean Sylvain Bailly
(1736-1793), member of the Académie française and of the
Académie des sciences, first deputy elected to represent Paris in
the Etats-généraux (1789), president of the first National
Assembly, and mayor of Paris (1789-1791). For his vigor as mayor in
keeping the peace, and for his manly defence of the Queen, he was
guillotined. He was an astronomer of ability, but is best known for his
histories of the science.
[366] These were the Histoire
de l'Astronomie ancienne (1775), Histoire de l'Astronomie
moderne (1778-1783), Histoire de l'Astronomie indienne et
orientale (1787), and Lettres sur l'origine des peuples de
l'Asie (1775).
[367] "The sick old man of
Ferney, V., a boy of a hundred years." Voltaire was born in 1694, and
hence was eighty-three at this time.
[368] In Palmézeaux's Vie de
Bailly, in Bailly's Ouvrage Posthume (1810), M. de Sales is
quoted as saying that the Lettres sur l'Atlantide were sent to
Voltaire and that the latter did not approve of the theory set forth.
[369] The British Museum
catalogue gives two editions, 1781 and 1782.
[370] A mystic and a
spiritualist. His chief work was the one mentioned here.
[371] Jacob Behmen, or Böhme
(1575-1624), known as "the German theosophist," was founder of the sect
of Boehmists, a cult allied to the Swedenborgians. He was given to the
study of alchemy, and brought the vocabulary of the science into his
mystic writings. His sect was revived in England in the eighteenth
century through the efforts of William Law. Saint-Martin translated into
French two of his Latin works under the titles L'Aurore naissante, ou
la Racine de la philosophie (1800), and Les trois principes de
l'essence divine (1802). The originals had appeared nearly two
hundred years earlier,—Aurora in 1612, and De tribus
principiis in 1619.
[372] "Unknown."
[373] "Skeptical."
[374] "Man, man, man."
[375] "Men, men, men."
[376] It is interesting to read
De Morgan's argument against Saint-Martin's authorship of this work. It
is attributed to Saint-Martin both by the Biographie Universelle
and by the British Museum Catalogue, and De Morgan says by
"various catalogues and biographies."
[377] "To explain things by man
and not man by things. On Errors and Truth, by a Ph....
Inc...."
[378] "If we would preserve
ourselves from all illusions, and above all from the allurements of
pride, by which man is so often seduced, we should never take man, but
always God, for our term of comparison."
[379] "And here is found already
an explanation of the numbers four and nine which caused some perplexity
in the work cited above. Man is lost in passing from four to nine."
[380] Williams also took part in
the preparation of some tables for the government to assist in the
determination of longitude. He had published a work two years before the
one here cited, on the same subject,—An entire new work and
method to discover the variation of the Earth's Diameters, London, 1786.
[381] This is Gabriel Mouton
(1618-1694), a vicar at Lyons, who suggested as a basis for a natural
system of measures the mille, a minute of a degree of the
meridian. This appeared in his Observationes diametrorum solis et
lunae apparentium, meridianarumque aliquot altitudinum cum tabula
declinationum solis.... Lyons, 1670.
[382] Jacques Cassini
(1677-1756), one of the celebrated Cassini family of astronomers. After
the death of his father he became director of the observatory at Paris.
The basis for a metric unit was set forth by him in his Traité de la
grandeur et de la figure de la terre, Paris, 1720. He was a prolific
writer on astronomy.
[383] Alexis Jean Pierre Paucton
(1732-1798). He was, for a time, professor of mathematics at Strassburg,
but later (1796) held office in Paris. His leading contribution to
metrology was his Métrologie ou Traité des mesures, Paris,
1780.
[384] He was an obscure writer,
born at Deptford.
[385] He was also a writer of no
scientific merit, his chief contributions being religious tracts. One of
his productions, however, went through many editions, even being
translated into French; Three dialogues between a Minister and one of
his Parishioners; on the true principles of Religion and salvation for
sinners by Jesus Christ. The twentieth edition appeared at Cambridge
in 1786.
[386] This was the Reflections
on the Revolution in France, and on the proceedings in certain societies
in London relative to that event (London, 1790) by Edmund Burke
(1729-1797). Eleven editions of the work appeared the first year.
[387] Paine (1736-1809) was born
in Norfolkshire, of Quaker parents. He went to America at the beginning
of the Revolution and published, in January 1776, a violent pamphlet
entitled Common Sense. He was a private soldier under Washington,
and on his return to England after the war he published The Rights of
Man. He was indicted for treason and was outlawed to France. He was
elected to represent Calais at the French convention, but his plea for
moderation led him perilously near the guillotine. His Age of
Reason (1794) was dedicated to Washington. He returned to America in
1802 and remained there until his death.
[388] Part I appeared in 1791 and
was so popular that eight editions appeared in that year. It was followed
in 1792 by Part II, of which nine editions appeared in that year. Both
parts were immediately republished in Paris, and there have been several
subsequent editions.
[389] Mary Wollstonecraft
(1759-1797) was only thirty-three when this work came out. She had
already published An historical and moral View of the Origin and
Progress of the French Revolution (1790), and Original Stories
from Real Life (1791). She went to Paris in 1792 and remained during
the Reign of Terror.
[390] Samuel Parr (1747-1827) was
for a time head assistant at Harrow (1767-1771), afterwards headmaster in
other schools. At the time this book was written he was vicar of Hatton,
where he took private pupils (1785-1798) to the strictly limited number
of seven. He was a violent Whig and a caustic writer.
[391] On Mary Wollstonecraft's
return from France she married (1797) William Godwin (1756-1836). He had
started as a strong Calvinistic Nonconformist minister, but had become
what would now be called an anarchist, at least by conservatives. He had
written an Inquiry concerning Political Justice (1793) and a novel
entitled Caleb Williams, or Things as they are (1794), both of
which were of a nature to attract his future wife.
[392] This child was a daughter.
She became Shelley's wife, and Godwin's influence on Shelley was very
marked.
[393] This was John Nichols
(1745-1826), the publisher and antiquary. He edited the Gentleman's
Magazine (1792-1826) and his works include the Literary Anecdotes
of the Eighteenth Century (1812-1815), to which De Morgan here
refers.
[394] William Bellenden, a Scotch
professor at the University of Paris, who died about 1633. His textbooks
are now forgotten, but Parr edited an edition of his works in 1787. The
Latin preface, Praefatio ad Bellendum de Statu, was addressed to
Burke, North, and Fox, and was a satire on their political opponents.
[395] As we have seen, he had
been head-master before he began taking "his handful of private
pupils."
[396] The story has evidently got
mixed up in the telling, for Tom Sheridan (1721-1788), the great actor,
was old enough to have been Dr. Parr's father. It was his son, Richard
Brinsley Sheridan (1751-1816), the dramatist and politician, who was the
pupil of Parr. He wrote The Rivals (1775) and The School for
Scandal (1777) soon after Parr left Harrow.
[397] Horner (1785-1864) was a
geologist and social reformer. He was very influential in improving the
conditions of child labor.
[398] William Cobbett
(1762-1835), the journalist, was a character not without interest to
Americans. Born in Surrey, he went to America at the age of thirty and
remained there eight years. Most of this time he was occupied as a
bookseller in Philadelphia, and while thus engaged he was fined for libel
against the celebrated Dr. Rush. On his return to England he edited the
Weekly Political Register (1802-1835), a popular journal among the
working classes. He was fined and imprisoned for two years because of his
attack (1810) on military flogging, and was also (1831) prosecuted for
sedition. He further showed his paradox nature by his History of the
Protestant Reformation (1824-1827), an attack on the prevailing
Protestant opinion. He also wrote a Life of Andrew Jackson (1834).
After repeated attempts he succeeded in entering parliament, a result of
the Reform Bill.
[399] Robinson (1735-1790) was a
Baptist minister who wrote several theological works and a number of
hymns. His work at Cambridge so offended the students that they at one
time broke up the services.
[400] This work had passed
through twelve editions by 1823.
[401] Dyer (1755-1841), the poet
and reformer, edited Robinson's Ecclesiastical Researches (1790).
He was a life-long friend of Charles Lamb, and in their boyhood they were
schoolmates at Christ's Hospital. His Complaints of the Poor People of
England (1793) made him a worthy companion of the paradoxers above
mentioned.
[402] These were John Thelwall
(1764-1834) whose Politics for the People or Hogswash (1794) took
its title from the fact that Burke called the people the "swinish
multitude." The book resulted in sending the author to the Tower for
sedition. In 1798 he gave up politics and started a school of elocution
which became very famous. Thomas Hardy (1752-1832), who kept a
bootmaker's shop in Piccadilly, was a fellow prisoner with Thelwall,
being arrested for high treason. He was founder (1792) of The London
Corresponding Society, a kind of clearing house for radical associations
throughout the country. Horne Tooke was really John Horne (1736-1812), he
having taken the name of his friend William Tooke in 1782. He was a
radical of the radicals, and organized a number of reform societies.
Among these was the Constitutional Society that voted money (1775) to
assist the American revolutionists, appointing him to give the
contribution to Franklin. For this he was imprisoned for a year. With his
fellow rebels in the Tower in 1794, however, he was acquitted. As a
philologist he is known for his early advocacy of the study of
Anglo-Saxon and Gothic, and his Diversions of Purley (1786) is
still known to readers.
[403] This was the admiral, Adam
Viscount Duncan (1731-1804), who defeated the Dutch off Camperdown in
1797.
[404] He was created Duke of
Clarence and St. Andrews in 1789 and was Admiral of the Fleet escorting
Louis XVIII on his return to France in 1814. He became Lord High Admiral
in 1827, and reigned as William IV from 1830 to 1837.
[405] This was Charles Abbott
(1762-1832) first Lord Tenterden. He succeeded Lord Ellenborough as Chief
Justice (1818) and was raised to the peerage in 1827. He was a strong
Tory and opposed the Catholic Relief Bill, the Reform Bill, and the
abolition of the death penalty for forgery.
[406] Edward Law (1750-1818),
first Baron Ellenborough. He was chief counsel for Warren Hastings, and
his famous speech in defense of his client is well known. He became Chief
Justice and was raised to the peerage in 1802. He opposed all efforts to
modernize the criminal code, insisting upon the reactionary principle of
new death penalties.
[407] Edmund Law (1703-1787),
Bishop of Carlisle (1768), was a good deal more liberal than his son. His
Considerations on the Propriety of requiring subscription to the
Articles of Faith (1774) was published anonymously. In it he asserts
that not even the clergy should be required to subscribe to the
thirty-nine articles.
[408] Joe Miller (1684-1738), the
famous Drury Lane comedian, was so illiterate that he could not have
written the Joe Miller's Jests, or the Wit's Vade-Mecum that
appeared the year after his death. It was often reprinted and probably
contained more or less of Miller's own jokes.
[409] The sixth duke (1766-1839)
was much interested in parliamentary reform. He was a member of the
Society of Friends of the People. He was for fourteen years a member of
parliament (1788-1802) and was later Lord Lieutenant of Ireland
(1806-1807). He afterwards gave up politics and became interested in
agricultural matters.
[410] George Jeffreys (c.
1648-1689), the favorite of James II, who was active in prosecuting the
Rye House conspirators. He was raised to the peerage in 1684 and held the
famous "bloody assize" in the following year, being made Lord Chancellor
as a result. He was imprisoned in the Tower by William III and died
there.
[411] The Every Day Book,
forming a Complete History of the Year, Months, and Seasons, and a
perpetual Key to the Almanack, 1826-1827.
[412] The first and second
editions appeared in 1820. Two others followed in 1821.
[413] The three trials of W.
H., for publishing three parodies; viz the late John Wilkes' Catechism,
the Political Litany, and the Sinecurists Creed; on three ex-officio
informations, at Guildhall, London, ... Dec. 18, 19, & 20,
1817,... London, 1818.
[414] The Political Litany
appeared in 1817.
[415] That is, Castlereagh's.
[416] The well-known caricaturist
(1792-1878), then only twenty-nine years old.
[417] Robert Stewart (1769-1822)
was second Marquis of Londonderry and Viscount Castlereagh. As Chief
Secretary for Ireland he was largely instrumental in bringing about the
union of Ireland and Great Britain. He was at the head of the war
department during most of the Napoleonic wars, and was to a great extent
responsible for the European coalition against the Emperor. He suicided
in 1822.
[418] John Murray (1778-1843),
the well-known London publisher. He refused to finish the publication of
Don Juan, after the first five cantos, because of his Tory
principles.
[419] Only the first two cantos
appeared in 1819.
[420] Proclus (412-485), one of
the greatest of the neo-Platonists, studied at Alexandria and taught
philosophy at Athens. He left commentaries on Plato and on part of
Euclid's Elements.
[421] Thomas Taylor (1758-1835),
called "the Platonist," had a liking for mathematics, and was probably
led by his interest in number mysticism to a study of neo-Platonism. He
translated a number of works from the Latin and Greek, and wrote two
works on theoretical arithmetic (1816, 1823).
[422] There was an earlier
edition, 1788-89.
[423] Georgius Gemistus, or
Georgius Pletho (Plethon), lived in the fourteenth and fifteenth
centuries. He was a native of Constantinople, but spent most of his time
in Greece. He devoted much time to the propagation of the Platonic
philosophy, but also wrote on divinity, geography, and history.
[424] Hannah More (1745-1833),
was, in her younger days, a friend of Burke, Reynolds, Dr. Johnson, and
Garrick. At this time she wrote a number of poems and aspired to become a
dramatist. Her Percy (1777), with a prologue and epilogue by
Garrick, had a long run at Covent Garden. Somewhat later she came to
believe that the playhouse was a grave public evil, and refused to attend
the revival of her own play with Mrs. Siddons in the leading part. After
1789 she and her sisters devoted themselves to starting schools for poor
children, teaching them religion and housework, but leaving them
illiterate.
[425] These were issued at the
rate of three each month,—a story, a ballad, and a Sunday tract.
They were collected and published in one volume in 1795. It is said that
two million copies were sold the first year. There were also editions in
1798, 1819, 1827, and 1836-37.
[426] That is, Dr. Johnson
(1709-1784). The Rambler was published in 1750-1752, and was an
imitation of Addison's Spectator.
[427] Dr. Moore, referred to
below.
[428] Dr. John Moore (1729-1802),
physician and novelist, is now best known for his Journal during a
Residence in France from the beginning of August to the middle of
December, 1792, a work quoted frequently by Carlyle in his French
Revolution.
[429] Sir John Moore (1761-1809),
Lieutenant General in the Napoleonic wars. He was killed in the battle of
Corunna. The poem by Charles Wolfe (1791-1823), The Burial of Sir John
Moore (1817), is well known.
[430] Referring to the novels of
Thomas Love Peacock (1785-1866), who succeeded James Mill as chief
examiner of the East India Company, and was in turn succeeded by John
Stuart Mill.
[431] Frances Burney, Madame
d'Arblay (1752-1840), married General d'Arblay, a French officer and
companion of Lafayette, in 1793. She was only twenty-five when she
acquired fame by her Evelina, or a Young Lady's Entrance into the
World. Her Letters and Diaries appeared posthumously
(1842-45).
[432] Henry Peter, Baron Brougham
and Vaux (1778-1868), well known in politics, science, and letters. He
was one of the founders of the Edinburgh Review, became Lord
Chancellor in 1830, and took part with men like William Frend, De
Morgan's father-in-law, in the establishing of London University. He was
also one of the founders of the Society for the Diffusion of Useful
Knowledge. He was always friendly to De Morgan, who entered the faculty
of London University, whose work on geometry was published by the Society
mentioned, and who was offered the degree of doctor of laws by the
University of Edinburgh while Lord Brougham was Lord Rector. The
Edinburgh honor was refused by De Morgan who said he "did not feel like
an LL.D."
[433] Maria Edgeworth
(1767-1849).
[434] Sydney Owenson (c.
1783-1859) married Sir Thomas Morgan, a well-known surgeon, in 1812. Her
Irish stories were very popular with the patriots but were attacked by
the Quarterly Review. The Wild Irish Girl (1806) went
through seven editions in two years.
[435] 1775-1817.
[436] 1771-1832.
[437] The famous preacher
(1732-1808). He was the first chairman of the Religious Tract Society. He
is also known as one of the earliest advocates of vaccination, in his
Cow-pock Inoculation vindicated and recommended from matters of
fact, 1806.
[438] Sir Rowland Hill
(1795-1879), the father of penny postage.
[439] Beilby Porteus (1731-1808),
Bishop of Chester (1776) and Bishop of London (1787). He encouraged the
Sunday-school movement and the dissemination of Hannah More's tracts. He
was an active opponent of slavery, but also of Catholic emancipation.
[440] Henrietta Maria Bowdler
(1754-1830), generally known as Mrs. Harriet Bowdler. She was the author
of many religious tracts and poems. Her Poems and Essays (1786)
were often reprinted. The story goes that on the appearance of her
Sermons on the Doctrines and duties of Christianity (published
anonymously), Bishop Porteus offered the author a living under the
impression that it was written by a man.
[441] William Frend (1757-1841),
whose daughter Sophia Elizabeth became De Morgan's wife (1837), was at
one time a clergyman of the Established Church, but was converted to
Unitarianism (1787). He came under De Morgan's definition of a true
paradoxer, carrying on a zealous warfare for what he thought right. As a
result of his Address to the Inhabitants of Cambridge (1787), and
his efforts to have abrogated the requirement that candidates for the
M.A. must subscribe to the thirty-nine articles, he was deprived of his
tutorship in 1788. A little later he was banished (see De Morgan's
statement in the text) from Cambridge because of his denunciation of the
abuses of the Church and his condemnation of the liturgy. His
eccentricity is seen in his declining to use negative quantities in the
operations of algebra. He finally became an actuary at London and was
prominent in radical associations. He was a mathematician of ability,
having been second wrangler and having nearly attained the first place,
and he was also an excellent scholar in Latin, Greek, and Hebrew.
[442] George Peacock (1791-1858),
Fellow of Trinity College, Cambridge, Lowndean professor of astronomy,
and Dean of Ely Cathedral (1839). His tomb may be seen at Ely where he
spent the latter part of his life. He was one of the group that
introduced the modern continental notation of the calculus into England,
replacing the cumbersome notation of Newton, passing from "the
dotage of fluxions to the deism of the calculus."
[443] Robert Simson (1687-1768);
professor of mathematics at Glasgow. His restoration of Apollonius (1749)
and his translation and restoration of Euclid (1756, and
1776—posthumous) are well known.
[444] Francis Maseres
(1731-1824), a prominent lawyer. His mathematical works had some
merit.
[445] These appeared annually
from 1804 to 1822.
[446] Henry Gunning (1768-1854)
was senior esquire bedell of Cambridge. The Reminiscences appeared
in two volumes in 1854.
[447] John Singleton Copley,
Baron Lyndhurst (1772-1863), the son of John Singleton Copley the
portrait painter, was born in Boston. He was educated at Trinity College,
Cambridge, and became a lawyer. He was made Lord Chancellor in 1827.
[448] Sir William Rough (c.
1772-1838), a lawyer and poet, became Chief Justice of Ceylon in 1836. He
was knighted in 1837.
[449] Herbert Marsh, afterwards
Bishop of Peterborough, a relation of my father.—S. E. De M.
He was born in 1757 and died in 1839. On the trial of Frend he
publicly protested against testifying against a personal confidant, and
was excused. He was one of the first of the English clergy to study
modern higher criticism of the Bible, and amid much opposition he wrote
numerous works on the subject. He was professor of theology at Cambridge
(1707), Bishop of Llandaff (1816), and Bishop of Peterborough.
[450] George Butler (1774-1853),
Headmaster of Harrow (1805-1829), Chancellor of Peterborough (1836), and
Dean of Peterborough (1842).
[451] James Tate (1771-1843),
Headmaster of Richmond School (1796-1833) and Canon of St. Paul's
Cathedral (1833). He left several works on the classics.
[452] Francis Place (1771-1854),
at first a journeyman breeches maker, and later a master tailor. He was a
hundred years ahead of his time as a strike leader, but was not so
successful as an agitator as he was as a tailor, since his shop in
Charing Cross made him wealthy. He was a well-known radical, and it was
largely due to his efforts that the law against the combinations of
workmen was repealed in 1824. His chief work was The Principles of
Population (1822).
[453] Speed (1552-1629) was a
tailor until Grevil (Greville) made him independent of his trade. He was
not only an historian of some merit, but a skilful cartographer. His maps
of the counties were collected in the Theatre of the Empire of Great
Britaine, 1611. About this same time he also published Genealogies
recorded in Sacred Scripture, a work that had passed through
thirty-two editions by 1640.
[454] The history of Great
Britaine under the conquests of ye Romans, Saxons, Danes, and
Normans.... London, 1611, folio. The second edition appeared in 1623;
the third, to which De Morgan here refers, posthumously in 1632; and the
fourth in 1650.
[455] William Nicolson
(1655-1727) became Bishop of Carlisle in 1702, and Bishop of Derry in
1718. His chief work was the Historical Library (1696-1724), in
the form of a collection of documents and chronicles. It was reprinted in
1736 and in 1776.
[456] Sir Fulk Grevil, or Fulke
Greville (1554-1628), was a favorite of Queen Elizabeth, Chancellor of
the Exchequer under James I, a patron of literature, and a friend of Sir
Philip Sidney.
[457] See note 443 on page 197.
[458] See note 444 on page 197.
[459] See note 439 on page 193.
[460] Edward Waring (1736-1796)
was Lucasian professor of mathematics at Cambridge. He published several
works on analysis and curves. The work referred to was the Miscellanea
Analytica de aequationibus algebraicis et curvarum proprietatibus,
Cambridge, 1762.
[461] A Dissertation on the
use of the Negative Sign in Algebra...; to which is added, Machin's
Quadrature of the Circle, London, 1758.
[462] The paper was probably one
on complex numbers, or possibly one on quaternions, in which direction as
well as absolute value is involved.
[463] De Morgan quotes from one
of the Latin editions. Descartes wrote in French, the title of his first
edition being: Discours de la méthode pour bien conduire sa raison et
chercher la vérité dans les sciences, plus la dioptrique, les météores et
la géométrie qui sont des essais de cette méthode, Leyden, 1637,
4to.
[464] "I have observed that
algebra indeed, as it is usually taught, is so restricted by definite
rules and formulas of calculation, that it seems rather a confused kind
of an art, by the practice of which the mind is in a certain manner
disturbed and obscured, than a science by which it is cultivated and made
acute."
[465] It appeared in 93 volumes,
from 1758 to 1851.
[466] The principles of the
doctrine of life-annuities; explained in a familiar manner ... with a
variety of new tables ..., London, 1783.
[467] I suppose the one who wrote
Conjectures on the physical causes of Earthquakes and Volcanoes,
Dublin, 1820.
[468] Scriptores Logarithmici;
or, a Collection of several curious tracts on the nature and
construction of Logarithms ... together with same tracts on the Binomial
Theorem ..., 6 vols., London, 1791-1807.
[469] Charles Babbage
(1792-1871), whose work on the calculating machine is well known. Maseres
was, it is true, ninety-two at this time, but Babbage was thirty-one
instead of twenty-nine. He had already translated Lacroix's Treatise
on the differential and integral calculus (1816), in collaboration
with Herschel and Peacock. He was Lucasian professor of mathematics at
Cambridge from 1828 to 1839.
[470] The great and new Art of
weighing Vanity, or a discovery of the ignorance of the great and new
artist in his pseudo-philosophical writings. The "great and new
artist" was Sinclair.
[471] George Sinclair, probably a
native of East Lothian, who died in 1696. He was professor of philosophy
and mathematics at Glasgow, and was one of the first to use the barometer
in measuring altitudes. The work to which De Morgan refers is his
Hydrostaticks (1672). He was a firm believer in evil spirits, his
work on the subject going through four editions: Satan's Invisible
World Discovered; or, a choice collection of modern relations, proving
evidently against the Saducees and Athiests of this present age, that
there are Devils, Spirits, Witches, and Apparitions, Edinburgh,
1685.
[472] This was probably William
Sanders, Regent of St. Leonard's College, whose Theses
philosophicae appeared in 1674, and whose Elementa geometriae
came out a dozen years later.
[473] Ars nova et magna
gravitatis et levitatis; sive dialogorum philosophicorum libri sex de
aeris vera ac reali gravitate, Rotterdam, 1669, 4to.
[474] Volume I, Nos. 1 and 2,
appeared in 1803.
[475] His daughter, Mrs. De
Morgan, says in her Memoir of her husband: "My father had been
second wrangler in a year in which the two highest were close together,
and was, as his son-in-law afterwards described him, an exceedingly clear
thinker. It is possible, as Mr. De Morgan said, that this mental
clearness and directness may have caused his mathematical heresy, the
rejection of the use of negative quantities in algebraical operations;
and it is probable that he thus deprived himself of an instrument of
work, the use of which might have led him to greater eminence in the
higher branches." Memoir of Augustus De Morgan, London, 1882, p.
19.
[476] "If it is not true it is a
good invention." A well-known Italian proverb.
[477] See page 86, note 132.
[478] He was born at Paris in
1713, and died there in 1765.
[479] Recherches sur les
courbes à double courbure, Paris, 1731. Clairaut was then only
eighteen, and was in the same year made a member of the Académie des
sciences. His Elémens de géométrie appeared in 1741. Meantime he
had taken part in the measurement of a degree in Lapland (1736-1737). His
Traité de la figure de la terre was published in 1741. The Academy
of St. Petersburg awarded him a prize for his Théorie de la lune
(1750). His various works on comets are well known, particularly his
Théorie du mouvement des comètes (1760) in which he applied the
"problem of three bodies" to Halley's comet as retarded by Jupiter and
Saturn.
[480] Joseph Privat, Abbé de
Molières (1677-1742), was a priest of the Congregation of the Oratorium.
In 1723 he became a professor in the Collège de France. He was well known
as an astronomer and a mathematician, and wrote in defense of Descartes's
theory of vortices (1728, 1729). He also contributed to the methods of
finding prime numbers (1705).
[481] "Deserves not only to be
printed, but to be admired as a marvel of imagination, of understanding,
and of ability."
[482] Blaise Pascal (1623-1662),
the well-known French philosopher and mathematician. He lived for some
time with the Port Royalists, and defended them against the Jesuits in
his Provincial Letters. Among his works are the following:
Essai pour les coniques (1640); Recit de la grande expérience
de l'équilibre des liqueurs (1648), describing his experiment in
finding altitudes by barometric readings; Histoire de la roulette
(1658); Traité du triangle arithmétique (1665); Aleae
geometria (1654).
[483] This proposition shows that
if a hexagon is inscribed in a conic (in particular a circle) and the
opposite sides are produced to meet, the three points determined by their
intersections will be in the same straight line.
[484] Jacques Curabelle,
Examen des Œuvres du Sr. Desargues, Paris, 1644. He also
published without date a work entitled: Foiblesse pitoyable du Sr. G.
Desargues employée contre l'examen fait de ses œuvres.
[485] See page 119, note 233.
[486] Until "this great
proposition called Pascal's should see the light."
[487] The story is that his
father, Etienne Pascal, did not wish him to study geometry until he was
thoroughly grounded in Latin and Greek. Having heard the nature of the
subject, however, he began at the age of twelve to construct figures by
himself, drawing them on the floor with a piece of charcoal. When his
father discovered what he was doing he was attempting to demonstrate that
the sum of the angles of a triangle equals two right angles. The story is
given by his sister, Mme. Perier.
[488] Sir John Wilson (1741-1793)
was knighted in 1786 and became Commissioner of the Great Seal in 1792.
He was a lawyer and jurist of recognized merit. He stated his theorem
without proof, the first demonstration having been given by Lagrange in
the Memoirs of the Berlin Academy for 1771,—Demonstration d'un
théorème nouveau concernant les nombres premiers. Euler also gave a
proof in his Miscellanea Analytica (1773). Fermat's works should
be consulted in connection with the early history of this theorem.
[489] He wrote, in 1760, a tract
in defense of Waring, a point of whose algebra had been assailed by a Dr.
Powell. Waring wrote another tract of the same date.—A. De M.
William Samuel Powell (1717-1775) was at this time a fellow of St.
John's College, Cambridge. In 1765 he became Vice Chancellor of the
University. Waring was a Magdalene man, and while candidate for the
Lucasian professorship he circulated privately his Miscellanea
Analytica. Powell attacked this in his Observations on the First
Chapter of a Book called Miscellanea (1760). This attack was probably
in the interest of another candidate, a man of his own college (St.
John's), William Ludlam.
[490] William Paley (1743-1805)
was afterwards a tutor at Christ's College, Cambridge. He never
contributed anything to mathematics, but his Evidences of
Christianity (1794) was long considered somewhat of a classic. He
also wrote Principles of Morality and Politics (1785), and
Natural Theology (1802).
[491] Edward, first Baron Thurlow
(1731-1806) is known to Americans because of his strong support of the
Royal prerogative during the Revolution. He was a favorite of George III,
and became Lord Chancellor in 1778.
[492] George Wilson Meadley
(1774-1818) published his Memoirs of ... Paley in 1809. He also
published Memoirs of Algernon Sidney in 1813. He was a merchant
and banker, and had traveled extensively in Europe and the East. He was a
convert to unitarianism, to which sect Paley had a strong leaning.
[493] Watson (1737-1816) was a
strange kind of man for a bishopric. He was professor of chemistry at
Cambridge (1764) at the age of twenty-seven. It was his experiments that
led to the invention of the black-bulb thermometer. He is said to have
saved the government £100,000 a year by his advice on the manufacture of
gunpowder. Even after he became professor of divinity at Cambridge (1771)
he published four volumes of Chemical Essays (vol. I, 1781). He
became Bishop of Llandaff in 1782.
[494] James Adair (died in 1798)
was counsel for the defense in the trial of the publishers of the
Letters of Junius (1771). As King's Serjeant he assisted in
prosecuting Hardy and Horne Tooke.
[495] Morgan (1750-1833) was
actuary of the Equitable Assurance Society of London (1774-1830), and it
was to his great abilities that the success of that company was due at a
time when other corporations of similar kind were meeting with disaster.
The Royal Society awarded him a medal (1783) for a paper on
Probability of Survivorship. He wrote several important works on
insurance and finance.
[496] Dr. Price (1723-1791) was a
non-conformist minister and a writer on ethics, economics, politics, and
insurance. He was a defender of the American Revolution and a personal
friend of Franklin. In 1778 Congress invited him to America to assist in
the financial administration of the new republic, but he declined. His
famous sermon on the French Revolution is said to have inspired Burke's
Reflections on the Revolution in France.
[497] Elizabeth Gurney
(1780-1845), a Quaker, who married Joseph Fry (1800), a London merchant.
She was the prime mover in the Association for the Improvement of the
Female Prisoners in Newgate, founded in 1817. Her influence in prison
reform extended throughout Europe, and she visited the prisons of many
countries in her efforts to improve the conditions of penal servitude.
The friendship of Mrs. Fry with the De Morgans began in 1837. Her scheme
for a female benefit society proved worthless from the actuarial
standpoint, and would have been disastrous to all concerned if it had
been carried out, and it was therefore fortunate that De Morgan was
consulted in time. Mrs. De Morgan speaks of the consultation in these
words: "My husband, who was very sensitive on such points, was charmed
with Mrs. Fry's voice and manner as much as by the simple
self-forgetfulness with which she entered into this business; her own
very uncomfortable share of it not being felt as an element in the
question, as long as she could be useful in promoting good or preventing
mischief. I can see her now as she came into our room, took off her
little round Quaker cap, and laying it down, went at once into the
matter. 'I have followed thy advice, and I think nothing further can be
done in this case; but all harm is prevented.' In the following year I
had an opportunity of seeing the effect of her most musical tones. I
visited her at Stratford, taking my little baby and nurse with me, to
consult her on some articles on prison discipline, which I had written
for a periodical. The baby—three months old—was restless, and
the nurse could not quiet her, neither could I entirely, until Mrs. Fry
began to read something connected with the subject of my visit, when the
infant, fixing her large eyes on the reader, lay listening till she fell
asleep." Memoirs, p. 91.
[498] Mrs. Fry certainly believed
that the writer was the old actuary of the Equitable, when she first
consulted him upon the benevolent Assurance project; but we were
introduced to her by our old and dear friend Lady Noel Byron, by whom she
had been long known and venerated, and who referred her to Mr. De Morgan
for advice. An unusual degree of confidence in, and appreciation of each
other, arose on their first meeting between the two, who had so much that
was externally different, and so much that was essentially alike, in
their natures.—S. E. De M.
Anne Isabella Milbanke (1792-1860) married Lord Byron in 1815, when
both took the additional name of Noel, her mother's name. They were
separated in 1816.
[499] An obscure writer not
mentioned in the ordinary biographies.
[500] Not mentioned in the
ordinary biographies, and for obvious reasons.
[501] "Before" and "after."
[502] On Bishop Wilkins see note
171 on page 100.
[503] Provision for a
journey.
[504] See note 179 on page 103.
[505] Thomas Bradwardine
(1290-1349), known as Doctor Profundus, proctor and professor of
theology at Oxford, and afterwards Chancellor of St. Paul's and confessor
to Edward III. The English ascribed their success at Crécy to his
prayers.
[506] He was consecrated
Archbishop of Canterbury by the Pope at Avignon, July 13, 1349, and died
of the plague at London in the same year.
[507] "One paltry little
year."
[508] The title is carelessly
copied, as is so frequently the case in catalogues, even of the Libri
class. It should read: Arithmetica thome brauardini || Olivier
Senant || Venum exponuntur ab Oliuiario senant in vico diui Jacobi
sub signo beate Barbare sedente. The colophon reads: Explicit
arithmetica speculatiua thōe brauardini bn reuisa et correcta a Petro sanchez Ciruelo
aragonensi mathematicas legēte Parisius, īpressa per
Thomā anguelart. There were Paris editions of 1495, 1496, 1498,
s. a. (c. 1500), 1502, 1504, 1505, s. a. (c. 1510), 1512, 1530, a
Valencia edition of 1503, two Wittenberg editions of 1534 and 1536, and
doubtless several others. The work is not "very rare," although of course
no works of that period are common. See the editor's Rara
Arithmetica, page 61.
[509] This is his Tractatus de
proportionibus, Paris, 1495; Venice, 1505; Vienna, 1515, with other
editions.
[510] The colophon of the 1495
edition reads: Et sic explicit Geometria Thome brauardini cū
tractatulo de quadratura circuli bene reuisa a Petro sanchez ciruelo:
operaqz Guidonis mercatoris diligētissime impresse
parisio in cāpo gaillardi. Anno dni. 1495. die. 20, maij.
This Petro Ciruelo was born in Arragon, and died in 1560 at Salamanca.
He studied mathematics and philosophy at Paris, and took the doctor's
degree there. He taught at the University of Alcalà and became canon of
the Cathedral at Salamanca. Besides his editions of Bradwardine he wrote
several works, among them the Liber arithmeticae practicae qui dicitur
algorithmus (Paris, 1495) and the Cursus quatuor mathematicarum
artium liberalium (Alcalà, 1516).
[511] Star polygons, a subject of
considerable study in the later Middle Ages. See note 35 on page 44.
[512] "A new theory that adds
lustre to the fourteenth century."
[513] There is nothing in the
edition of 1495 that leads to this conclusion.
[514] The full title is:
Nouvelle théorie des parallèles, avec un appendice contenant la
manière de perfectionner la théorie des parallèles de A. M. Legendre.
The author had no standing as a scientist.
[515] Adrien Marie Legendre
(1752-1833) was one of the great mathematicians of the opening of the
nineteenth century. His Eléments de géométrie (1794) had great
influence on the geometry of the United States. His Essai sur la
théorie des nombres (1798) is one of the classics upon the subject.
The work to which Kircher refers is the Nouvelle théorie des
parallèles (1803), in which the attempt is made to avoid using
Euclid's postulate of parallels, the result being merely the substitution
of another assumption that was even more unsatisfactory. The best
presentations of the general theory are W. B. Frankland's Theories of
Parallelism, Cambridge, 1910, and Engel and Stäckel's Die Theorie
der Parallellinien von Euclid bis auf Gauss, Leipsic, 1895. Legendre
published a second work on the theory the year of his death,
Réflexions sur ... la théorie des parallèles (1833). His other
works include the Nouvelles méthodes pour la détermination des orbites
des comètes (1805), in which he uses the method of least squares; the
Traité des fonctions elliptiques et des intégrales (1827-1832),
and the Exercises de calcul intégral (1811, 1816, 1817).
[516] Johann Joseph Ignatz von
Hoffmann (1777-1866), professor of mathematics at Aschaffenburg,
published his Theorie der Parallellinien in 1801. He supplemented
this by his Kritik der Parallelen-Theorie in 1807, and his Das
eilfte Axiom der Elemente des Euclidis neu bewiesen in 1859. He wrote
other works on mathematics, but none of his contributions was of any
importance.
[517] Johann Karl Friedrich Hauff
(1766-1846) was successively professor of mathematics at Marburg,
director of the polytechnic school at Augsburg, professor at the
Gymnasium at Cologne, and professor of mathematics and physics at Ghent.
The work to which Kircher refers is his memoirs on the Euclidean
Theorie der Parallelen in Hindenburg's Archiv, vol. III
(1799), an article of no merit in the general theory.
[518] Wenceslaus Johann Gustav
Karsten (1732-1787) was professor of logic at Rostock (1758) and Butzow
(1760), and later became professor of mathematics and physics at Halle.
His work on parallels is the Versuch einer völlig berichtigten Theorie
der Parallellinien (1779). He also wrote a work entitled
Anfangsgründe der mathematischen Wissenschaften (1780), but
neither of these works was more than mediocre.
[519] Johann Christoph Schwab
(not Schwal) was born in 1743 and died in 1821. He was professor at the
Karlsschule at Stuttgart. De Morgan's wish was met, for the catalogues
give "c. fig. 8," so that it evidently had eight illustrations instead of
eight volumes. He wrote several other works on the principles of
geometry, none of any importance.
[520] Gaetano Rossi of Catanzaro.
This was the libretto writer (1772-1855), and hence the imperfections of
the work can better be condoned. De Morgan should have given a little
more of the title: Solusione esatta e regolare ... del ... problema
della quadratura del circolo. There was a second edition, London,
1805.
[521] This identifies Rossi, for
Joséphine Grassini (1773-1850) was a well-known contralto, prima
donna at Napoleon's court opera.
[522] William Spence (1783-1860)
was an entomologist and economist of some standing, a fellow of the Royal
Society, and one of the founders of the Entomological Society of London.
The work here mentioned was a popular one, the first edition appearing in
1807, and four editions being justified in a single year. He also wrote
Agriculture the Source of Britain's Wealth (1808) and
Objections against the Corn Bill refuted (1815), besides a work in
four volumes on entomology (1815-1826) in collaboration with William
Kirby.
[523] "That used to be so, but we
have changed all that."
[524] "Meet the coming
disease."
[525] George Douglas (or
Douglass) was a Scotch writer. He got out an edition of the Elements
of Euclid in 1776, with an appendix on trigonometry and a set of
tables. His work on Mathematical Tables appeared in 1809, and his
Art of Drawing in Perspective, from mathematical principles, in
1810.
[526] See note 443, on page 197.
[527] John Playfair (1748-1848)
was professor of mathematics (1785) and natural philosophy (1805) at the
University of Edinburgh. His Elements of Geometry went through
many editions.
[528] "Tell Apella" was an
expression current in classical Rome to indicate incredulity and to show
the contempt in which the Jew was held. Horace says: Credat Judæus
Apella, "Let Apella the Jew believe it." Our "Tell it to the
marines," is a similar phrase.
[529] As De Morgan says two lines
later, "No mistake is more common than the natural one of imagining that
the"—University of Virginia is at Richmond. The fact is that it is
not there, and that it did not exist in 1810. It was not chartered until
1819, and was not opened until 1825, and then at Charlottesville. The act
establishing the Central College, from which the University of Virginia
developed, was passed in 1816. The Jean Wood to whom De Morgan refers was
one John Wood who was born about 1775 in Scotland and who emigrated to
the United States in 1800. He published a History of the
Administration of J. Adams (New York, 1802) that was suppressed by
Aaron Burr. This act called forth two works, a Narrative of the
Suppression, by Col. Burr, of the 'History of the Administration of John
Adams' (1802), in which Wood was sustained; and the Antidote to
John Wood's Poison (1802), in which he was attacked. The work
referred to in the "printed circular" may have been the New theory of
the diurnal rotation of the earth (Richmond, Va., 1809). Wood spent
the last years of his life in Richmond, Va., making county maps. He died
there in 1822. A careful search through works relating to the University
of Virginia fails to show that Wood had any connection with it.
[530] There seems to be nothing
to add to Dobson's biography beyond what De Morgan has so deliciously set
forth.
[531] "Give to each man his
due."
[532] Hester Lynch Salusbury
(1741-1821), the friend of Dr. Johnson, married Henry Thrale (1763), a
brewer, who died in 1781. She then married Gabriel Piozzi (1784), an
Italian musician. Her Anecdotes of the late Samuel Johnson (1786)
and Letters to and from Samuel Johnson (1788) are well known. She
also wrote numerous essays and poems.
[533] Samuel Pike (c. 1717-1773)
was an independent minister, with a chapel in London and a theological
school in his house. He later became a disciple of Robert Sandeman and
left the Independents for the Sandemanian church (1765). The
Philosophia Sacra was first published at London in 1753. De Morgan
here cites the second edition.
[534] Pike had been dead over
forty years when Kittle published this second edition. Kittle had already
published a couple of works: King Solomon's portraiture of Old Age
(Edinburgh, 1813), and Critical and Practical Lectures on the
Apocalyptical Epistles to the Seven Churches of Asia Minor (London,
1814).
[535] See note 334, on page 152.
[536] William Stukely (1687-1765)
was a fellow of the Royal Society and of the College of Physicians and
Surgeons. He afterwards (1729) entered the Church. He was prominent as an
antiquary, especially in the study of the Roman and Druidic remains of
Great Britain. He was the author of numerous works, chiefly on
paleography.
[537] William Jones (1726-1800),
who should not be confused with his namesake who is mentioned in note 281 on page 135. He was a
lifelong friend of Bishop Horne, and his vicarage at Nayland was a
meeting place of an influential group of High Churchmen. Besides the
Physiological Disquisitions (1781) he wrote The Catholic
Doctrine of the Trinity (1756) and The Grand Analogy
(1793).
[538] Robert Spearman (1703-1761)
was a pupil of John Hutchinson, and not only edited his works but wrote
his life. He wrote a work against the Newtonian physics, entitled An
Enquiry after Philosophy and Theology (Edinburgh, 1755), besides the
Letters to a Friend concerning the Septuagint Translation
(Edinburgh, 1759) to which De Morgan refers.
[539] A writer of no importance,
at least in the minds of British biographers.
[540] Alexander Catcott
(1725-1779), a theologian and geologist, wrote not only a work on the
creation (1756) but a Treatise on the Deluge (1761, with a second
edition in 1768). Sir Charles Lyell considered the latter work a valuable
contribution to geology.
[541] James Robertson
(1714-1795), professor of Hebrew at the University of Edinburgh. Probably
De Morgan refers to his Grammatica Linguae Hebrææ (Edinburgh,
1758; with a second edition in 1783). He also wrote Clavis
Pentateuchi (1770).
[542] Benjamin Holloway (c.
1691-1759), a geologist and theologian. He translated Woodward's
Naturalis Historia Telluris, and was introduced by Woodward to
Hutchinson. The work referred to by De Morgan appeared at Oxford in two
volumes in 1754.
[543] His work was The
Christian plan exhibited in the interpretation of Elohim: with
observations upon a few other matters relative to the same subject,
Oxford, 1752, with a second edition in 1755.
[544] Duncan Forbes (1685-1747)
studied Oriental languages and Civil law at Leyden. He was Lord President
of the Court of Sessions (1737). He wrote a number of theological
works.
[545] Should be 1756.
[546] Edward Henry Bickersteth
(1825-1906), bishop of Exeter (1885-1900); published The Rock of Ages;
or scripture testimony to the one Eternal Godhead of the Father, and of
the Son, and of the Holy Ghost at Hampstead in 1859. A second edition
appeared at London in 1860.
[547] Thomas Sadler (1822-1891)
took his Ph.D. at Erlangen in 1844, and became a Unitarian minister at
Hampstead, where Bickersteth's work was published. Besides writing the
Gloria Patri (1859), he edited Crabb Robinson's Diaries.
[548] This was his Virgil's
Bucolics and the two first Satyrs of Juvenal, 1634.
[549] Possibly in his Twelve
Questions or Arguments drawn out of Scripture, wherein the commonly
received Opinion touching the Deity of the Holy Spirit is clearly and
fully refuted, 1647. This was his first heretical work, and it was
followed by a number of others that were written during the intervals in
which the Puritan parliament allowed him out of prison. It was burned by
the hangman as blasphemous. Biddle finally died in prison, unrepentant to
the last.
[550] The first edition of the
anonymous
Ἁιρεσεων
ἀναστασις (by
Vicars?) appeared in 1805.
[551] Possibly by Thomas Pearne
(c. 1753-1827), a fellow of St. Peter's College, Cambridge, and a
Unitarian minister.
[552] Thomas Wentworth, Earl of
Strafford, was borne in London in 1593, and was executed there in 1641.
He was privy councilor to Charles I, and was Lord Deputy of Ireland. On
account of his repressive measures to uphold the absolute power of the
king he was impeached by the Long Parliament and was executed for
treason. The essence of his defence is in the sentence quoted by De
Morgan, to which Pym replied that taken as a whole, the acts tended to
show an intention to change the government, and this was in itself
treason.
[553] The name assumed by a
writer who professed to give a mathematical explanation of the Trinity,
see farther on.—S. E. De M.
[554] Sabellius (fl. 230 A.D.)
was an early Christian of Libyan origin. He taught that Father, Son, and
Holy Spirit were different names for the same person.
[555] Sir Richard Phillips was
born in London in 1767 (not 1768 as stated above), and died there in
1840. He was a bookseller and printer in Leicester, where he also edited
a radical newspaper. He went to London to live in 1795 and started the
Monthly Magazine there in 1796. Besides the works mentioned by De
Morgan he wrote on law and economics.
[556] It was really eighteen
months.
[557] While he was made sheriff
in 1807 he was not knighted until the following year.
[558] James Mitchell (c.
1786-1844) was a London actuary, or rather a Scotch actuary living a good
part of his life in London. Besides the work mentioned he compiled a
Dictionary of Chemistry, Mineralogy, and Geology (1823), and wrote
On the Plurality of Worlds (1813) and The Elements of
Astronomy (1820).
[559] Richarda Smith, wife of Sir
George Biddell Airy (see note 129, page 85) the astronomer. In 1835 Sir Robert Peel offered a
pension of £300 a year to Airy, who requested that it be settled on his
wife.
[560] Mary Fairfax (1780-1872)
married as her second husband Dr. William Somerville. In 1826 she
presented to the Royal Society a paper on The Magnetic Properties of
the Violet Rays of the Solar Spectrum, which attracted much
attention. It was for her Mechanism of the Heavens (1831), a
popular translation of Laplace's Mécanique Céleste, that she was
pensioned.
[561] Dominique François Jean
Arago (1786-1853) the celebrated French astronomer and physicist.
[562] For there is a well-known
series
1 + 1/22 + 1/32 + ... = π2/6.
If, therefore, the given series equals 1, we have
But c = πd, and twice the diagonal of a
cube on the diameter is 2d √3.
[563] There was a second edition
in 1821.
[564] London, 1830.
[565] He was a resident of
Chatham, and seems to have published no other works.
[566] Richard Whately (1787-1863)
was, as a child, a calculating prodigy (see note 132, page 86), but lost the
power as is usually the case with well-balanced minds. He was a fellow of
Oriel College, Oxford, and in 1825 became principal of St. Alban Hall. He
was a friend of Newman, Keble, and others who were interested in the
religious questions of the day. He became archbishop of Dublin in 1831.
He was for a long time known to students through his Logic (1826)
and Rhetoric (1828).
[567] William King, D.C.L.
(1663-1712), student at Christ Church, Oxford, and celebrated as a wit
and scholar. His Dialogues of the Dead (1699) is a satirical
attack on Bentley.
[568] Thomas Ebrington
(1760-1835) was a fellow of Trinity College, Dublin, and taught divinity,
mathematics, and natural philosophy there. He became provost of the
college in 1811, bishop of Limerick in 1820, and bishop of Leighlin and
Ferns in 1822. His edition of Euclid was reprinted a dozen times. The
Reply to John Search's Considerations on the Law of Libel appeared
at Dublin in 1834.
[569] Joseph Blanco White
(1775-1841) was the son of an Irishman living in Spain. He was born at
Seville and studied for orders there, being ordained priest in 1800. He
lost his faith in the Roman Catholic Church, and gave up the ministry,
escaping to England at the time of the French invasion. At London he
edited Español, a patriotic journal extensively circulated in
Spain, and for this service he was pensioned after the expulsion of the
French. He then studied at Oriel College, Oxford, and became intimate
with men like Whately, Newman, and Keble. In 1835 he became a Unitarian.
Among his theological writings is his Evidences against
Catholicism (1825). The "rejoinder" to which De Morgan refers
consisted of two letters: The law of anti-religious Libel
reconsidered (Dublin, 1834) and An Answer to some Friendly Remarks
on "The Law of Anti-Religious Libel Reconsidered" (Dublin, 1834).
[570] The work was translated
from the French.
[571] J. Hoëné Wronski
(1778-1853) served, while yet a mere boy, as an artillery officer in
Kosciusko's army (1791-1794). He was imprisoned after the battle of
Maciejowice. He afterwards lived in Germany, and (after 1810) in Paris.
For the bibliography of his works see S. Dickstein's article in the
Bibliotheca Mathematica, vol. VI (2), page 48.
[572] Perhaps referring to his
Introduction à la philosophie des mathématiques (1811).
[573] Read "equation of the."
[574] Thomas Young (1773-1829),
physician and physicist, sometimes called the founder of physiological
optics. He seems to have initiated the theory of color blindness that was
later developed by Helmholtz. The attack referred to was because of his
connection with the Board of Longitude, he having been made (1818)
superintendent of the Nautical Almanac and secretary of the Board. He
opposed introducing into the Nautical Almanac anything not immediately
useful to navigation, and this antagonized many scientists.
[575] Isaac Milner (1750-1820)
was professor of natural philosophy at Cambridge (1783) and later became,
as De Morgan states, president of Queens' College (1788). In 1791 he
became dean of Carlisle, and in 1798 Lucasian professor of mathematics.
His chief interest was in chemistry and physics, but he contributed
nothing of importance to these sciences or to mathematics.
[576] Thomas Perronet Thompson
(1783-1869), fellow of Queens' College, Cambridge, saw service in Spain
and India, but after 1822 lived in England. He became major general in
1854, and general in 1868. Besides some works on economics and politics
he wrote a Geometry without Axioms (1830) that De Morgan includes
later on in his Budget. In it Thompson endeavored to prove the
parallel postulate.
[577] De Morgan's father-in-law.
See note 441, page 196.
[578] Johann Friedrich Herbart
(1776-1841), successor of Kant as professor of philosophy at Königsberg
(1809-1833), where he established a school of pedagogy. From 1833 until
his death he was professor of philosophy at Göttingen. The title of the
pamphlet is: De Attentionis mensura causisque primariis. Psychologiae
principia statica et mechanica exemplo illustraturus.... Regiomonti,...
1822. The formulas in question are given on pages 15 and 17, and De
Morgan has omitted the preliminary steps, which are, for the first
one:
unde βt= Const / (φ - z).
Pro t = 0 etiam z = 0; hinc βt = log φ/(φ - z).
These are, however, quite elementary as compared with other portions
of the theory.
[579] See note 371, page 168.
[580] William Law (1686-1761) was
a clergyman, a fellow of Emanuel College, Cambridge, and in later life a
convert to Behmen's philosophy. He was so free in his charities that the
village in which he lived became so infested by beggars that he was urged
by the citizens to leave. He wrote A serious call to a devout and holy
life (1728).
[581] He was a curate at
Cheshunt, and wrote the Spiritual voice to the Christian Church and to
the Jews (London, 1760), A second warning to the world by the
Spirit of Prophecy (London, 1760), and Signs of the Times; or a
Voice to Babylon (London, 1773).
[582] His real name was Thomas
Vaughan (1622-1666). He was a fellow of Jesus College, Oxford, taking
orders, but was deprived of his living on account of drunkenness. He
became a mystic philosopher and gave attention to alchemy. His works had
a large circulation, particularly on the continent. He wrote Magia
Adamica (London, 1650), Euphrates; or the Waters of the East
(London, 1655), and The Chymist's key to shut, and to open; or the
True Doctrine of Corruption and Generation (London, 1657).
[583] Emanuel Swedenborg, or
Svedberg (1688-1772) the mystic. It is not commonly known to
mathematicians that he was one of their guild, but he wrote on both
mathematics and chemistry. Among his works are the Regelkonst eller
algebra (Upsala, 1718) and the Methodus nova inveniendi
longitudines locorum, terra marique, ope lunae (Amsterdam, 1721,
1727, and 1766). After 1747 he devoted his attention to mystic
philosophy.
[584] Pierre Simon Laplace
(1749-1827), whose Exposition du système du monde (1796) and
Traité de mécanique celeste (1799) are well known.
[585] See note 117, page 76.
[586] John Dalton (1766-1844),
who taught mathematics and physics at New College, Manchester (1793-1799)
and was the first to state the law of the expansion of gases known by his
name and that of Gay-Lussac. His New system of Chemical Philosophy
(Vol. I, pt. i, 1808; pt. ii, 1810; vol. II, 1827) sets forth his atomic
theory.
[587] Howison was a poet and
philosopher. He lived in Edinburgh and was a friend of Sir Walter Scott.
This work appeared in 1822.
[588] He was a shoemaker, born
about 1765 at Haddiscoe, and his "astro-historical" lectures at Norwich
attracted a good deal of attention at one time. He traced all geologic
changes to differences in the inclination of the earth's axis to the
plane of its orbit. Of the works mentioned by De Morgan the first
appeared at Norwich in 1822-1823, and there was a second edition in 1824.
The second appeared in 1824-1825. The fourth was Urania's Key to the
Revelation; or the analyzation of the writings of the Jews..., and
was first published at Norwich in 1823, there being a second edition at
London in 1833. His books were evidently not a financial success, for
Mackey died in an almshouse at Norwich.
[589] Godfrey Higgins
(1773-1833), the archeologist, was interested in the history of religious
beliefs and in practical sociology. He wrote Horae Sabbaticae
(1826), The Celtic Druids (1827 and 1829), and Anacalypsis, an
attempt to draw aside the veil of the Saitic Isis; or an Inquiry into the
Origin of Languages, Nations, and Religions (posthumously published,
1836), and other works. See also page 274,
infra.
[590] The work also appeared in
French. Wirgman wrote, or at least began, two other works:
Divarication of the New Testament into Doctrine and History; part I,
The Four Gospels (London, 1830), and Mental Philosophy; part I,
Grammar of the five senses; being the first step to infant education
(London, 1838).
[591] He was born at Shandrum,
County Limerick, and supported himself by teaching writing and
arithmetic. He died in an almshouse at Cork.
[592] George Boole (1815-1864),
professor of mathematics at Queens' College, Cork. His Laws of
Thought (1854) was the first work on the algebra of logic.
[593] Oratio Grassi (1582-1654),
the Jesuit who became famous for his controversy with Galileo over the
theory of comets. Galileo ridiculed him in Il Saggiatore, although
according to the modern view Grassi was the more nearly right. It is said
that the latter's resentment led to the persecution of Galileo.
[594] De Morgan might have found
much else for his satire in the letters of Walsh. He sought, in his
Theory of Partial Functions, to substitute "partial equations" for
the differential calculus. In his diary there is an entry: "Discovered
the general solution of numerical equations of the fifth degree at 114
Evergreen Street, at the Cross of Evergreen, Cork, at nine o'clock in the
forenoon of July 7th, 1844; exactly twenty-two years after the invention
of the Geometry of Partial Equations, and the expulsion of the
differential calculus from Mathematical Science."
[595] "It has been ordered, sir,
it has been ordered."
[596] Bartholomew Prescot was a
Liverpool accountant. De Morgan gives this correct spelling on page 278. He died after 1849. His Inverted Scheme of
Copernicus appeared in Liverpool in 1822.
[597] Robert Taylor (1784-1844)
had many more ups and downs than De Morgan mentions. He was a priest of
the Church of England, but resigned his parish in 1818 after preaching
against Christianity. He soon recanted and took another parish, but was
dismissed by the Bishop almost immediately on the ground of heresy. As
stated in the text, he was convicted of blasphemy in 1827 and was
sentenced to a year's imprisonment, and again for two years on the same
charge in 1831. He then married a woman who was rich in money and in
years, and was thereupon sued for breach of promise by another woman. To
escape paying the judgment that was rendered against him he fled to Tours
where he took up surgery.
[598] Herbert Marsh, Bishop of
Peterborough. See note 449 on page 199.
[599] "Argument from the
prison."
[600] Richard Carlile
(1790-1843), one of the leading radicals of his time. He published Hone's
parodies (see note 250, page 124) after they had been suppressed, and an edition
of Thomas Paine (1818). He was repeatedly imprisoned, serving nine years
in all. His continued conflict with the authorities proved a good
advertisement for his bookshop.
[601] Wilhelm Ludwig Christmann
(1780-1835) was a protestant clergyman and teacher of mathematics. For a
while he taught under Pestalozzi. Disappointed in his ambition to be
professor of mathematics at Tubingen, he became a confirmed misanthrope
and is said never to have left his house during the last ten years of his
life. He wrote several works: Ein Wort über Pestalozzi und
Pestalozzismus (1812); Ars cossae promota (1814);
Philosophia cossica (1815); Aetas argentea cossae (1819);
Ueber Tradition und Schrift, Logos und Kabbala (1829), besides the
one mentioned above. The word coss in the above titles was a
German name for algebra, from the Italian cosa (thing), the name
for the unknown quantity. It appears in English in the early name for
algebra, "the cossic art."
[602] See note 174, page 101.
[603] See note 589, page 257.
[604] He seems to have written
nothing else.
[605] See note 596 on page 270. The name is
here spelled correctly.
[606] Joseph Jacotot (1770-1840),
the father of this Fortuné Jacotot, was an infant prodigy. At nineteen he
was made professor of the humanities at Dijon. He served in the army, and
then became professor of mathematics at Dijon. He continued in his chair
until the restoration of the Bourbons, and then fled to Louvain. It was
here that he developed the method with which his name is usually
connected. He wrote a Mathématiques in 1827, which went through
four editions. The Epitomé is by his son, Fortuné.
[607] He wrote on educational
topics and a Sacred History that went through several
editions.
[608] "All is in all."
[609] "Know one thing and refer
everything else to it," as it is often translated.
[610] A writer of no
reputation.
[611] Sir John Lubbock
(1803-1865), banker, scientist, publicist, astronomer, one of the
versatile men of his time.
[612] See note 165, page 99.
[613] "Those about to die salute
you."
[614] Georges Louis Leclerc
Buffon (1707-1788), the well-known biologist. He also experimented with
burning mirrors, his results appearing in his Invention des miroirs
ardens pour brûler à une grande distance (1747). The reference here
may be to his Resolution des problèmes qui regardent le jeu du franc
carreau (1733). The prominence of his Histoire naturelle (36
volumes, 1749-1788) has overshadowed the credit due to him for his
translation of Newton's work on Fluxions.
[615] See page 285. This article was a supplement to No. 14 in the
Athenæum Budget.—A. De M.
[616] There are many similar
series and products. Among the more interesting are the following:
π
2 | = | 2·2·4·4·6·6·8...
1·3·3·5·5·7·7... | ,
|
π-3
4 | = | 1
2·3·4 | - | 1
4·5·6 | + | 1
6·7·8 | -...,
|
π
6 | = |  | | 1
3 | · |  | 1 - | 1
3·3 | + | 1
32·5 | - | 1
33·7 | + | 1
34·9 | - ... |  | ,
|
π
4 | = 4 | | | 1
5 | - | 1
3·53 | + | 1
5·55 | - | 1
7·57 | + ... | | - | | | 1
239 | - | 1
3·2393 | + | 1
5·2395 | - ... | | .
|
[617] "To a privateer, a
privateer and a half."
[618] Joshua Milne (1776-1851)
was actuary of the Sun Life Assurance Society. He wrote A Treatise on
the Valuation of Annuities and Assurances on Lives and Survivorships; on
the Construction of tables of mortality; and on the Probabilities and
Expectations of Life, London, 1815. Upon the basis of the Carlisle
bills of mortality of Dr. Heysham he reconstructed the mortality tables
then in use and which were based upon the Northampton table of Dr. Price.
His work revolutionized the actuarial science of the time. In later years
he devoted his attention to natural history.
[619] See note 576, page 252. He also wrote
the Theory of Parallels. The proof of Euclid's axiom looked for in the
properties of the equiangular spiral (London, 1840), which went
through four editions, and the Theory of Parallels. The proof that the
three angles of a triangle are equal to two right angles looked for in
the inflation of the sphere (London, 1853), of which there were three
editions.
[620] For the latest summary, see
W. B. Frankland, Theories of Parallelism, an historical critique,
Cambridge, 1910.
[621] Joseph Louis Lagrange
(1736-1813), author of the Mécanique analytique (1788), Théorie
des functions analytiques (1797), Traité de la résolution des
équations numériques de tous degrés (1798), Leçons sur le calcul
des fonctions (1806), and many memoirs. Although born in Turin and
spending twenty of his best years in Germany, he is commonly looked upon
as the great leader of French mathematicians. The last twenty-seven years
of his life were spent in Paris, and his remarkable productivity
continued to the time of his death. His genius in the theory of numbers
was probably never excelled except by Fermat. He received very high
honors at the hands of Napoleon and was on the first staff of the Ecole
polytechnique (1797).
[622] "I shall have to think it
over again."
[623] Henry Goulburn (1784-1856)
held various government posts. He was under-secretary for war and the
colonies (1813), commissioner to negotiate peace with America (1814),
chief secretary to the Lord Lieutenant of Ireland (1821), and several
times Chancellor of the Exchequer. On the occasion mentioned by De Morgan
he was standing for parliament, and was successful.
[624] On Drinkwater Bethune see
note 165, page 99.
[625] Charles Henry Cooper
(1808-1866) was a biographer and antiquary. He was town clerk of
Cambridge (1849-1866) and wrote the Annals of Cambridge
(1842-1853). His Memorials of Cambridge (1874) appeared after his
death. Thompson Cooper was his son, and the two collaborated in the
Athenae Cantabrigiensis (1858).
[626] William Yates Peel
(1789-1858) was a brother of Sir Robert Peel, he whose name degenerated
into the familiar title of the London "Bobby" or "Peeler." Yates Peel was
a member of parliament almost continuously from 1817 to 1852. He
represented Cambridge at Westminster from 1831 to 1835.
[627] Henry John Temple, third
Viscount of Palmerston (1784-1865), was member for Cambridge in 1811,
1818, 1820, 1826 (defeating Goulburn), and 1830. He failed of reelection
in 1831 because of his advocacy of reform. This must have been the time
when Goulburn defeated him. He was Foreign Secretary (1827) and Secretary
of State for Foreign Affairs (1830-1841, and 1846-1851). It is said of
him that he "created Belgium, saved Portugal and Spain from absolutism,
rescued Turkey from Russia and the highway to India from France." He was
Prime Minister almost continuously from 1855 to 1865, a period covering
the Indian Mutiny and the American Civil War.
[628] William Cavendish, seventh
Duke of Devonshire (1808-1891). He was member for Cambridge from 1829 to
1831, but was defeated in 1831 because he had favored parliamentary
reform. He became Earl of Burlington in 1834, and Duke of Devonshire in
1858. He was much interested in the promotion of railroads and in the
iron and steel industries.
[629] Richard Sheepshanks
(1794-1855) was a brother of John Sheepshanks the benefactor of art. (See
note 314, p. 147.) He was a
fellow of Trinity College, Cambridge, a fellow of the Royal Society and
secretary of the Astronomical Society. Babbage (See note 469, p. 207) suspected him of
advising against the government support of his calculating machine and
attacked him severely in his Exposition of 1851, in the chapter on
The Intrigues of Science. Babbage also showed that Sheepshanks got
an astronomical instrument of French make through the custom house by
having Troughton's (See note 332, page 152) name engraved on it. Sheepshanks admitted this
second charge, but wrote a Letter in Reply to the Calumnies of Mr.
Babbage, which was published in 1854. He had a highly controversial
nature.
[630] See note 469, page 207. The work
referred to is Passages from the Life of a Philosopher, London,
1864.
[631] Drinkwater Bethune. See
note 165, page 99.
[632] Siméon-Denis Poisson
(1781-1840) was professor of calculus and mechanics at the Ecole
polytechnique. He was made a baron by Napoleon, and was raised to the
peerage in 1837. His chief works are the Traité de mécanìque
(1811) and the Traité mathématique de la chaleur (1835).
[633] "As to M. Poisson, I really
wish I had a thousandth part of his mathematical knowledge that I might
prove my system to the incredulous."
[634] This list includes most of
the works of Antoine-Louis-Guénard Demonville. There was also the
Nouveau système du monde ... et hypothèses conformes aux expériences
sur les vents, sur la lumière et sur le fluide électro-magnétique,
Paris, 1830.
[635] Paris, 1835.
[636] Paris, 1833.
[637] The second part appeared in
1837. There were also editions in 1850 and 1852, and one edition appeared
without date.
[638] Paris, 1842.
[639] Parsey also wrote The
Art of Miniature Painting on Ivory (1831), Perspective
Rectified (1836), and The Science of Vision (1840), the third
being a revision of the second.
[640] William Ritchie (1790-1837)
was a physicist who had studied at Paris under Biot and Gay-Lussac. He
contributed several papers on electricity, heat, and elasticity, and was
looked upon as a good experimenter. Besides the geometry he wrote the
Principles of the Differential and Integral Calculus (1836).
[641] Alfred Day (1810-1849) was
a man who was about fifty years ahead of his time in his attempt to get
at the logical foundations of geometry. It is true that he laid himself
open to criticism, but his work was by no means bad. He also wrote A
Treatise on Harmony (1849, second edition 1885), The Rotation of
the Pendulum (1851), and several works on Greek and Latin
Grammar.
[642] Walter Forman wrote a
number of controversial tracts. His first seems to have been A plan
for improving the Revenue without adding to the burdens of the
people, a letter to Canning in 1813. He also wrote A New Theory of
the Tides (1822). His Letter to Lord John Russell, on Lord
Brougham's most extraordinary conduct; and another to Sir J. Herschel, on
the application of Kepler's third law appeared in 1832.
[643] Lord John Russell
(1792-1878) first Earl Russell, was one of the strongest supporters of
the reform measures of the early Victorian period. He became prime
minister in 1847, and again in 1865.
[644] Lauder seems never to have
written anything else.
[645] See note 22, page 40.
[646] The names of Alphonso Cano
de Molina, Yvon, and Robert Sara have no standing in the history of the
subject beyond what would be inferred from De Morgan's remark.
[647] Claude Mydorge (1585-1647),
an intimate friend of Descartes, was a dilletante in mathematics who read
much but accomplished little. His Récréations mathématiques is his
chief work. Boncompagni published the "Problèmes de Mydorge" in his
Bulletino.
[648] Claude Hardy was born
towards the end of the 16th century and died at Paris in 1678. In 1625 he
edited the Data Euclidis, publishing the Greek text with a Latin
translation. He was a friend of Mydorge and Descartes, but an opponent of
Fermat.
[649] That is, in the
Bibliotheca Realis of Martin Lipen, or Lipenius (1630-1692), which
appeared in six folio volumes, at Frankfort, 1675-1685.
[650] See note 29, page 43.
[651] Baldassare Boncompagni
(1821-1894) was the greatest general collector of mathematical works that
ever lived, possibly excepting Libri. His magnificent library was
dispersed at his death. His Bulletino (1868-1887) is one of the
greatest source books on the history of mathematics that we have. He also
edited the works of Leonardo of Pisa.
[652] He seems to have attracted
no attention since De Morgan's search, for he is not mentioned in recent
bibliographies.
[653] Joseph-Louis Vincens de
Mouléon de Causans was born about the beginning of the l8th century. He
was a Knight of Malta, colonel in the infantry, prince of Conti, and
governor of the principality of Orange. His works on geometry are the
Prospectus apologétique pour la quadrature du cercle (1753), and
La vraie géométrie transcendante (1754).
[654] See note 119, page 80.
[655] See note 120, page 81.
[656] Lieut. William Samuel
Stratford (1791-1853), was in active service during the Napoleonic wars
but retired from the army in 1815. He was first secretary of the
Astronomical Society (1820) and became superintendent of the Nautical
Almanac in 1831. With Francis Baily he compiled a star catalogue, and
wrote on Halley's (1835-1836) and Encke's (1838) comets.
[657] See Sir J. Herschel's
Astronomy, p. 369.—A. De M.
[658] Captain Ross had just stuck
a bit of brass there.—A. De M.
Sir James Clark Ross (1800-1862) was a rear admiral in the British
navy and an arctic and antarctic explorer of prominence. De Morgan's
reference is to Ross's discovery of the magnetic pole on June 1, 1831. In
1838 he was employed by the Admiralty on a magnetic survey of the United
Kingdom. He was awarded the gold medal of the geographical societies of
London and Paris in 1842.
[659] John Partridge (1644-1715),
the well-known astrologer and almanac maker. Although bound to a
shoemaker in his early boyhood, he had acquired enough Latin at the age
of eighteen to read the works of the astrologers. He then mastered Greek
and Hebrew and studied medicine. In 1680 he began the publication of his
almanac, the Merlinus Liberatus, a book that acquired literary
celebrity largely through the witty comments upon it by such writers as
Swift and Steele.
[660] See note 642 on page 296.
[661] William Woodley also
published several almanacs (1838, 1839, 1840) after his rejection by the
Astronomical Society in 1834.
[662] It appeared at London.
[663] The first edition appeared
in 1830, also at London.
[664] See note 441, page 196.
[665] Thomas Kerigan wrote The
Young Navigator's Guide to the siderial and planetary parts of Nautical
Astronomy (London, 1821, second edition 1828), a work on eclipses
(London, 1844), and the work on tides (London, 1847) to which De Morgan
refers.
[666] Jean Sylvain Bailly, who
was guillotined. See note 365, page 166.
[667] See note 670, page 309.
[668] Laurent seems to have had
faint glimpses of the modern theory of matter. He is, however,
unknown.
[669] See note 133, page 87.
[670] Francis Baily (1774-1844)
was a London stockbroker. His interest in science in general and in
astronomy in particular led to his membership in the Royal Society and to
his presidency of the Astronomical Society. He wrote on interest and
annuities (1808), but his chief works were on astronomy.
[671] If the story is correctly
told Baily must have enjoyed his statement that Gauss was "the oldest
mathematician now living." As a matter of fact he was then only 58, three
years the junior of Baily himself. Gauss was born in 1777 and died in
1855, and Baily was quite right in saying that he was "generally thought
to be the greatest" mathematician then living.
[672] Margaret Cooke, who married
Flamsteed in 1692.
[673] John Brinkley (1763-1835),
senior wrangler, first Smith's prize-man (1788), Andrews professor of
astronomy at Dublin, first Astronomer Royal for Ireland (1792), F.R.S.
(1803), Copley medallist, president of the Royal Society and Bishop of
Cloyne. His Elements of Astronomy appeared in 1808.
[674] See note 248, page 124.
[675] See note 276, page 133.
[676] See note 352, page 161.
[677] "It becomes the doctors of
the Sorbonne to dispute, the Pope to decree, and the mathematician to go
to Paradise on a perpendicular line."
[678] See note 124, page 83.
[679] See note 621, page 288.
[680] Sylvain van de Weyer, who
was born at Louvain in 1802. He was a jurist and statesman, holding the
portfolio for foreign affairs (1831-1833), and being at one time
ambassador to England.
[681] Henry Crabb Robinson
(1775-1867), correspondent of the Times at Altona and in the
Peninsula, and later foreign editor. He was one of the founders of the
Athenæum Club and of University College, London. He seems to have known
pretty much every one of his day, and his posthumous Diary
attracted attention when it appeared.
[682] Was this Whewell, who was
at Trinity from 1812 to 1816 and became a fellow in 1817?
[683] Tom Cribb (1781-1848) the
champion pugilist. He had worked as a coal porter and hence received his
nickname, the Black Diamond.
[684] John Finleyson, or
Finlayson, was born in Scotland in 1770 and died in London in 1854. He
published a number of pamphlets that made a pretense to being scientific.
Among his striking phrases and sentences are the statements that the
stars were made "to amuse us in observing them"; that the earth is "not
shaped like a garden turnip as the Newtonians make it," and that the
stars are "oval-shaped immense masses of frozen water." The first edition
of the work here mentioned appeared at London in 1830.
[685] Richard Brothers
(1757-1824) was a native of Newfoundland. He went to London when he was
about 30, and a little later set forth his claim to being a descendant of
David, prince of the Hebrews, and ruler of the world. He was confined as
a criminal lunatic in 1795 but was released in 1806.
[686] Charles Grey (1764-1845),
second Earl Grey, Viscount Howick, was then Prime Minister. The Reform
Bill was introduced and defeated in 1831. The following year, with the
Royal guarantees to allow him to create peers, he finally carried the
bill in spite of "the number of the beast."
[687] The letters of obscure men,
the Epistolæ obscurorum virorum ad venerabilem virum Magistrum
Ortuinum Gratium Dauentriensem, by Joannes Crotus, Ulrich von Hutten,
and others appeared at Venice about 1516.
[688] The lamentations of obscure
men, the Lamentationes obscurorum virorum, non prohibete per sedem
Apostolicam. Epistola D. Erasmi Roterodami: quid de obscuris sentiat,
by G. Ortwinus, appeared at Cologne in 1518.
[689] The criticism was timely
when De Morgan wrote it. At present it would have but little force with
respect to the better class of algebras.
[690] Thomas Ignatius Maria
Forster (1789-1860) was more of a man than one would infer from this
satire upon his theory. He was a naturalist, astronomer, and
physiologist. In 1812 he published his Researches about Atmospheric
Phenomena, and seven years later (July 3, 1819) he discovered a
comet. With Sir Richard Phillips he founded a Meteorological Society, but
it was short lived. He declined a fellowship in the Royal Society because
he disapproved of certain of its rules, so that he had a recognized
standing in his day. The work mentioned by De Morgan is the second
edition, the first having appeared at Frankfort on the Main in 1835 under
the title, Recueil des ouvrages et des pensées d'un physicien et
metaphysicien.
[691] Zadkiel, whose real name
was Richard James Morrison (1795-1874), was in his early years an officer
in the navy. In 1831 he began the publication of the Herald of
Astrology, which was continued as Zadkiel's Almanac. His name
became familiar throughout Great Britain as a result.
[692] See note 566, page 246.
[693] Sumner (1780-1862) was an
Eton boy. He went to King's College, Cambridge, and was elected fellow in
1801. He took many honors, and in 1807 became M.A. He was successively
Canon of Durham (1820), Bishop of Chester (1828), and Archbishop of
Canterbury (1848). Although he voted for the Catholic Relief Bill (1829)
and the Reform Bill (1832), he opposed the removal of Jewish
disabilities.
[694] Charles Richard Sumner
(1790-1874) was not only Bishop of Winchester (1827), but also Bishop of
Llandaff and Dean of St. Paul's, London (1826). He lost the king's favor
by voting for the Catholic Relief Bill.
[695] John Bird Sumner, brother
of Charles Richard.
[696] Thomas Musgrave (1788-1860)
became Fellow of Trinity in 1812, and senior proctor in 1831. He was also
Dean of Bristol.
[697] Charles Thomas Longley
(1794-1868) was educated at Westminster School and at Christ Church,
Oxford. He became M.A. in 1818 and D.D. in 1829. Besides the bishoprics
mentioned he was Bishop of Ripon (1836-1856), and before that was
headmaster of Harrow (1829-1836).
[698] Thomson (1819-1890) was
scholar and fellow of Queen's College, Oxford. He became chaplain to the
Queen in 1859.
[699] This is worthy of the
statistical psychologists of the present day.
[700] The famous Moon Hoax was
written by Richard Adams Locke, who was born in New York in 1800 and died
in Staten Island in 1871. He was at one time editor of the Sun,
and the Hoax appeared in that journal in 1835. It was reprinted in London
(1836) and Germany, and was accepted seriously by most readers. It was
published in book form in New York in 1852 under the title The Moon
Hoax. Locke also wrote another hoax, the Lost Manuscript of Mungo
Park, but it attracted relatively little attention.
[701] It is true that
Jean-Nicolas Nicollet (1756-1843) was at that time in the United States,
but there does not seem to be any very tangible evidence to connect him
with the story. He was secretary and librarian of the Paris observatory
(1817), member of the Bureau of Longitudes (1822), and teacher of
mathematics in the Lycée Louis-le-Grand. Having lost his money through
speculations he left France for the United States in 1831 and became
connected with the government survey of the Mississippi Valley.
[702] This was Alexis Bouvard
(1767-1843), who made most of the computations for Laplace's Mécanique
céleste (1793). He discovered eight new comets and calculated their
orbits. In his tables of Uranus (1821) he attributed certain
perturbations to the presence of an undiscovered planet, but unlike
Leverrier and Adams he did not follow up this clue and thus discover
Neptune.
[703] Patrick Murphy (1782-1847)
awoke to find himself famous because of his natural guess that there
would be very cold weather on January 20, although that is generally the
season of lowest temperature. It turned out that his forecasts were
partly right on 168 days and very wrong on 197 days.
[704] He seems to have written
nothing else. If one wishes to enter into the subject of the mathematics
of the Great Pyramid there is an extensive literature awaiting him.
Richard William Howard Vyse (1784-1853) published in 1840 his
Operations carried on at the Pyramids of Gizeh in 1837, and in
this he made a beginning of a scientific metrical study of the subject.
Charles Piazzi Smyth (1819-1900), astronomer Royal for Scotland
(1845-1888) was much carried away with the number mysticism of the Great
Pyramid, so much so that he published in 1864 a work entitled Our
Inheritance in the Great Pyramid, in which his vagaries were set
forth. Although he was then a Fellow of the Royal Society (1857), his
work was so ill received that when he offered a paper on the subject it
was rejected (1874) and he resigned in consequence of this action. The
latest and perhaps the most scholarly of all investigators of the subject
is William Matthew Flinders Petrie (born in 1853), Edwards professor of
Egyptology at University College, London, whose Pyramids and Temples
of Gizeh (1883) and subsequent works are justly esteemed as
authorities.
[705] As De Morgan subsequently
found, this name reversed becomes Oliver B...e, for Oliver Byrne, one of
the odd characters among the minor mathematical writers of the middle of
the last century. One of his most curious works is The first six Books
of the Elements of Euclid; in which coloured diagrams and symbols are
used instead of letters (1847). There is some merit in speaking of
the red triangle instead of the triangle ABC, but not enough to give the
method any standing. His Dual Arithmetic (1863-1867) was also a
curious work.
[706] Brenan also wrote on
English composition (1829), a work that went through fourteen editions by
1865; a work entitled The Foreigner's English Conjugator (1831),
and a work on the national debt.
[707] See note 211, page 112.
[708] See note 592, page 261.
[709] Sir William Rowan Hamilton
(1805-1865), the discoverer of quaternions (1852), was an infant prodigy,
competing with Zerah Colburn as a child. He was a linguist of remarkable
powers, being able, at thirteen years of age, to boast that he knew as
many languages as he had lived years. When only sixteen he found an error
in Laplace's Mécanique céleste. When only twenty-two he was
appointed Andrews professor of astronomy, and he soon after became
Astronomer Royal of Ireland. He was knighted in 1835. His earlier work
was on optics, his Theory of Systems of Rays appearing in 1823. In
1827 he published a paper on the principle of Varying Action. He
also wrote on dynamics.
[710] "Let him not leave the
kingdom,"—a legal phrase.
[711] Probably De Morgan is
referring to Johann Bernoulli III (1744-1807), who edited Lambert's
Logische und philosophische Abhandlungen, Berlin, 1782. He was
astronomer of the Academy of Sciences at Berlin.
[712] Jacob Bernoulli (1654-1705)
was one of the two brothers who founded the famous Bernoulli family of
mathematicians, the other being Johann I. His Ars conjectandi
(1713), published posthumously, was the first distinct treatise on
probabilities.
[713] Johann Heinrich Lambert
(1728-1777) was one of the most learned men of his time. Although
interested chiefly in mathematics, he wrote also on science, logic, and
philosophy.
[714] Joseph Diez Gergonne
(1771-1859), a soldier under Napoleon, and founder of the Annales de
mathématiques (1810).
[715] Gottfried Ploucquet
(1716-1790) was at first a clergyman, but afterwards became professor of
logic at Tübingen.
[716] "In the premises let the
middle term be omitted; what remains indicates the conclusion."
[717] Probably Sir William Edmond
Logan (1789-1875), who became so interested in geology as to be placed at
the head of the geological survey of Canada (1842). The University of
Montreal conferred the title LL.D. upon him, and Napoleon III gave him
the cross of the Legion of Honor.
[718] "So strike that he may
think himself to die."
[719] "Witticism or piece of
stupidity."
[720] A very truculently unjust
assertion: for Sir W. was as great a setter up of some as he was a puller
down of others. His writings are a congeries of praises and blames, both
cruel smart, as they say in the States. But the combined
instigation of prose, rhyme, and retort would send Aristides himself to
Tartarus, if it were not pretty certain that Minos would grant a stet
processus under the circumstances. The first two verses are
exaggerations standing on a basis of truth. The fourth verse is quite
true: Sir W. H. was an Edinburgh Aristotle, with the difference of
ancient and modern Athens well marked, especially the perfervidum
ingenium Scotorum.—A. De M.
[721] See note 576, p. 252. There was also a
Theory of Parallels that differed from these, London, 1853, second
edition 1856, third edition 1856.
[722] The work was written by
Robert Chambers (1802-1871), the Edinburgh publisher, a friend of Scott
and of many of his contemporaries in the literary field. He published the
Vestiges of the Natural History of Creation in 1844, not 1840.
[723] Everett (1784-1872) was at
that time a good Wesleyan, but was expelled from the ministry in 1849 for
having written Wesleyan Takings and as under suspicion for having
started the Fly Sheets in 1845. In 1857 he established the United
Methodist Free Church.
[724] Smith was a Primitive
Methodist preacher. He also wrote an Earnest Address to the
Methodists (1841) and The Wealth Question (1840?).
[725] He wrote the Nouveau
traité de Balistique, Paris, 1837.
[726] Joseph Denison, known to
fame only through De Morgan. See also page 353.
[727] The radical (1784?-1858),
advocate of the founding of London university (1826), of medical reform
(1827-1834), and of the repeal of the duties on newspapers and corn, and
an ardent champion of penny postage.
[728] I. e., Roman Catholic
Priest.
[729] Murphy (1806-1843) showed
extraordinary powers in mathematics even before the age of thirteen. He
became a fellow of Caius College, Cambridge, in 1829, dean in 1831, and
examiner in mathematics in London University in 1838.
[730] See note 442, page 196.
[731] Sir John Bowring
(1792-1872), the linguist, writer, and traveler, member of many learned
societies and a writer of high reputation in his time. His works were
not, however, of genuine merit.
[732] Joseph Hume (1777-1855)
served as a surgeon with the British army in India early in the
nineteenth century. He returned to England in 1808 and entered parliament
as a radical in 1812. He was much interested in all reform movements.
[733] Sir Robert Harry Inglis
(1786-1855), a strong Tory, known for his numerous addresses in the House
of Commons rather than for any real ability.
[734] Sir Robert Peel (1788-1850)
began his parliamentary career in 1809 and was twice prime minister. He
was prominent in most of the great reforms of his time.
[735] See note 627, page 290.
[736] John Taylor (1781-1864) was
a publisher, and published several pamphlets opposed to Peel's currency
measures. De Morgan refers to his work on the Junius question. This was
done early in his career, and resulted in A Discovery of the author of
the Letters of Junius (1813), and The Identity of Junius with a
distinguished living character established (1816), this being Sir
Philip Francis.
[737] See note 665, page 308.
[738] See page 348.
[739] See note 348, page 160.
[740] Sir Nicholas Harris Nicolas
(1799-1848) was a reformer in various lines,—the Record Commission,
the Society of Antiquaries, and the British Museum,—and his work
was not without good results.
[741] See note 98, page 69.
[742] In the Companion to the
Almanac for 1845 is a paper by Prof. De Morgan, "On the
Ecclesiastical Calendar," the statements of which, so far as concerns the
Gregorian Calendar, are taken direct from the work of Clavius, the
principal agent in the arrangement of the reformed reckoning. This was
followed, in the Companion to the Almanac for 1846, by a second
paper, by the same author, headed "On the Earliest Printed Almanacs,"
much of which is written in direct supplement to the former
article.—S. E. De Morgan.
[743] It may be necessary to
remind some English readers that in Latin and its derived European
languages, what we call Easter is called the passover (pascha).
The Quartadecimans had the name on their side: a possession which
often is, in this world, nine points of the law.—A. De M.
[744] Socrates Scholasticus was
born at Constantinople c. 379, and died after 439. His Historia
Ecclesiastica (in Greek) covers the period from Constantine the Great
to about 439, and includes the Council of Nicæa. The work was printed in
Paris 1544.
[745] Theodoretus or Theodoritus
was born at Antioch and died about 457. He was one of the greatest
divines of the fifth century, a man of learning, piety, and judicial
mind, and a champion of freedom of opinion in all religious matters.
[746] He died in 417. He was a
man of great energy and of high attainments.
[747] He died in 461, having
reigned as pope for twenty-one years. It was he who induced Attila to
spare Rome in 452.
[748] He succeeded Leo as pope in
461, and reigned for seven years.
[749] Victorinus or Victorius
Marianus seems to have been born at Limoges. He was a mathematician and
astronomer, and the cycle mentioned by De Morgan is one of 532 years, a
combination of the Metonic cycle of 19 years with the solar cycle of 28
years. His canon was published at Antwerp in 1633 or 1634, De doctrina
temporum sive commentarius in Victorii Aquitani et aliorum canones
paschales.
[750] He went to Rome about 497,
and died there in 540. He wrote his Liber de paschate in 525, and
it was in this work that the Christian era was first used for calendar
purposes.
[751] See note 259, page 126.
[752] Johannes de Sacrobosco
(Holy wood), or John of Holywood. The name was often written, without
regard to its etymology, Sacrobusto. He was educated at Oxford and taught
in Paris until his death (1256). He did much to make the Hindu-Arabic
numerals known to European scholars.
[753] See note 36, page 44.
[754] See note 45, page 48.
[755] The Julian year is a year
of the Julian Calendar, in which there is leap year every fourth year.
Its average length is therefore 365 days and a quarter.—A. De
M.
[756] Ugo Buoncompagno
(1502-1585) was elected pope in 1572.
[757] He was a Calabrian, and as
early as 1552 was professor of medicine at Perugia. In 1576 his
manuscript on the reform of the calendar was presented to the Roman Curia
by his brother, Antonius. The manuscript was not printed and it has not
been preserved.
[758] The title of this work,
which is the authority on all points of the new Calendar, is
Kalendarium Gregorianum Perpetuum. Cum Privilegio Summi Pontificis Et
Aliorum Principum. Romæ, Ex Officina Dominici Basæ. MDLXXXII. Cum
Licentia Superiorum (quarto, pp. 60).—A. De M.
[759] Manuels-Roret. Théorie
du Calendrier et collection de tous les Calendriers des Années passées et
futures.... Par L. B. Francœur,... Paris, à la librairie
encyclopédique de Roret, rue Hautefeuille, 10 bis. 1842. (12mo.) In this
valuable manual, the 35 possible almanacs are given at length, with such
preliminary tables as will enable any one to find, by mere inspection,
which almanac he is to choose for any year, whether of old or new style.
[1866. I may now refer to my own Book of Almanacs, for the same
purpose].—A. De M.
Louis Benjamin Francœur (1773-1849), after holding positions in
the Ecole polytechnique (1804) and the Lycée Charlemagne (1805), became
professor of higher algebra in the University of Paris (1809). His
Cours complet des mathématiques pures was well received, and he
also wrote on mechanics, astronomy, and geodesy.
[760] Albertus Pighius, or Albert
Pigghe, was born at Kempen c. 1490 and died at Utrecht in 1542. He was a
mathematician and a firm defender of the faith, asserting the supremacy
of the Pope and attacking both Luther and Calvin. He spent some time in
Rome. His greatest work was his Hierarchiæ ecclesiasticæ assertio
(1538).
[761] This was A. F. Vogel. The
work was his translation from the German edition which appeared at
Leipsic the same year, Entdeckung einer numerischen General-Auflösung
aller höheren endlichen Gleichungen von jeder beliebigen algebraischen
und transcendenten Form.
[762] The latest edition of
Burnside and Panton's Theory of Equations has this brief summary
of the present status of the problem: "Demonstrations have been given by
Abel and Wantzel (see Serret's Cours d'Algèbre Supérieure, Art.
516) of the impossibility of resolving algebraically equations
unrestricted in form, of a degree higher than the fourth. A
transcendental solution, however, of the quintic has been given by M.
Hermite, in a form involving elliptic integrals."
[763] There was a second edition
of this work in 1846. The author's Astronomy Simplified was
published in 1838, and the Thoughts on Physical Astronomy in 1840,
with a second edition in 1842.
[764] This was The Science of
the Weather, by several authors... edited by B., Glasgow, 1867.
[765] This was Y. Ramachandra,
son of Sundara Lāla. He was a teacher of science in Delhi College,
and the work to which De Morgan refers is A Treatise on problems of
Maxima and Minima solved by Algebra, which appeared at Calcutta in
1850. De Morgan's edition was published at London nine years later.
[766] Abraham de Moivre
(1667-1754), French refugee in London, poor, studying under difficulties,
was a man with tastes in some respects like those of De Morgan. For one
thing, he was a lover of books, and he had a good deal of interest in the
theory of probabilities to which De Morgan also gave much thought. His
introduction of imaginary quantities into trigonometry was an event of
importance in the history of mathematics, and the theorem that bears his
name, (cos φ + i sin φ)n = cos nφ + i sin nφ, is one of the most important ones in all
analysis.
[767] John Dolland (1706-1761),
the silk weaver who became the greatest maker of optical instruments in
his time.
[768] Thomas Simpson (1710-1761),
also a weaver, taking his leisure from his loom at Spitalfields to teach
mathematics. His New Treatise on Fluxions (1737) was written only
two years after he began working in London, and six years later he was
appointed professor of mathematics at Woolwich. He wrote many works on
mathematics and Simpson's Formulas for computing trigonometric tables are
still given in the text-books.
[769] Nicholas Saunderson
(1682-1739), the blind mathematician. He lost his eyesight through
smallpox when only a year old. At the age of 25 he began lecturing at
Cambridge on the principles of the Newtonian philosophy. His
Algebra, in two large volumes, was long the standard treatise on
the subject.
[770] He was not in the class
with the others mentioned.
[771] Not known in the literature
of mathematics.
[772] Probably J. Butler Williams
whose Practical Geodesy appeared in 1842, with a third edition in
1855.
[773] Benjamin Gompertz
(1779-1865) was debarred as a Jew from a university education. He studied
mathematics privately and became president of the Mathematical Society.
De Morgan knew him professionally through the fact that he was prominent
in actuarial work.
[774] Referring to the
contributions of Archimedes (287-212 B.C.) to the mensuration of the
sphere.
[775] The famous Alexandrian
astronomer (c. 87-c. 165 A.D.), author of the Almagest, a treatise
founded on the works of Hipparchus.
[776] Dr. Whewell, when I
communicated this song to him, started the opinion, which I had before
him, that this was a very good idea, of which too little was
made.—A. De M.
[777] See note 117, page 76.
[778] The common epithet of rank:
nobilis Tycho, as he was a nobleman. The writer had been at
history.—A. De M.
See note 117, page 76.
[779] He lost it in a duel, with
Manderupius Pasbergius. A contemporary, T. B. Laurus, insinuates that
they fought to settle which was the best mathematician! This seems odd,
but it must be remembered they fought in the dark, "in tenebris
densis"; and it is a nice problem to shave off a nose in the dark,
without any other harm.—A. De M.
Was this T. B. Laurus Joannes Baptista Laurus or Giovanni Battista
Lauro (1581-1621), the poet and writer?
[780] See note 117, page 76.
[781] Referring to Kepler's
celebrated law of planetary motion. He had previously wasted his time on
analogies between the planetary orbits and the polyhedrons.—A. De
M.
[782] See note 117, page 76.
[783] "It does move though."
[784] As great a lie as ever was
told: but in 1800 a compliment to Newton without a fling at Descartes
would have been held a lopsided structure.—A. De M.
[785] Jean-le-Rond D'Alembert
(1717-1783), the foundling who was left on the steps of Jean-le-Rond in
Paris, and who became one of the greatest mathematical physicists and
astronomers of his century.
[786] Leonhard Euler (1707-1783),
friend of the Bernoullis, the greatest of Swiss mathematicians, prominent
in the theory of numbers, and known for discoveries in all lines of
mathematics as then studied.
[787] See notes 478, 479, page 219.
[788] See note 621, page 288.
[789] See note 584, page 255.
[790] The siderial day is
about four minutes short of the solar; there are 366 sidereal days in the
year.—A. De M.
[791] The founding of the London
Mathematical Society is discussed by Mrs. De Morgan in her Memoir
(p. 281). The idea came from a conversation between her brilliant son,
George Campbell De Morgan, and his friend Arthur Cowper Ranyard in 1864.
The meeting of organization was held on Nov. 7, 1864, with Professor De
Morgan in the chair, and the first regular meeting on January 16,
1865.
[792] See note 33, page 43.
[793] See note 119, page 80.
[794] John Russell Hind (b.
1823), the astronomer. Between 1847 and 1854 he discovered ten
planetoids.
[795] Sir Roderick Impey
Murchison (1792-1871), the great geologist. He was knighted in 1846 and
devoted the latter part of his life to the work of the Royal Geographical
Society and to the geology of Scotland.
[796] Friedrich Wilhelm Bessel
(1784-1846), the astronomer and physicist. He was professor of astronomy
at Königsberg.
[797] This was the Reduction
of the Observations of Planets made ... from 1750 to 1830: computed ...
under the superintendence of George Biddell Airy (1848). See note 129, page 85.
[798] The expense of this
magnificent work was defrayed by Government grants, obtained, at the
instance of the British Association, in 1833—A. De M.
[799] See note 32, page 43.
[800] Franz Friedrich Ernst
Brünnow (1821-1891) was at that time or shortly before director of the
observatory at Dusseldorf. He then went to Berlin and thence (1854) to
Ann Arbor, Michigan. He then went to Dublin and finally became Royal
Astronomer of Ireland.
[801] Johann Gottfried Galle
(1812-1910), at that time connected with the Berlin observatory, and
later professor of astronomy at Breslau.
[802] George Bishop (1785-1861),
in whose observatory in Regent's Park important observations were made by
Dawes, Hind, and Marth.
[803] James Challis (1803-1882),
director of the Cambridge observatory, and successor of Airy as Plumian
professor of astronomy.
[804] On Leverrier and Arago see
note 33, page 43, and note 561, page 243.
[805] Robert Grant's (1814-1892)
History of Physical Astronomy from the Earliest Ages to the Middle of
the Nineteenth Century appeared in 1852. He was professor of
astronomy and director of the observatory at Glasgow.
[806] John Debenham was more
interested in religion than in astronomy. He wrote The Strait Gate;
or, the true scripture doctrine of salvation clearly explained,
London, 1843, and Tractatus de magis et Bethlehemæ stella et Christi
in deserto tentatione, privately printed at London in 1845.
[807] More properly the Sydney
Smirke reading room, since it was built from his designs.
[808] The Antinomians were
followers of Johannes Agricola (1494-1566). They believed that Christians
as such were released from all obligations to the Old Testament. Some
went so far as to assert that, since all Christians were sanctified, they
could not lose this sanctity even though they disobeyed God. The sect was
prominent in England in the seventeenth century, and was transferred to
New England. Here it suffered a check in the condemnation of Mrs. Ann
Hutchinson (1636) by the Newton Synod.
[809] Aside from this work and
his publications on Reeve and Muggleton he wrote nothing. With Joseph
Frost he published A list of Books and general index to J.
Reeve and L. Muggleton's works (1846), Divine Songs of the
Muggletonians (1829), and the work mentioned on page 396. The works of J. Reeve and L. Muggleton
(1832).
[810] About 1650 he and his
cousin John Reeve (1608-1658) began to have visions. As part of their
creed they taught that astronomy was opposed by the Bible. They asserted
that the sun moves about the earth, and Reeve figured out that heaven was
exactly six miles away. Both Muggleton and Reeve were imprisoned for
their unitarian views. Muggleton wrote a Transcendant Spirituall
Treatise (1652). I have before me A true Interpretation of All the
Chief Texts ... of the whole Book of the Revelation of St. John.... By
Lodowick Muggleton, one of the two last Commissioned Witnesses &
Prophets of the onely high, immortal, glorious God, Christ Jesus
(1665), in which the interpretation of the "number of the beast" occupies
four pages without arriving anywhere.
[811] In 1652 he was, in a
vision, named as the Lord's "last messenger," with Muggleton as his
"mouth," and died six years later, probably of nervous tension resulting
from his divine "illumination." He was the more spiritual of the two.
[812] William Guthrie (1708-1770)
was a historian and political writer. His History of England
(1744-1751) was the first attempt to base history on parliamentary
records. He also wrote a General History of Scotland in 10 volumes
(1767). The work to which Frost refers is the Geographical,
Historical, and Commercial Grammar (1770) which contained an
astronomical part by J. Ferguson. By 1827 it had passed through 24
editions.
[813] George Fox (1624-1691),
founder of the Society of Friends; a mystic and a disciple of Boehme. He
was eight times imprisoned for heresy.
[814] If they were friends they
were literary antagonists, for Muggleton wrote against Fox The Neck of
the Quakers Broken (1663), and Fox replied in 1667. Muggleton also
wrote A Looking Glass for George Fox.
[815] John Conduitt (1688-1737),
who married (1717) Newton's half niece, Mrs. Katherine Barton. See note
284, page 136.
[816] Probably Peter Mark Roget's
(1779-1869) Thesaurus of English Words (1852) is not much used at
present, but it went through 28 editions in his lifetime. Few who use the
valuable work are aware that Roget was a professor of physiology at the
Royal Institution (London), that he achieved his title of F. R. S.
because of his work in perfecting the slide rule, and that he followed
Sir John Herschel as secretary of the Royal Society.
[817] See note 703, page 327. This work went
into a second edition in the year of its first publication.
[818] See note 398, page 177.
[819] See note 528, page 233.
[820] George Jacob Holyoake
(1817-1906) entered into a controversial life at an early age. In 1841 he
was imprisoned for six months for blasphemy. He founded and edited The
Reasoner (Vols. 1-26, 1846-1861). In his later life he did much to
promote cooperation among the working class.
[821] See note 176, page 102.
[822] William Thomas Lowndes
(1798-1843), whose Bibliographer's Manual of English Literature, 4
vols., London, 1834 (also 1857-1864, and 1869) is a classic in its
line.
[823] Jacques Charles Brunet
(1780-1867), the author of the great French bibliography, the Manuel
du Libraire (1810).
