The Pre-eminence of Sir Isaac Newton’s Reputation—The Interest
attached to the Study of his Life and Writings—His Birth and
Parentage—His early Education—Is sent to Grantham School—His
early Attachment to Mechanical Pursuits—His Windmill—His
Waterclock—His Self-moving Cart—His Sundials—His Preparation
for the University.
The name of Sir Isaac Newton has by general
consent been placed at the head of those great men
who have been the ornaments of their species.
However imposing be the attributes with which
time has invested the sages and the heroes of antiquity,
the brightness of their fame has been eclipsed
by the splendour of his reputation; and neither the
partiality of rival nations, nor the vanity of a presumptuous
age, has ventured to dispute the ascendency
of his genius. The philosopher,1 indeed, to whom
posterity will probably assign the place next to Newton,
has characterized the Principia as pre-eminent
above all the productions of human intellect, and
has thus divested of extravagance the contemporary
encomium upon its author,
Nec fas est propius mortali attingere Divos.
Halley.
So near the gods—man cannot nearer go.
The biography of an individual so highly renowned
cannot fail to excite a general interest. Though
his course may have lain in the vale of private life,
and may have been unmarked with those dramatic
events which throw a lustre even round perishable
names, yet the inquiring spirit will explore the history
of a mind so richly endowed,—will study its
intellectual and moral phases, and will seek the
shelter of its authority on those great questions
which reason has abandoned to faith and hope.
If the conduct and opinions of men of ordinary
talent are recorded for our instruction, how interesting
must it be to follow the most exalted genius
through the incidents of common life;—to mark the
steps by which he attained his lofty pre-eminence;
to see how he performs the functions of the social
and the domestic compact; how he exercises his
lofty powers of invention and discovery; how he
comports himself in the arena of intellectual strife;
and in what sentiments, and with what aspirations
he quits the world which he has adorned.
In almost all these bearings, the life and writings
of Sir Isaac Newton abound with the richest counsel.
Here the philosopher will learn the art by which
alone he can acquire an immortal name. The moralist
will trace the lineaments of a character adjusted
to all the symmetry of which our imperfect
nature is susceptible; and the Christian will contemplate
with delight the high-priest of science
quitting the study of the material universe,—the
scene of his intellectual triumphs,—to investigate
with humility and patience the mysteries of his faith.
* * * * *
Sir Isaac Newton was born at Woolsthorpe, a
hamlet in the parish of Colsterworth, in Lincolnshire,
about six miles south of Grantham, on the
25th December, O. S., 1642, exactly one year after
Galileo died, and was baptized at Colsterworth on
the 1st January, 1642–3. His father, Mr. Isaac Newton,
died at the early age of thirty-six, a little more
than a year after the death of his father Robert
Newton, and only a few months after his marriage
to Harriet Ayscough, daughter of James Ayscough
of Market Overton in Rutlandshire. This lady was
accordingly left in a state of pregnancy, and appears
to have given a premature birth to her only and
posthumous child. The helpless infant thus ushered
into the world was of such an extremely diminutive
size,2 and seemed of so perishable a frame, that
two women who were sent to Lady Pakenham’s at
North Witham, to bring some medicine to strengthen
him, did not expect to find him alive on their return.
Providence, however, had otherwise decreed; and
that frail tenement which seemed scarcely able to
imprison its immortal mind was destined to enjoy
a vigorous maturity, and to survive even the average
term of human existence. The estate of Woolsthorpe,
in the manor-house of which this remarkable
birth took place, had been more than a hundred
years in the possession of the family, who came
originally from Newton in Lancashire, but who had,
previous to the purchase of Woolsthorpe, settled at
Westby, in the county of Lincoln. The manor-house,
of which we have given an engraving, is
situated in a beautiful little valley, remarkable for
its copious wells of pure spring water, on the west
side of the river Witham, which has its origin in the
neighbourhood, and commands an agreeable prospect
to the east towards Colsterworth. The manor
of Woolsthorpe was worth only 30l. per annum;
but Mrs. Newton possessed another small estate at
Sewstern,3 which raised the annual value of their
property to about 80l.; and it is probable that the
cultivation of the little farm on which she resided
somewhat enlarged the limited income upon which
she had to support herself, and educate her child.
For three years Mrs. Newton continued to watch
over her tender charge with parental anxiety; but
in consequence of her marriage to the Reverend
Barnabas Smith, rector of North Witham, about a
mile south of Woolsthorpe, she left him under the
care of her own mother. At the usual age he was
sent to two day-schools at Skillington and Stoke,
where he acquired the education which such seminaries
afforded; but when he reached his twelfth
year he went to the public school at Grantham,
taught by Mr. Stokes, and was boarded at the house
of Mr. Clark, an apothecary in that town. According
to information which Sir Isaac himself gave to
Mr. Conduit, he seems to have been very inattentive
to his studies, and very low in the school. The
boy, however, who was above him, having one day
given him a severe kick upon his stomach, from
which he suffered great pain, Isaac laboured incessantly
till he got above him in the school, and from
that time he continued to rise till he was the head
boy. From the habits of application which this
incident had led him to form, the peculiar character
of his mind was speedily displayed. During the
hours of play, when the other boys were occupied
with their amusements, his mind was engrossed with
mechanical contrivances, either in imitation of something
which he had seen, or in execution of some
original conception of his own. For this purpose
he provided himself with little saws, hatchets, hammers,
and all sorts of tools, which he acquired the
art of using with singular dexterity. The principal
pieces of mechanism which he thus constructed
were a windmill, a waterclock, and a carriage put in
motion by the person who sat in it. When a windmill
was erecting near Grantham on the road to
Gunnerby, Isaac frequently attended the operations
of the workmen, and acquired such a thorough
knowledge of the machinery that he completed a
working model of it, which excited universal admiration.
This model was frequently placed on the top
of the house in which he lodged at Grantham, and
was put in motion by the action of the wind upon
its sails. Not content with this exact imitation of
the original machine, he conceived the idea of driving
it by animal power, and for this purpose he enclosed
in it a mouse which he called the miller, and
which, by acting upon a sort of treadwheel, gave
motion to the machine. According to some accounts,
the mouse was made to advance by pulling
a string attached to its tail, while others allege that
the power of the little agent was called forth by its
unavailing attempts to reach a portion of corn placed
above the wheel.
His waterclock was formed out of a box which
he had solicited from Mrs. Clark’s brother. It was
about four feet high, and of a proportional breadth,
somewhat like a common houseclock. The index
of the dialplate was turned by a piece of wood, which
either fell or rose by the action of dropping water.
As it stood in his own bedroom he supplied it every
morning with the requisite quantity of water, and it
was used as a clock by Mr. Clark’s family, and remained
in the house long after its inventor had
quitted Grantham.4 His mechanical carriage was a
vehicle with four wheels, which was put in motion
with a handle wrought by the person who sat in it,
but, like Merlin’s chair, it seems to have been used
only on the smooth surface of a floor, and not fitted
to overcome the inequalities of a road. Although
Newton was at this time “a sober, silent, thinking
lad,” who scarcely ever joined in the ordinary games
of his schoolfellows, yet he took great pleasure in
providing them with amusements of a scientific
character. He introduced into the school the flying
of paper kites; and he is said to have been at great
pains in determining their best forms and proportions,
and in ascertaining the position and number
of the points by which the string should be attached.
He made also paper lanterns, by the light of which
he went to school in the winter mornings, and he
frequently attached these lanterns to the tails of
his kites in a dark night, so as to inspire the country
people with the belief that they were comets.
In the house where he lodged there were some
female inmates in whose company he appears to have
taken much pleasure. One of these, a Miss Storey,
sister to Dr. Storey, a physician at Buckminster,
near Colsterworth, was two or three years younger
than Newton, and to great personal attractions she
seems to have added more than the usual allotment
of female talent. The society of this young lady
and her companions was always preferred to that
of his own schoolfellows, and it was one of his most
agreeable occupations to construct for them little
tables and cupboards, and other utensils for holding
their dolls and their trinkets. He had lived nearly
six years in the same house with Miss Storey, and
there is reason to believe that their youthful friendship
gradually rose to a higher passion; but the
smallness of her portion and the inadequacy of his
own fortune appear to have prevented the consummation
of their happiness. Miss Storey was afterward
twice married, and under the name of Mrs.
Vincent, Dr. Stukely visited her at Grantham in 1727,
at the age of eighty-two, and obtained from her
many particulars respecting the early history of our
author. Newton’s esteem for her continued unabated
during his life. He regularly visited her when
he went to Lincolnshire, and never failed to relieve
her from little pecuniary difficulties which seem to
have beset her family.
Among the early passions of Newton we must
recount his love of drawing; and even of writing
verses. His own room was furnished with pictures
drawn, coloured, and framed by himself, sometimes
from copies, but often from life.5 Among these
were portraits of Dr. Donne, Mr. Stokes, the master
of Grantham school, and King Charles I. under
whose picture were the following verses.
A secret art my soul requires to try,
If prayers can give me what the wars deny.
Three crowns distinguished here, in order do
Present their objects to my knowing view.
Earth’s crown, thus at my feet I can disdain,
Which heavy is, and at the best but vain.
But now a crown of thorns I gladly greet,
Sharp is this crown, but not so sharp as sweet;
The crown of glory that I yonder see
Is full of bliss and of eternity.
These verses were repeated to Dr. Stukely by Mrs.
Vincent, who believed them to be written by Sir
Isaac, a circumstance which is the more probable,
as he himself assured Mr. Conduit, with some expression
of pleasure, that he “excelled in making
verses,” although he had been heard to express a
contempt for poetical composition.
But while the mind of our young philosopher was
principally occupied with the pursuits which we have
now detailed, it was not inattentive to the movements
of the celestial bodies, on which he was destined
to throw such a brilliant light. The imperfections
of his waterclock had probably directed his
thoughts to the more accurate measure of time which
the motion of the sun afforded. In the yard of the
house where he lived, he traced the varying movements
of that luminary upon the walls and roofs of the
buildings, and by means of fixed pins he had marked
out the hourly and half-hourly subdivisions. One
of these dials, which went by the name of Isaac’s
dial, and was often referred to by the country people
for the hour of the day, appears to have been drawn
solely from the observations of several years; but
we are not informed whether all the dials which he
drew on the wall of his house at Woolsthorpe, and
which existed after his death, were of the same
description, or were projected from his knowledge
of the doctrine of the sphere.
Upon the death of the Reverend Mr. Smith in the
year 1656, his widow left the rectory of North
Witham, and took up her residence at Woolsthorpe
along with her three children, Mary, Benjamin, and
Hannah Smith. Newton had now attained the
fifteenth year of his age, and had made great progress
in his studies; and as he was thought capable
of being useful in the management of the farm and
country business at Woolsthorpe, his mother, chiefly
from a motive of economy, recalled him from the
school at Grantham. In order to accustom him to
the art of selling and buying, two of the most important
branches of rural labour, he was frequently
sent on Saturday to Grantham market to dispose
of grain and other articles of farm produce, and to
purchase such necessaries as the family required.
As he had yet acquired no experience, an old trustworthy
servant generally accompanied him on these
errands. The inn which they patronised was the
Saracen’s Head at West Gate; but no sooner had
they put up their horses than our young philosopher
deserted his commercial concerns, and betook himself
to his former lodging in the apothecary’s garret,
where a number of Mr. Clark’s old books afforded
him abundance of entertainment till his aged guardian
had executed the family commissions, and announced
to him the necessity of returning. At other
times he deserted his duties at an earlier stage, and
intrenched himself under a hedge by the way-side,
where he continued his studies till the servant returned
from Grantham. The more immediate affairs
of the farm were not more prosperous under his
management than would have been his marketings
at Grantham. The perusal of a book, the execution
of a model, or the superintendence of a waterwheel
of his own construction, whirling the glittering
spray from some neighbouring stream, absorbed
all his thoughts when the sheep were going astray,
and the cattle were devouring or treading down the
corn.
Mrs. Smith was soon convinced from experience
that her son was not destined to cultivate the soil,
and as his passion for study, and his dislike for every
other occupation increased with his years, she wisely
resolved to give him all the advantages which education
could confer. He was accordingly sent back
to Grantham school, where he continued for some
months in busy preparation for his academical studies.
His uncle, the Reverend W. Ayscough, who
was rector of Burton Coggles, about three miles
east of Woolsthorpe, and who had himself studied
at Trinity College, recommended to his nephew to
enter that society, and it was accordingly determined
that he should proceed to Cambridge at the approaching
term.6
Newton enters Trinity College, Cambridge—Origin of his Propensity
for Mathematics—He studies the Geometry of Descartes unassisted—Purchases
a Prism—Revises Dr. Harrow’s Optical Lectures—Dr.
Barrow’s Opinion respecting Colours—Takes his Degrees—Is appointed
a Fellow of Trinity College—Succeeds Dr. Barrow in the
Lucasian Chair of Mathematics.
To a young mind thirsting for knowledge, and
ambitious of the distinction which it brings, the
transition from a village school to a university like
that of Cambridge,—from the absolute solitude of
thought to the society of men imbued with all the
literature and science of the age,—must be one of
eventful interest. To Newton it was a source of
peculiar excitement. The history of science affords
many examples where the young aspirant had been
early initiated into her mysteries, and had even exercised
his powers of invention and discovery before
he was admitted within the walls of a college; but he
who was to give philosophy her laws did not exhibit
such early talent; no friendly counsel regulated his
youthful studies, and no work of scientific eminence
seems to have guided him in his course. In yielding
to the impulse of his mechanical genius, his
mind obeyed the laws of its own natural expansion,
and, following the line of least resistance, it was
thus drawn aside from the strongholds with which
it was destined to grapple.
When Newton, therefore, arrived at Trinity College,
he brought with him a more slender portion of
science than falls to the lot of ordinary scholars;
but this state of his acquirements was perhaps not
unfavourable to the development of his powers.
Unexhausted by premature growth, and invigorated
by healthful repose, his mind was the better fitted to
make those vigorous and rapid shoots which soon
covered with foliage and with fruit the genial soil
to which it had been transferred.
Cambridge was consequently the real birthplace
of Newton’s genius. Her teachers fostered his earliest
studies;—her institutions sustained his mightiest
efforts;—and within her precincts were all his discoveries
made and perfected. When he was called
to higher official functions, his disciples kept up the
pre-eminence of their master’s philosophy, and their
successors have maintained this seat of learning in
the fulness of its glory, and rendered it the most
distinguished among the universities of Europe.
It was on the 5th of June, 1660, in the 18th year
of his age, that Newton was admitted into Trinity
College, Cambridge, during the same year that Dr.
Barrow was elected professor of Greek in the university.
His attention was first turned to the study
of mathematics by a desire to inquire into the truth
of judicial astrology; and he is said to have discovered
the folly of that study by erecting a figure
with the aid of one or two of the problems of
Euclid. The propositions contained in this ancient
system of geometry he regarded as self-evident
truths; and without any preliminary study he made
himself master of Descartes’s Geometry by his
genius and patient application. This neglect of the
elementary truths of geometry he afterward regarded
as a mistake in his mathematical studies, and he expressed
to Dr. Pemberton his regret that “he had applied
himself to the works of Descartes, and other algebraic
writers, before he had considered the elements
of Euclid with that attention which so excellent a
writer deserved.7 Dr. Wallis’s Arithmetic of Infinites,
Saunderson’s Logic, and the Optics of Kepler were
among the books which he had studied with care. On
these works he wrote comments during their perusal;
and so great was his progress, that he is reported to
have found himself more deeply versed in some
branches of knowledge than the tutor who directed
his studies.
Neither history nor tradition has handed down to
us any particular account of his progress during the
first three years that he spent at Cambridge. It
appears from a statement of his expenses, that in
1664 he purchased a prism, for the purpose, as has
been said, of examining Descartes’s theory of colours;
and it is stated by Mr. Conduit, that he soon
established his own views on the subject, and detected
the errors in those of the French philosopher.
This, however, does not seem to have been the case.
Had he discovered the composition of light in 1664
or 1665, it is not likely that he would have withheld
it, not only from the Royal Society, but from his
own friends at Cambridge till the year 1671. His
friend and tutor, Dr. Barrow, was made Lucasian
Professor of Mathematics in 1663, and the optical
lectures which he afterward delivered were published
in 1669. In the preface of this work he acknowledges
his obligations to his colleague, Mr. Isaac
Newton,8 for having revised the MSS., and corrected
several oversights, and made some important suggestions.
In the twelfth lecture there are some observations
on the nature and origin of colours,
which Newton could not have permitted his friend
to publish had he been then in possession of their
true theory. According to Dr. Barrow, White is
that which discharges a copious light equally clear
in every direction; Black is that which does not
emit light at all, or which does it very sparingly.
Red is that which emits a light more clear than
usual, but interrupted by shady interstices. Blue is
that which discharges a rarified light, as in bodies
which consist of white and black particles arranged
alternately. Green is nearly allied to blue. Yellow
is a mixture of much white and a little red; and
Purple consists of a great deal of blue mixed with
a small portion of red. The blue colour of the sea
arises from the whiteness of the salt which it contains,
mixed with the blackness of the pure water
in which the salt is dissolved; and the blueness of
the shadows of bodies, seen at the same time by
candle and daylight, arises from the whiteness of
the paper mixed with the faint light or blackness of
the twilight. These opinions savour so little of
genuine philosophy that they must have attracted
the observation of Newton, and had he discovered
at that time that white was a mixture of all the
colours, and black a privation of them all, he could
not have permitted the absurd speculations of his
master to pass uncorrected.
That Newton had not distinguished himself by
any positive discovery so early as 1664 or 1665, may
be inferred also from the circumstances which attended
the competition for the law fellowship of
Trinity College. The candidates for this appointment
were himself and Mr. Robert Uvedale; and
Dr. Barrow, then Master of Trinity, having found
them perfectly equal in their attainments, conferred
the fellowship on Mr. Uvedale as the senior
candidate.
In the books of the university, Newton is recorded
as having been admitted sub-sizer in 1661. He
became a scholar in 1664. In 1665 he took his degree
of Bachelor of Arts, and in 1666, in consequence
of the breaking out of the plague, he retired
to Woolsthorpe. In 1667 he was made Junior Fellow.
In 1668 he took his degree of Master of Arts,
and in the same year he was appointed to a Senior
Fellowship. In 1669, when Dr. Barrow had resolved
to devote his attention to theology, he resigned
the Lucasian Professorship of Mathematics
in favour of Newton, who may now be considered
as having entered upon that brilliant career of discovery
the history of which will form the subject of
some of the following chapters.
Newton, occupied in grinding Hyperbolical Lenses—His first Experiments
with the Prism made in 1666—He discovers the Composition of
White Light, and the different Refrangibility of the Rays which compose
it—Abandons his Attempts to improve Refracting Telescopes and
resolves to attempt the Construction of Reflecting ones—He quits Cambridge
on account of the Plague—Constructs two Reflecting Telescopes
in 1668, the first ever executed—One of them examined by the Royal Society,
and shown to the King—He constructs a Telescope with Glass
Specula—Recent History of the Reflecting Telescope—Mr. Airy’s
Glass Specula—Hadley’s Reflecting Telescopes—Short’s—Herschel’s—Ramage’s—Lord
Oxmantown’s.
The appointment of Newton to the Lucasian
chair at Cambridge seems to have been coeval with
his grandest discoveries. The first of these of
which the date is well authenticated is that of the
different refrangibility of the rays of light, which he
established in 1666. The germ of the doctrine of
universal gravitation seems to have presented itself
to him in the same year, or at least in 1667; and “in
the year 1666 or before”9 he was in possession of
his method of fluxions, and he had brought it to such
a state in the beginning of 1669, that he permitted
Dr. Barrow to communicate it to Mr. Collins on the
20th of June in that year.
Although we have already mentioned, on the authority
of a written memorandum of Newton himself,
that he purchased a prism at Cambridge in 1664,
yet he does not appear to have made any use of it,
as he informs us that it was in 1666 that he “procured
a triangular glass prism to try therewith the
celebrated phenomena of colours.”10 During that
year he had applied himself to the grinding of “optic
glasses, of other figures than spherical,” and
having, no doubt, experienced the impracticability
of executing such lenses, the idea of examining the
phenomena of colour was one of those sagacious
and fortunate impulses which more than once led
him to discovery. Descartes in his Dioptrice, published
in 1629, and more recently James Gregory in
his Optica Promota published in 1663, had shown
that parallel and diverging rays could be reflected or
refracted, with mathematical accuracy, to a point or
focus, by giving the surface a parabolic, an elliptical,
or a hyperbolic form, or some other form not spherical.
Descartes had even invented and described
machines by which lenses of these shapes could be
ground and polished, and the perfection of the refracting
telescope was supposed to depend on the
degree of accuracy with which they could be executed.
In attempting to grind glasses that were not spherical,
Newton seems to have conjectured that the defects
of lenses, and consequently of refracting telescopes,
might arise from some other cause than the
imperfect convergency of rays to a single point, and
this conjecture was happily realized in those fine
discoveries of which we shall now endeavour to
give some account.
When Newton began this inquiry, philosophers of
the highest genius were directing all the energies of
their mind to the subject of light, and to the improvement
of the refracting telescope. James
Gregory of Aberdeen had invented his reflecting
telescope. Descartes had explained the theory and
exerted himself in perfecting the construction of the
common refracting telescope, and Huygens had not
only executed the magnificent instruments by which
he discovered the ring and the satellites of Saturn,
but had begun those splendid researches respecting
the nature of light, and the phenomena of double
refraction, which have led his successors to such
brilliant discoveries. Newton, therefore, arose when
the science of light was ready for some great accession,
and at the precise time when he was required
to propagate the impulse which it had received
from his illustrious predecessors.
The ignorance which then prevailed respecting
the nature and origin of colours is sufficiently apparent
from the account we have already given of
Dr. Barrow’s speculations on this subject. It was
always supposed that light of every colour was
equally refracted or bent out of its direction when
it passed through any lens or prism, or other refracting
medium; and though the exhibition of colours
by the prism had been often made previous to the
time of Newton, yet no philosopher seems to have
attempted to analyze the phenomena.
Fig. 1.
When he had procured his triangular glass prism,
a section of which is shown at ABC, (fig. 1,) he
made a hole H in one of his window-shutters, SHT,
and having darkened his chamber, he let in a convenient
quantity of the sun’s light RR, which, passing
through the prism ABC, was so refracted as to
exhibit all the different colours on the wall at MN,
forming an image about five times as long as it was
broad. “It was at first,” says our author, “a very
pleasing divertisement to view the vivid and intense
colours produced thereby,” but this pleasure was
immediately succeeded by surprise at various circumstances
which he had not expected. According to
the received laws of refraction, he expected the
image MN to be circular, like the white image at W,
which the sunbeam RR had formed on the wall
previous to the interposition of the prism; but when
he found it to be no less than five times larger than
its breadth, it “excited in him a more than ordinary
curiosity to examine from whence it might proceed.
He could scarcely think that the various thickness of
the glass, or the termination with shadow or darkness,
could have any influence on light to produce such
an effect: yet he thought it not amiss first to examine
those circumstances, and so find what would happen
by transmitting light through parts of the glass of
divers thicknesses, or through holes in the window
of divers bignesses, or by setting the prism without
(on the other side of ST), so that the light might
pass through it and be refracted before it was terminated
by the hole; but he found none of these circumstances
material. The fashion of the colours
was in all those cases the same.”
Newton next suspected that some unevenness in
the glass, or other accidental irregularity, might
cause the dilatation of the colours. In order to try
this, he took another prism BCB′, and placed it in
such a manner that the light RRW passing through
them both might be refracted contrary ways, and
thus returned by BCB′ into that course RRW, from
which the prism ABC had diverted it, for by this
means he thought the regular effects of the prism
ABC would be destroyed by the prism BCB′, and the
irregular ones more augmented by the multiplicity
of refractions. The result was, that the light which
was diffused by the first prism ABC into an oblong
form, was reduced by the second prism BCB′ into a
circular one W, with as much regularity as when it
did not pass through them at all; so that whatever
was the cause of the length of the image MN, it did
not arise from any irregularity in the prism.
Our author next proceeded to examine more critically
what might be effected by the difference of the
incidence of the rays proceeding from different parts
of the sun’s disk: but by taking accurate measures
of the lines and angles, he found that the angle of
the emergent rays should be 31 minutes equal to the
sun’s diameter, whereas the real angle subtended by
MN at the hole H was 2° 49′. But as this computation
was founded on the hypothesis, that the sine of
the angle of incidence was proportional to the sine
of the angle of refraction, which from his own experience
he could not imagine to be so erroneous as
to make that angle but 31′, which was in reality 2°
49′, yet “his curiosity caused him again to take up
his prism” ABC, and having turned it round in both
directions, so as to make the rays RR fall both with
greater and with less obliquity upon the face AC, he
found that the colours on the wall did not sensibly
change their place; and hence he obtained a decided
proof that they could not be occasioned by a difference
in the incidence of the light radiating from different
parts of the sun’s disk.
Newton then began to suspect that the rays, after
passing through the prism, might move in curve lines,
and, in proportion to the different degrees of curvature,
might tend to different parts of the wall; and
this suspicion was strengthened by the recollection
that he had often seen a tennis-ball struck with an
oblique racket describe such a curve line. In this
case a circular and a progressive motion is communicated
to the ball by the stroke, and in consequence
of this, the direction of its motion was curvilineal,
so that if the rays of light were globular bodies,
they might acquire a circulating motion by their oblique
passage out of one medium into another, and
thus move like the tennis-ball in a curve line. Notwithstanding,
however, “this plausible ground of
suspicion,” he could discover no such curvature in
their direction, and, what was enough for his purpose,
he observed that the difference between the
length MN of the image, and the diameter of the
hole H, was proportional to their distance HM,
which could not have happened had the rays moved
in curvilineal paths.
These different hypotheses, or suspicions, as Newton
calls them, being thus gradually removed, he
was at length led to an experiment which determined
beyond a doubt the true cause of the elongation
of the coloured image. Having taken a board
with a small hole in it, he placed it behind the face
BC of the prism, and close to it, so that he could
transmit through the hole any one of the colours in
MN, and keep back all the rest. When the hole,
for example, was near C, no other light but the red
fell upon the wall at N. He then placed behind N
another board with a hole in it, and behind this
board he placed another prism, so as to receive the
red light at N, which passed through this hole in the
second board. He then turned round the first prism
ABC so as to make all the colours pass in succession
through these two holes, and he marked their places
on the wall. From the variation of these places,
he saw that the red rays at N were less refracted by
the second prism than the orange rays, the orange
less than the yellow, and so on, the violet being more
refracted than all the rest.
Hence he drew the grand conclusion, that light
was not homogeneous, but consisted of rays, some of
which were more refrangible than others.
As soon as this important truth was established,
Sir Isaac saw that a lens which refracts light exactly
like a prism must also refract the differently coloured
rays with different degrees of force, bringing the
violet rays to a focus nearer the glass than the red
rays. This is shown in fig. 2, where LL is a convex
lens, and S, L, SL rays of the sun falling upon it
in parallel directions. The violet rays existing in
the white light SL being more refrangible than the
rest, will be more refracted or bent, and will meet at
V, forming there a violet image of the sun. In like
manner the yellow rays will form an image of the
sun at Y, and so on, the red rays, which are the least
refrangible, being brought to a focus at R, and there
forming a red image of the sun.
Fig. 2.
Hence, if we suppose LL to be the object-glass of
a telescope directed to the sun, and MM an eye-glass
through which the eye at E sees magnified the image
or picture of the sun formed by LL, it cannot see
distinctly all the different images between R and V.
If it is adjusted so as to see distinctly the yellow
image at Y, as it is in the figure, it will not see distinctly
either the red or violet images, nor indeed any
of them but the yellow one. There will consequently
be a distinct yellow image, with indistinct
images of all the other colours, producing great confusion
and indistinctness of vision. As soon as Sir
Isaac perceived this result of his discovery, he abandoned
his attempts to improve the refracting telescope,
and took into consideration the principle of reflection;
and as he found that rays of all colours
were reflected regularly, so that the angle of reflection
was equal to the angle of incidence, he concluded
that, upon this principle, optical instruments
might be brought to any degree of perfection imaginable,
provided a reflecting substance could be found which
could polish as finely as glass, and reflect as much
light as glass transmits, and provided a method of
communicating to it a parabolic figure could be obtained.
These difficulties, however, appeared to him
very great, and he even thought them insuperable
when he considered that, as any irregularity in a reflecting
surface makes the rays deviate five or six
times more from their true path than similar irregularities
in a refracting surface, a much greater degree
of nicety would be required in figuring reflecting
specula than refracting lenses.
Such was the progress of Newton’s optical discoveries,
when he was forced to quit Cambridge in
1666 by the plague which then desolated England,
and more than two years elapsed before he proceeded
any farther. In 1668 he resumed the inquiry,
and having thought of a delicate method of polishing,
proper for metals, by which, as he conceived,
“the figure would be corrected to the last,” he began
to put this method to the test of experiment. At
this time he was acquainted with the proposal of
Mr. James Gregory, contained in his Optica Promota,
to construct a reflecting telescope with two concave
specula, the largest of which had a hole in the
middle of the larger speculum, to transmit the light
to an eye-glass;11 but he conceived that it would be
an improvement on this instrument to place the eye-glass
at the side of the tube, and to reflect the rays
to it by an oval plane speculum. One of these
instruments he actually executed with his own
hands; and he gave an account of it in a letter to a
friend, dated February 23d, 1668–9, a letter which is
also remarkable for containing the first allusion to
his discoveries respecting colours. Previous to this
he was in correspondence on the subject with Mr.
Ent, afterward Sir George Ent, one of the original
council of the Royal Society, an eminent medical
writer of his day, and President of the College of
Physicians. In a letter to Mr. Ent he had promised
an account of his telescope to their mutual friend,
and the letter to which we now allude contained the
fulfilment of that promise. The telescope was six
inches long. It bore an aperture in the large speculum
something more than an inch, and as the eye-glass
was a plano-convex lens, whose focal length
was one-sixth or one-seventh of an inch, it magnified
about forty times, which, as Newton remarks,
was more than any six-foot tube (meaning refracting
telescopes) could do with distinctness. On account
of the badness of the materials, however, and the
want of a good polish, it represented objects less
distinct than a six-feet tube, though he still thought
it would be equal to a three or four feet tube directed
to common objects. He had seen through it
Jupiter distinctly with his four satellites, and also
the horns or moon-like phases of Venus, though this
last phenomenon required some niceness in adjusting
the instrument.
Although Newton considered this little instrument
as in itself contemptible, yet he regarded it as
an “epitome of what might be done;” and he expressed
his conviction that a six-feet telescope might
be made after this method, which would perform as
well as a sixty or a hundred feet telescope made in
the common way; and that if a common refracting
telescope could be made of the “purest glass exquisitely
polished, with the best figure that any geometrician
(Descartes, &c.) hath or can design,” it
would scarcely perform better than a common telescope.
This, he adds, may seem a paradoxical assertion,
yet he continues, “it is the necessary consequence
of some experiments which I have made
concerning the nature of light.”
The telescope now described possesses a very peculiar
interest, as being the first reflecting one which
was ever executed and directed to the heavens.
James Gregory, indeed, had attempted, in 1664 or
1665, to construct his instrument. He employed
Messrs. Rives and Cox, who were celebrated glass-grinders
of that time, to execute a concave speculum
of six feet radius, and likewise a small one; but as
they had failed in polishing the large one, and as Mr.
Gregory was on the eve of going abroad, he troubled
himself no farther about the experiment, and the
tube of the telescope was never made. Some time
afterward, indeed, he “made some trials both with a
little concave and convex speculum,” but, “possessed
with the fancy of the defective figure, he
would not be at the pains to fix every thing in its due
distance.”
Such were the earliest attempts to construct the
reflecting telescope, that noble instrument which
has since effected such splendid discoveries in astronomy.
Looking back from the present advanced
state of practical science, how great is the contrast
between the loose specula of Gregory and the fine
Gregorian telescopes of Hadley, Short, and Veitch,—between
the humble six-inch tube of Newton and
the gigantic instruments of Herschel and Ramage.
The success of this first experiment inspired Newton
with fresh zeal, and though his mind was now
occupied with his optical discoveries, with the elements
of his method of fluxions, and with the expanding
germ of his theory of universal gravitation,
yet with all the ardour of youth he applied himself
to the laborious operation of executing another reflecting
telescope with his own hands. This instrument,
which was better than the first, though it lay
by him several years, excited some interest at Cambridge;
and Sir Isaac himself informs us, that one
of the fellows of Trinity College had completed a
telescope of the same kind, which he considered as
somewhat superior to his own. The existence of
these telescopes having become known to the Royal
Society, Newton was requested to send his instrument
for examination to that learned body. He accordingly
transmitted it to Mr. Oldenburg in December,
1671, and from this epoch his name began to
acquire that celebrity by which it has been so peculiarly
distinguished.
On the 11th of January, 1672, it was announced
to the Royal Society that his reflecting telescope
had been shown to the king, and had been examined
by the president, Sir Robert Moray, Sir Paul Neale,
Sir Christopher Wren, and Mr. Hook. These gentlemen
entertained so high an opinion of it, that, in
order to secure the honour of the contrivance to its
author, they advised the inventor to send a drawing
and description of it to Mr. Huygens at Paris. Mr.
Oldenburg accordingly drew up a description of it
in Latin, which, after being corrected by Mr. Newton,
was transmitted to that eminent philosopher.
This telescope, of which the annexed is an accurate
drawing, is carefully preserved in the library of the
Royal Society of London, with the following inscription:—
“Invented by Sir Isaac Newton and made with his
own hands, 1671.”
Fig. 3.
Sir Isaac Newton’s Reflecting Telescope.
It does not appear that Newton executed any other
reflecting telescopes than the two we have mentioned.
He informs us that he repolished and greatly improved
a fourteen-feet object-glass, executed by a
London artist, and having proposed in 1678 to substitute
glass reflectors in place of metallic specula,
he tried to make a reflecting telescope on this
principle four feet long, and with a magnifying power
of 150. The glass was wrought by a London artist,
and though it seemed well finished, yet, when it was
quicksilvered on its convex side, it exhibited all over
the glass innumerable inequalities, which gave an
indistinctness to every object. He expresses, however,
his conviction that nothing but good workmanship
is wanting to perfect these telescopes, and
he recommends their consideration “to the curious
in figuring glasses.”
For a period of fifty years this recommendation
excited no notice. At last Mr. James Short of
Edinburgh, an artist of consummate skill, executed
about the year 1730 no fewer than six reflecting
telescopes with glass specula, three of fifteen inches,
and three of nine inches in focal length. He found
it extremely troublesome to give them a true figure
with parallel surfaces; and several of them when
finished turned out useless, in consequence of the
veins which then appeared in the glass. Although
these instruments performed remarkably well, yet
the light was fainter than he expected, and from this
cause, combined with the difficulty of finishing them,
he afterward devoted his labours solely to those
with metallic specula.
At a later period, in 1822, Mr. G. B. Airy of
Trinity College, and one of the distinguished successors
of Newton in the Lucasian chair, resumed
the consideration of glass specula, and demonstrated
that the aberration both of figure and of colour
might be corrected in these instruments. Upon this
ingenious principle Mr. Airy executed more than
one telescope, but though the result of the experiment
was such as to excite hopes of ultimate success,
yet the construction of such instruments is
still a desideratum in practical science.
Such were the attempts which Sir Isaac Newton
made to construct reflecting telescopes; but notwithstanding
the success of his labours, neither the philosopher
nor the practical optician seems to have
had courage to pursue them. A London artist, indeed,
undertook to imitate these instruments; but
Sir Isaac informs us, that “he fell much short of
what he had attained, as he afterward understood
by discoursing with the under workmen he had employed.”
After a long period of fifty years, John
Hadley, Esq. of Essex, a Fellow of the Royal Society,
began in 1719 or 1720 to execute a reflecting
telescope. His scientific knowledge and his manual
dexterity fitted him admirably for such a task, and,
probably after many failures, he constructed two
large telescopes about five feet three inches long,
one of which, with a speculum six inches in diameter,
was presented to the Royal Society in 1723. The
celebrated Dr. Bradley and the Rev. Mr. Pound
compared it with the great Huygenian refractor 123
feet long. It bore as high a magnifying power as
the Huygenian telescope: it showed objects equally
distinct, though not altogether so clear and bright,
and it exhibited every celestial object that had been
discovered by Huygens,—the five satellites of Saturn,
the shadow of Jupiter’s satellites on his disk,
the black list in Saturn’s ring, and the edge of his
shadow cast on the ring. Encouraged and instructed
by Mr. Hadley, Dr. Bradley began the construction
of reflecting telescopes, and succeeded so well that
he would have completed one of them, had he not
been obliged to change his residence. Some time
afterward he and the Honourable Samuel Molyneux
undertook the task together at Kew, and attempted
to execute specula about twenty-six inches in focal
length; but notwithstanding Dr. Bradley’s former
experience, and Mr. Hadley’s frequent instructions,
it was a long time before they succeeded. The first
good instrument which they finished was in May,
1724. It was twenty-six inches in focal length; but
they afterward completed a very large one of eight
feet, the largest that had ever been made. The first
of these instruments was afterward elegantly fitted
up by Mr. Molyneux, and presented to his majesty
John V. King of Portugal.
The great object of these two able astronomers
was to reduce the method of making specula to
such a degree of certainty that they could be manufactured
for public sale. Mr. Hauksbee had indeed
made a good one about three and a half feet long,
and had proceeded to the execution of two others,
one of six feet, and another of twelve feet in focal
length; but Mr. Scarlet and Mr. Hearne, having received
all the information which Mr. Molyneux had
acquired, constructed them for public sale; and the
reflecting telescope has ever since been an article of
trade with every regular optician.
As Sir Isaac Newton was at this time President
of the Royal Society, he had the high satisfaction
of seeing his own invention become an instrument
of public use, and of great advantage to science,
and he no doubt felt the full influence of this triumph
of his skill. Still, however, the reflecting telescope
had not achieved any new discovery in the heavens.
The latest accession to astronomy had been made
by the ordinary refractors of Huygens, labouring
under all the imperfections of coloured light; and
this long pause in astronomical discovery seemed
to indicate that man had carried to its farthest limits
his power of penetrating into the depths of the universe.
This, however, was only one of those stationary
positions from which human genius takes a
new and a loftier elevation. While the English opticians
were thus practising the recent art of grinding
specula, Mr. James Short of Edinburgh was devoting
to the subject all the energies of his youthful
mind. In 1732, and in the 22d year of his age, he
began his labours, and he carried to such high perfection
the art of grinding and polishing specula, and
of giving them the true parabolic figure, that, with
a telescope fifteen inches in focal length, he read in
the Philosophical Transactions at the distance of
500 feet, and frequently saw the five satellites of
Saturn together,—a power which was beyond the
reach even of Hadley’s six-feet instrument. The
celebrated Maclaurin compared the telescopes of
Short with those made by the best London artists,
and so great was their superiority, that his small
telescopes were invariably superior to larger ones
from London. In 1742, after he had settled as an
optician in the metropolis, he executed for Lord
Thomas Spencer a reflecting telescope, twelve feet
in focal length, for 630l.; in 1752 he completed one for
the King of Spain, at the expense of 1200l.; and a
short time before his death, which took place in
1768, he finished the specula of the large telescope
which was mounted equatorially for the observatory
of Edinburgh by his brother Thomas Short, who was
offered twelve hundred guineas for it by the King of
Denmark.
Although the superiority of these instruments,
which were all of the Gregorian form, demonstrated
the value of the reflecting telescope, yet no skilful
hand had yet directed it to the heavens; and it was
reserved for Dr. Herschel to employ it as an instrument
of discovery, to exhibit to the eye of man new
worlds and new systems, and to bring within the
grasp of his reason those remote regions of space
to which his imagination even had scarcely ventured
to extend its power. So early as 1774 he completed
a five-feet Newtonian reflector, and he afterward
executed no fewer than two hundred 7 feet, one hundred
and fifty 10 feet, and eighty 20 feet specula. In
1781 he began a reflector thirty feet long, and having
a speculum thirty-six inches in diameter; and under
the munificent patronage of George III. he completed,
in 1789, his gigantic instrument forty feet
long, with a speculum forty-nine and a half inches
in diameter. The genius and perseverance which
created instruments of such transcendent magnitude
were not likely to terminate with their construction.
In the examination of the starry heavens, the ultimate
object of his labours, Dr. Herschel exhibited
the same exalted qualifications, and in a few years
he rose from the level of humble life to the enjoyment
of a name more glorious than that of the sages
and warriors of ancient times, and as immortal as
the objects with which it will be for ever associated.
Nor was it in the ardour of the spring of life that
these triumphs of reason were achieved. Dr. Herschel
had reached the middle of his course before
his career of discovery began, and it was in the autumn
and winter of his days that he reaped the full
harvest of his glory. The discovery of a new planet
at the verge of the solar system was the first trophy
of his skill, and new double and multiple stars, and
new nebulæ, and groups of celestial bodies were
added in thousands to the system of the universe.
The spring-tide of knowledge which was thus let in
upon the human mind continued for a while to spread
its waves over Europe; but when it sank to its ebb in
England, there was no other bark left upon the strand
but that of the Deucalion of Science, whose home
had been so long upon its waters.
During the life of Dr. Herschel, and during the
reign, and within the dominions of his royal patron,
four new planets were added to the solar system,
but they were detected by telescopes of ordinary
power; and we venture to state, that since the reign
of George III. no attempt has been made to keep
up the continuity of Dr. Herschel’s discoveries.
Mr. Herschel, his distinguished son, has indeed
completed more than one telescope of considerable
size; Mr. Ramage, of Aberdeen, has executed reflectors
rivalling almost those of Slough;—and Lord
Oxmantown, an Irish nobleman of high promise, is
now engaged on an instrument of great size. But
what avail the enthusiasm and the efforts of individual
minds in the intellectual rivalry of nations?
When the proud science of England pines in obscurity,
blighted by the absence of the royal favour, and
of the nation’s sympathy;—when its chivalry fall
unwept and unhonoured;—how can it sustain the
conflict against the honoured and marshalled genius
of foreign lands?
He delivers a Course of Optical Lectures at Cambridge—Is elected Fellow
of the Royal Society—He communicates to them his Discoveries on
the different Refrangibility and Nature of Light—Popular Account
of them—They involve him in various Controversies—His Dispute
with Pardies—Linus—Lucas—Dr. Hooke and Mr. Huygens—The
Influence of these Disputes on the Mind of Newton.
Although Newton delivered a course of lectures
on optics in the University of Cambridge in the
years 1669, 1670, and 1671, containing his principal
discoveries relative to the different refrangibility of
light, yet it is a singular circumstance, that these
discoveries should not have become public through
the conversation or correspondence of his pupils.
The Royal Society had acquired no knowledge of
them till the beginning of 1672, and his reputation
in that body was founded chiefly on his reflecting
telescope. On the 23d December, 1671, the celebrated
Dr. Seth Ward, Lord Bishop of Sarum, who
was the author of several able works on astronomy,
and had filled the astronomical chair at Oxford,
proposed Mr. Newton as a Fellow of the Royal
Society. The satisfaction which he derived from this
circumstance appears to have been considerable;
and in a letter to Mr. Oldenburg, of the 6th January,
he says, “I am very sensible of the honour done
me by the Bishop of Sarum in proposing me a candidate;
and which, I hope, will be further conferred
upon me by my election into the Society; and if
so, I shall endeavour to testify my gratitude, by
communicating what my poor and solitary endeavours
can effect towards the promoting your philosophical
designs.” His election accordingly took
place on the 11th January, the same day on which
the Society agreed to transmit a description of his
telescope to Mr. Huygens at Paris. The notice of
his election, and the thanks of the Society for the
communication of his telescope, were conveyed in
the same letter, with an assurance that the Society
“would take care that all right should be done him
in the matter of this invention.” In his next letter
to Oldenburg, written on the 18th January, 1671–2,
he announces his optical discoveries in the following
remarkable manner: “I desire that in your next
letter you would inform me for what time the Society
continue their weekly meetings; because if
they continue them for any time, I am purposing
them, to be considered of and examined, an account
of a philosophical discovery which induced me to the
making of the said telescope; and I doubt not but
will prove much more grateful than the communication
of that instrument; being in my judgment the
oddest, if not the most considerable detection which
hath hitherto been made in the operations of nature.”
This “considerable detection” was the discovery
of the different refrangibility of the rays of light
which we have already explained, and which led
to the construction of his reflecting telescope. It
was communicated to the Royal Society in a letter
to Mr. Oldenburg, dated February 6th, and excited
great interest among its members. The “solemn
thanks” of the meeting were ordered to be transmitted
to its author for his “very ingenious discourse.”
A desire was expressed to have it immediately
printed, both for the purpose of having it
well considered by philosophers, and for “securing
the considerable notices thereof to the author against
the arrogations of others;” and Dr. Seth Ward,
Bishop of Salisbury, Mr. Boyle, and Dr. Hooke
were desired to peruse and consider it, and to bring
in a report upon it to the Society.
The kindness of this distinguished body, and the
anxiety which they had already evinced for his
reputation, excited on the part of Newton a corresponding
feeling, and he gladly accepted of their proposal
to publish his discourse in the monthly numbers
in which the Transactions were then given to
the world. “It was an esteem,” says he,12 “of the
Royal Society for most candid and able judges in
philosophical matters, encouraged me to present
them with that discourse of light and colours, which
since they have so favourably accepted of, I do earnestly
desire you to return them my cordial thanks.
I before thought it a great favour to be made a
member of that honourable body; but I am now
more sensible of the advantages; for believe me,
sir, I do not only esteem it a duty to concur with
you in the promotion of real knowledge; but a great
privilege, that, instead of exposing discourses to a
prejudiced and common multitude, (by which means
many truths have been baffled and lost), I may with
freedom apply myself to so judicious and impartial
an assembly. As to the printing of that letter, I am
satisfied in their judgment, or else I should have
thought it too straight and narrow for public view.
I designed it only to those that know how to improve
upon hints of things; and, therefore, to spare
tediousness, omitted many such remarks and experiments
as might be collected by considering the
assigned laws of refractions; some of which I believe,
with the generality of men, would yet be
almost as taking as any I described. But yet, since
the Royal Society have thought it fit to appear publicly,
I leave it to their pleasure: and perhaps to
supply the aforesaid defects, I may send you some
more of the experiments to second it (if it be so
thought fit), in the ensuing Transactions.”
Following the order which Newton himself adopted,
we have, in the preceding chapter, given an account
of the leading doctrine of the different refrangibility
of light, and of the attempts to improve the reflecting
telescope which that discovery suggested. We
shall now, therefore, endeavour to make the reader
acquainted with the other discoveries respecting
colours which he at this time communicated to the
Royal Society.
Fig. 4.
Having determined, by experiments
already described, that a beam of
white light, as emitted from the sun,
consisted of seven different colours,
which possess different degrees of
refrangibility, he measured the relative
extent of the coloured spaces,
and found them to have the proportions
shown in fig. 4, which represents
the prismatic spectrum, and
which is nothing more than an elongated
image of the sun produced by
the rays being separated in different
degrees from their original direction,
the red being refracted least, and the
violet most powerfully.
If we consider light as consisting
of minute particles of matter, we may
form some notion of its decomposition
by the prism from the following
popular illustration. If we take steel
filings of seven different degrees of fineness and
mix them together, there are two ways in which we
may conceive the mass to be decomposed, or, what
is the same thing, all the seven different kinds of
filings separated from each other. By means of
seven sieves of different degrees of fineness, and so
made that the finest will just transmit the finest
powder and detain all the rest, while the next in
fineness transmits the two finest powders and detains
all the rest, and so on, it is obvious that all the powders
may be completely separated from each other.
If we again mix all the steel filings, and laying them
upon a table, hold high above them a flat bar magnet,
so that none of the filings are attracted, then if we
bring the magnet nearer and nearer, we shall come
to a point where the finest filings are drawn up to it.
These being removed, and the magnet brought
nearer still, the next finest powders will be attracted,
and so on till we have thus drawn out of the mass
all the powders in a separate state. We may conceive
the bar magnet to be inclined to the surface
of the steel filings, and so moved over the mass,
that at the end nearest to them the heaviest or
coarsest will be attracted, and all the remotest and
the finest or lighter filings, while the rest are attracted
to intermediate points, so that the seven
different filings are not only separated, but are found
adhering in separate patches to the surface of the
flat magnet. The first of these methods, with the
sieves, may represent the process of decomposing
light, by which certain rays of white light are absorbed,
or stifled, or stopped in passing through
bodies, while certain other rays are transmitted.
The second method may represent the process of
decomposing light by refraction, or by the attraction
of certain rays farther from their original direction
than other rays, and the different patches of filings
upon the flat magnet may represent the spaces on
the spectrum.
When a beam of white light is decomposed into
the seven different colours of the spectrum, any
particular colour, when once separated from the
rest, is not susceptible of any change, or farther
decomposition, whether it is refracted through prisms
or reflected from mirrors. It may become fainter
or brighter, but Newton never could, by any process,
alter its colour or its refrangibility.
Among the various bodies which act upon light,
it is conceivable that there might have been some
which acted least upon the violet rays and most
upon the red rays. Newton, however, found that
this never took place; but that the same degree of
refrangibility always belonged to the same colour,
and the same colour to the same degree of refrangibility.
Having thus determined that the seven different
colours of the spectrum were original or simple, he
was led to the conclusion that whiteness or white
light is a compound of all the seven colours of the
spectrum, in the proportions in which they are represented
in fig. 4. In order to prove this, or what
is called the recomposition of white light out of the
seven colours, he employed three different methods.
Fig. 5.
When the beam RR was separated into its elementary
colours by the prism ABC, he received the
colours on another prism BCB′, held either close to
the first or a little behind it, and by the opposite refraction
of this prism they were all refracted back
into a beam of white light BW, which formed a
white circular image on the wall at W, similar to
what took place before any of the prisms were
placed in its way.
The other method of recomposing white light
consisted in making the spectrum fall upon a lens at
some distance from it. When a sheet of white
paper was held behind the lens, and removed to a
proper distance, the colours were all refracted into
a circular spot, and so blended as to reproduce light
so perfectly white as not to differ sensibly from the
direct light of the sun.
The last method of recomposing white light was
one more suited to vulgar apprehension. It consisted
in attempting to compound a white by mixing
the coloured powders used by painters. He
was aware that such colours, from their very nature,
could not compose a pure white; but even this imperfection
in the experiment he removed by an ingenious
device. He accordingly mixed one part of
red lead, four parts of blue bice, and a proper proportion
of orpiment and verdigris. This mixture was
dun, like wood newly cut, or like the human skin.
He now took one-third of the mixture and rubbed
it thickly on the floor of his room, where the sun
shone upon it through the opened casement, and beside
it, in the shadow, he laid a piece of white paper
of the same size. “Then going from them to the
distance of twelve or eighteen feet, so that he could
not discern the unevenness of the surface of the
powder nor the little shadows let fall from the gritty
particles thereof; the powder appeared intensely
white, so as to transcend even the paper itself in
whiteness.” By adjusting the relative illumination
of the powders and the paper, he was able to
make them both appear of the very same degree of
whiteness. “For,” says he, “when I was trying
this, a friend coming to visit me, I stopped him at
the door, and before I told him what the colours
were, or what I was doing, I asked him which of the
two whites were the best, and wherein they differed!
And after he had at that distance viewed them well, he
answered, that they were both good whites, and that
he could not say which was best, nor wherein their
colours differed.” Hence Newton inferred that
perfect whiteness may be compounded of different
colours.
As all the various shades of colour which appear
in the material world can be imitated by intercepting
certain rays in the spectrum, and uniting all the
rest, and as bodies always appear of the same colour
as the light in which they are placed, he concluded,
that the colours of natural bodies are not qualities
inherent in the bodies themselves, but arise from the
disposition of the particles of each body to stop or
absorb certain rays, and thus to reflect more copiously
the rays which are not thus absorbed.
No sooner were these discoveries given to the
world than they were opposed with a degree of virulence
and ignorance which have seldom been combined
in scientific controversy. Unfortunately for
Newton, the Royal Society contained few individuals
of pre-eminent talent capable of appreciating the
truth of his discoveries, and of protecting him against
the shafts of his envious and ignorant assailants.
This eminent body, while they held his labours in
the highest esteem, were still of opinion that his
discoveries were fair subjects of discussion, and
their secretary accordingly communicated to him all
the papers which were written in opposition to his
views. The first of these was by a Jesuit named
Ignatius Pardies, Professor of Mathematics at Clermont,
who pretended that the elongation of the sun’s
image arose from the inequal incidence of the different
rays on the first face of the prism, although
Newton had demonstrated in his own discourse that
this was not the case. In April, 1672, Newton transmitted
to Oldenburg a decisive reply to the animadversions
of Pardies; but, unwilling to be vanquished,
this disciple of Descartes took up a fresh position,
and maintained that the elongation of the spectrum
might be explained by the diffusion of light on the
hypothesis of Grimaldi, or by the diffusion of undulations
on the hypothesis of Hook. Newton again
replied to these feeble reasonings; but he contented
himself with reiterating his original experiments,
and confirming them by more popular arguments,
and the vanquished Jesuit wisely quitted the field.
Another combatant soon sprung up in the person
of one Francis Linus, a physician in Liege,13 who,
on the 6th October, 1674, addressed a letter to a
friend in London, containing animadversions on
Newton’s doctrine of colours. He boldly affirms,
that in a perfectly clear sky the image of the sun
made by a prism is never elongated, and that the
spectrum observed by Newton was not formed by
the true sunbeams, but by rays proceeding from
some bright cloud. In support of these assertions,
he appeals to frequently repeated experiments on
the refractions and reflections of light which he
had exhibited thirty years before to Sir Kenelm
Digby, “who took notes upon them;” and he unblushingly
states, that, if Newton had used the
same industry as he did, he would never have
“taken so impossible a task in hand, as to explain
the difference between the length and breadth of
the spectrum by the received laws of refraction.”
When this letter was shown to Newton, he refused
to answer it; but a letter was sent to Linus referring
him to the answer to Pardies, and assuring him that
the experiments on the spectrum were made when
there was no bright cloud in the heavens. This
reply, however, did not satisfy the Dutch experimentalist.
On the 25th February, 1675, he addressed
another letter to his friend, in which he gravely
attempts to prove that the experiment of Newton
was not made in a clear day;—that the prism was
not close to the hole,—and that the length of the
spectrum was not perpendicular, or parallel to the
length of the prism. Such assertions could not but
irritate even the patient mind of Newton. He more
than once declined the earnest request of Oldenburg
to answer these observations; he stated, that, as
the dispute referred to matters of fact, it could only
be decided before competent witnesses, and he
referred to the testimony of those who had seen
his experiments. The entreaties of Oldenburg, however,
prevailed over his own better judgment, and,
“lest Mr. Linus should make the more stir,” this
great man was compelled to draw up a long and
explanatory reply to reasonings utterly contemptible,
and to assertions altogether unfounded. This
answer, dated November 13th, 1675, could scarcely
have been perused by Linus, who was dead on the
15th December, when his pupil Mr. Gascoigne, took
up the gauntlet, and declared that Linus had shown
to various persons in Liege the experiment which
proved the spectrum to be circular, and that Sir
Isaac could not be more confident on his side
than they were on the other. He admitted, however,
that the different results might arise from different
ways of placing the prism. Pleased with the
“handsome genius of Mr. Gascoigne’s letter,” Newton
replied even to it, and suggested that the spectrum
seen by Linus may have been the circular one,
formed by one reflexion, or, what he thought more
probable, the circular one formed by two refractions,
and one intervening reflection from the base of the
prism, which would be coloured if the prism was
not an isosceles one. This suggestion seems to
have enlightened the Dutch philosophers. Mr. Gascoigne,
having no conveniences for making the experiments
pointed out by Newton, requested Mr.
Lucas of Liege to perform them in his own house.
This ingenious individual, whose paper gave great
satisfaction to Newton, and deserves the highest
praise, confirmed the leading results of the English
philosopher; but though the refracting angle of his
prism was 60° and the refractions equal, he never
could obtain a spectrum whose length was more
than from three to three and a half times its breadth,
while Newton found the length to be five times its
breadth. In our author’s reply, he directs his attention
principally to this point of difference. He
repeated his measures with each of the three angles
of three different prisms, and he affirmed that Mr.
Lucas might make sure to find the image as long or
longer than he had yet done, by taking a prism with
plain surfaces, and with an angle of 66° or 67°.
He admitted that the smallness of the angle in Mr.
Lucas’s prism, viz. 60°, did not account for the
shortness of the spectrum which he obtained with
it; and he observed in one of his own prisms that
the length of the image was greater in proportion
to the refracting angle than it should have been; an
effect which he ascribes to its having a greater
refractive power. There is every reason to believe
that the prism of Lucas had actually a less dispersive
power than that of Newton; and had the Dutch
philosopher measured its refractive power instead
of guessing it, or had Newton been less confident
than he was14 that all other prisms must give a
spectrum of the same length as his in relation to its
refracting angle and its index of refraction, the invention
of the achromatic telescope would have
been the necessary result. The objections of Lucas
drove our author to experiments which he had never
before made,—to measure accurately the lengths of
the spectra with different prisms of different angles
and different refractive powers; and had the Dutch
philosopher maintained his position with more obstinacy,
he would have conferred a distinguished
favour upon science, and would have rewarded
Newton for all the vexation which had sprung from
the minute discussion of his optical experiments.
Such was the termination of his disputes with the
Dutch philosophers, and it can scarcely be doubted
that it cost him more trouble to detect the origin of
his adversaries’ blunders, than to establish the great
truths which they had attempted to overturn.
Harassing as such a controversy must have been
to a philosopher like Newton, yet it did not touch
those deep-seated feelings which characterize the
noble and generous mind. No rival jealousy yet
pointed the arguments of his opponents;—no charges
of plagiarism were yet directed against his personal
character. These aggravations of scientific controversy,
however, he was destined to endure; and in
the dispute which he was called to maintain both
against Hooke and Huygens, the agreeable consciousness
of grappling with men of kindred powers
was painfully imbittered by the personality and
jealousy with which it was conducted.
Dr. Robert Hooke was about seven years older
than Newton, and was one of the ninety-eight
original or unelected members of the Royal Society.
He possessed great versatility of talent, yet, though
his genius was of the most original cast, and his
acquirements extensive, he had not devoted himself
with fixed purpose to any particular branch of
knowledge. His numerous and ingenious inventions,
of which it is impossible to speak too highly,
gave to his studies a practical turn which unfitted
him for that continuous labour which physical researches
so imperiously demand. The subjects
of light, however, and of gravitation seem to have
deeply occupied his thoughts before Newton appeared
in the same field, and there can be no doubt
that he had made considerable progress in both of
these inquiries. With a mind less divergent in its
pursuits, and more endowed with patience of thought,
he might have unveiled the mysteries in which both
these subjects were enveloped, and preoccupied the
intellectual throne which was destined for his rival;
but the infirm state of his health, the peevishness
of temper which this occasioned, the number of
unfinished inventions from which he looked both
for fortune and fame, and, above all, his inordinate
love of reputation, distracted and broke down the
energies of his powerful intellect. In the more
matured inquiries of his rivals he recognised, and
often truly, his own incompleted speculations; and
when he saw others reaping the harvest for which
he had prepared the ground, and of which he had
sown the seeds, it was not easy to suppress the
mortification which their success inspired. In the
history of science, it has always been a difficult task
to adjust the rival claims of competitors, when the
one was allowed to have completed what the other
was acknowledged to have begun. He who commences
an inquiry, and publishes his results, often
goes much farther than he has announced to the
world, and, pushing his speculations into the very
heart of the subject, frequently submits them to the
ear of friendship. From the pedestal of his published
labours his rival begins his researches, and
brings them to a successful issue; while he has in
reality done nothing more than complete and demonstrate
the imperfect speculations of his predecessor.
To the world, and to himself, he is no
doubt in the position of the principal discoverer:
but there is still some apology for his rival when
he brings forward his unpublished labours; and some
excuse for the exercise of personal feeling, when he
measures the speed of his rival by his own proximity
to the goal.
The conduct of Dr. Hooke would have been
viewed with some such feeling, had not his arrogance
on other occasions checked the natural current
of our sympathy. When Newton presented
his reflecting telescope to the Royal Society, Dr.
Hooke not only criticised the instrument with undue
severity, but announced that he possessed an infallible
method of perfecting all kinds of optical instruments,
so that “whatever almost hath been in
notion and imagination, or desired in optics, may
be performed with great facility and truth.”
Hooke had been strongly impressed with the
belief, that light consisted in the undulations of a
highly elastic medium pervading all bodies; and,
guided by his experimental investigation of the phenomena
of diffraction, he had even announced the
great principle of interference, which has performed
such an important part in modern science. Regarding
himself, therefore, as in possession of the true
theory of light, he examined the discoveries of
Newton in their relation to his own speculative
views, and, finding that their author was disposed to
consider that element as consisting of material particles,
he did not scruple to reject doctrines which
he believed to be incompatible with truth. Dr.
Hooke was too accurate an observer not to admit
the general correctness of Newton’s observations.
He allowed the existence of different refractions,
the unchangeableness of the simple colours, and the
production of white light by the union of all the
colours of the spectrum; but he maintained that the
different refractions arose from the splitting and
rarefying of ethereal pulses, and that there are only
two colours in nature, viz. red and violet, which produce
by their mixture all the rest, and which are
themselves formed by the two sides of a split pulse
or undulation.
In reply to these observations, Newton wrote an
able letter to Oldenburg, dated June 11, 1672, in
which he examined with great boldness and force
of argument the various objections of his opponent,
and maintained the truth of his doctrine of colours,
as independent of the two hypotheses respecting
the origin and production of light. He acknowledged
his own partiality to the doctrine of the
materiality of light; he pointed out the defects of
the undulatory theory; he brought forward new experiments
in confirmation of his former results;
and he refuted the opinions of Hooke respecting the
existence of only two simple colours. No reply
was made to the powerful arguments of Newton;
and Hooke contented himself with laying before the
Society his curious observations on the colours of
soap-bubbles, and of plates of air, and in pursuing
his experiments on the diffraction of light, which,
after an interval of two years, he laid before the
same body.
After he had thus silenced the most powerful of
his adversaries, Newton was again called upon to
defend himself against a new enemy. Christian
Huygens, an eminent mathematician and natural
philosopher, who, like Hooke, had maintained the
undulatory theory of light, transmitted to Oldenburg
various animadversions on the Newtonian doctrine;
but though his knowledge of optics was of
the most extensive kind, yet his objections were
nearly as groundless as those of his less enlightened
countryman. Attached to his own hypothesis respecting
the nature of light, namely, to the system
of undulation, he seems, like Dr. Hooke, to have
regarded the discoveries of Newton as calculated to
overturn it; but his principal objections related to
the composition of colours, and particularly of white
light, which he alleged could be obtained from the
union of two colours, yellow and blue. To and
similar objections, Newton replied that the colours
in question were not simple yellows and blues, but
were compound colours, in which, together, all the
colours of the spectrum were themselves blended;
and though he evinced some strong traces of feeling
at being again put upon his defence, yet his high
respect for Huygens induced him to enter with
patience on a fresh development of his doctrine.
Huygens felt the reproof which the tone of this
answer so gently conveyed, and in writing to Oldenburg,
he used the expression, that Mr. Newton
“maintained his doctrine with some concern.” To
this our author replied, “As for Mr. Huygens’s expression,
I confess it was a little ungrateful to me,
to meet with objections which had been answered
before, without having the least reason given me
why those answers were insufficient.” But though
Huygens appears in this controversy as a rash
objector to the Newtonian doctrine, it was afterward
the fate of Newton to play a similar part
against the Dutch philosopher. When Huygens
published his beautiful law of double refraction in
Iceland spar, founded on the finest experimental
analysis of the phenomena, though presented as a
result of the undulatory system, Newton not only
rejected it, but substituted for it another law entirely
inconsistent with the experiments of Huygens, which
Newton himself had praised, and with those of all
succeeding philosophers.
The influence of these controversies on the mind
of Newton seems to have been highly exciting.
Even the satisfaction of humbling all his antagonists
he did not feel as a sufficient compensation
for the disturbance of his tranquillity. “I intend,”
says he,15 “to be no farther solicitous about matters
of philosophy. And therefore I hope you will not
take it ill if you find me never doing any thing more
in that kind; or rather that you will favour me in
my determination, by preventing, so far as you can
conveniently, any objections or other philosophical
letters that may concern me.” In a subsequent letter
in 1675, he says, “I had some thoughts of writing
a further discourse about colours, to be read at one
of your assemblies; but find it yet against the grain
to put pen to paper any more on that subject;” and
in a letter to Leibnitz, dated December the 9th, 1675,
he observes, “I was so persecuted with discussions
arising from the publication of my theory of light,
that I blamed my own imprudence for parting with
so substantial a blessing as my quiet to run after a
shadow.”
Mistake of Newton in supposing that the Improvement of Refracting
Telescopes was hopeless—Mr. Hall invents the Achromatic Telescope—Principles
of the Achromatic Telescope explained—It is re-invented
by Dollond, and improved by future Artists—Dr. Blair’s Aplanatic
Telescope—Mistakes in Newton’s Analysis of the Spectrum—Modern
Discoveries respecting the Structure of the Spectrum.
The new doctrines of the composition of light,
and of the different refrangibility of the rays which
compose it, having been thus established upon an
impregnable basis, it will be interesting to take a
general view of the changes which they have undergone
since the time of Newton, and of their influence
on the progress of optical discovery.
There is no fact in the history of science more
singular than that Newton should have believed
that all bodies produced spectra of equal length, or
separated the red and violet rays to equal distances
when the refraction of the mean rays was the
same. This opinion, unsupported by experiments,
and not even sanctioned by any theoretical views,
seems to have been impressed upon his mind with
all the force of an axiom.16 Even the shortness of
the spectrum observed by Lucas did not rouse him
to further inquiry; and when, under the influence
of this blind conviction he pronounced the improvement
of the refracting telescope to be desperate, he
checked for a long time the progress of this branch
of science, and furnished to future philosophers a
lesson which cannot be too deeply studied.
In 1729, about two years after the death of Sir
Isaac, an individual unknown to science broke the
spell in which the subject of the spectrum had been
so singularly bound. Mr. Chester More Hall, of
More Hall in Essex, while studying the mechanism
of the human eye, was led to suppose that telescopes
might be improved by a combination of
lenses of different refractive powers, and he actually
completed several object-glasses upon this principle.
The steps by which he arrived at such a construction
have not been recorded; but it is obvious that
he must have discovered what escaped the sagacity
of Newton, that prisms made of different kinds of
glass produced different degrees of separation of the
red and violet rays, or gave spectra of different
lengths when the refraction of the middle ray of the
spectrum was the same.
Fig. 6.
In order to explain how such a property led him
to the construction of a telescope without colour, or
an achromatic telescope, let us take a lens LL of
crown or plate glass, whose focal length LY is
about twelve inches. When the sun’s rays SL,
SL fall upon it, the red will be refracted to R, the
yellow to Y, and the violet to V. If we now place
behind it a concave lens ll of the same glass, and
of the same focus or curvature, it will be found,
both by experiment and by drawing the refracted
rays, according to the rules given in elementary
works, that the concave glass ll will refract the
rays LR, LR into LS′, LS′, and the rays LV, LV
into LS′, LS′ free of all colour; but as these rays
will be parallel, the two lenses will not have a
focus, and consequently cannot form an image so
as to be used as the object-glass of a telescope.
This is obvious from another consideration; for
since the curvatures of the convex and concave
lenses are the same, the two put together will be
exactly the same as if they were formed out of a
single piece of glass, having parallel surfaces like a
watch-glass, so that the parallel rays of light SL,
SL will pass on in the same direction LS′, LS′
affected by equal and opposite refractions as in a
piece of plane glass.
Now, since the convex lens LL separated the
white light SL, SL into its component coloured
rays, LV, LV being the extreme violet, and LR, LR
the extreme red; it follows that a similar concave
lens of the same glass is capable of uniting
into white light LS′, LS′ rays, as much separated
as LV, LR are. Consequently, if we take a concave
lens ll of the same, or of a greater refractive
power than the convex one, and having the power
of uniting rays farther separated than LV, LR are,
a less concavity in the lens ll will be sufficient to
unite the rays LV, LR into a white ray LS′; but
as the lens ll is now less concave than the lens LL
is convex, the concavity will predominate, and the
uncoloured rays LS′, LS′ will no longer be parallel,
but will converge to some point O, where they will
form a colourless or achromatic image of the sun.
The effect now described may be obtained by
making the convex lens LL of crown or of plate
glass, and the concave one of flint glass, or that of
which wineglasses are made. If the concave lens
ll has a greater refractive power than LL, which is
always the case, the only effect of it will be to
make the rays converge to a focus more remote
than O, or to render a less curvature necessary in
ll, if O is fixed for the focus of the combined lenses.
Such is the principle of the achromatic telescope
as constructed by Mr. Hall. This ingenious individual
employed working opticians to grind his
lenses, and he furnished them with the radii of the
surfaces, which were adjusted to correct the aberration
of figure as well as of colour. His invention,
therefore, was not an accidental combination of a
convex and a concave lens of different kinds of
glass, which might have been made merely for experiment;
but it was a complete achromatic telescope,
founded on a thorough knowledge of the
different dispersive powers of crown and flint glass.
It is a curious circumstance, however, in the history
of the telescope, that this invention was actually
lost. Mr. Hall never published any account
of his labours, and it is probable that he kept them
secret till he should be able to present his instrument
to the public in a more perfect form; and it
was not till John Dollond had discovered the property
of light upon which the instrument depends,
and had actually constructed many fine telescopes,
that the previous labours of Mr. Hall were laid before
the public.17 From this period the achromatic
telescope underwent gradual improvement, and by
the successive labours of Dollond, Ramsden, Blair,
Tulley, Guinand, Lerebours, and Fraunhofer, it has
become one of the most valuable instruments in
physical science.
Although the achromatic telescope, as constructed
by Dollond, was founded on the principle that the
spectra formed by crown and flint glass differed
only in their relative lengths, when the refraction
of the mean ray was the same, yet by a more minute
examination of the best instruments, it was
found that they exhibited white or luminous objects
tinged on one side with a green fringe, and on the
other with one of a claret colour. These colours,
which did not arise from any defect of skill in the
artist, were found to arise from a difference in the
extent of the coloured spaces in two equal spectra
formed by crown and by flint glass. This property
was called the irrationality of the coloured spaces,
and the uncorrected colours which remained when
the primary spectrum of the crown glass was corrected
by the primary spectrum of the flint glass
were called the secondary or residual spectrum. By
a happy contrivance, which it would be out of place
here to describe, Dr. Blair succeeded in correcting
this secondary spectrum, or in removing the green
and claret-coloured fringes which appeared in the
best telescopes, and to this contrivance he gave the
name of the Aplanatic Telescope.
But while Newton thus overlooked these remarkable
properties of the prismatic spectrum, as formed
by different bodies, he committed some considerable
mistakes in his examination of the spectrum
which was under his own immediate examination.
It does not seem to have occurred to him that the
relations of the coloured spaces must be greatly
modified by the angular magnitude of the sun or the
luminous body, or aperture from which the spectrum
is obtained; and misled by an apparent analogy
between the length of the coloured spaces and
the divisions of a musical chord,18 he adopted the
latter, as representing the proportion of the coloured
spaces in every beam of white light. Had
two other observers, one situated in Mercury, and
the other in Jupiter, studied the prismatic spectrum
of the sun by the same instruments, and with the
same sagacity as Newton, it is demonstrable that
they would have obtained very different results. On
account of the apparent magnitude of the sun in Mercury,
the observer there would obtain a spectrum
entirely without green, having red, orange, and yellow
at one end, the white in the middle, and terminated
at the other end with blue and violet. The
observer in Jupiter would, on the contrary, have
obtained a spectrum in which the colours were
much more condensed. On the planet Saturn a
spectrum exactly similar would have been obtained,
notwithstanding the greater diminution of the sun’s
apparent diameter. It may now be asked, which of
all these spectra are we to consider as exhibiting
the number, and arrangement, and extent of the
coloured spaces proper to be adopted as the true
analysis of a solar ray.
The spectrum observed by Newton has surely no
claim to our notice, merely because it was observed
upon the surface of the earth. The spectrum obtained
in Mercury affords no analysis at all of the
incident beam, the colours being almost all compound,
and not homogeneous, and that of Newton
is liable to the same objection. Had Newton examined
his spectrum under the very same circumstances
in winter and in summer, he would have
found the analysis of the beam more complete in
summer, on account of the diminution of the sun’s
diameter; and, therefore, we are entitled to say that
neither the number nor the extent of the coloured
spaces, as given by Newton, are those which belong
to homogeneous and uncompounded light.
The spectrum obtained in Jupiter and Saturn is
the only one where the analysis is complete, as it is
incapable of having its character altered by any farther
diminution of the sun’s diameter. Hence we
are forced to conclude, not only that the number
and extent of the primitive homogeneous colours,
as given by Newton, are incorrect; but that if he had
attempted to analyze some of the primitive tints in
the spectrum, he would have found them decidedly
composed of heterogeneous rays. There is one
consequence of these observations which is somewhat
interesting. A rainbow formed in summer,
when the sun’s diameter is least, must have its colours
more condensed and homogeneous than in winter,
when the size of its disk is a maximum, and
when the upper or the under limb of the sun is
eclipsed, a rainbow formed at that time will lose
entirely the yellow rays, and have the green and the
red in perfect contact. For the same reason, a rainbow
formed in Venus and Mercury will be destitute
of green rays, and have a brilliant bow of white
light separating two coloured arches; while in Mars,
Jupiter, Saturn, and the Georgian planet, the bow
will exhibit only four homogeneous colours.
From his analysis of the solar spectrum, Newton
concluded, “that to the same degree of refrangibility
ever belonged the same colour, and to the same
colour ever belonged the same degree of refrangibility;”
and hence he inferred, that red, orange, yellow,
green, blue, indigo, and violet were primary and
simple colours. He admitted, indeed, that “the
same colours in specie with these primary ones may
be also produced by composition. For a mixture of
yellow and blue makes green, and of red and yellow
makes orange;” but such compound colours were
easily distinguished from the simple colours of the
spectrum by the circumstance, that they are always
capable of being resolved by the action of the prism
into the two colours which compose them.
This view of the composition of the spectrum
might have long remained unchallenged, had we not
been able to apply to it a new mode of analysis.
Though we cannot separate the green rays of the
spectrum into yellow and blue by the refraction of
prisms, yet if we possessed any substance which
had a specific attraction for blue rays, and which
stopped them in their course, and allowed the yellow
rays to pass, we should thus analyze the green
as effectually as if they were separated by refraction.
The substance which possesses this property is a
purplish blue glass, similar to that of which finger-glasses
are made. When we view through a piece
of this glass, about the twentieth of an inch thick,
a brilliant prismatic spectrum, we find that it has
exercised a most extraordinary absorptive action on
the different colours which compose it. The red
part of the spectrum is divided into two red spaces,
separated by an interval entirely devoid of light.
Next to the inner red space comes a space of bright
yellow, separated from the red by a visible interval.
After the yellow comes the green, with an obscure
space between them, then follows the blue and the
violet, the last of which has suffered little or no
diminution. Now it is very obvious, that in this
experiment, the blue glass has actually absorbed
the red rays, which, when mixed with the yellow
on one side, constituted orange, and the blue rays,
which, when mixed with the yellow on the other
side, constituted green, so that the insulation of
the yellow rays thus effected, and the disappearance
of the orange, and of the greater part of the green
light, proves beyond a doubt that the orange and
green colours in the spectrum are compound colours,
the former consisting of red and yellow rays,
and the latter of yellow and blue rays of the very
same refrangibility. If we compare the two red
spaces of the spectrum seen through the blue glass
with the red space seen without the blue glass, it
will be obvious that the red has experienced such
an alteration in its tint by the action of the blue
glass, as would be effected by the absorption of a
small portion of yellow rays; and hence we conclude,
that the red of the spectrum contains a slight
tinge of yellow, and that the yellow space extends
over more than one-half of the spectrum, including
the red, orange, yellow, green, and blue spaces.
I have found also that red light exists in the yellow
space, and it is certain that in the violet space
red light exists in a state of combination with the
blue rays. From these and other facts which it
would be out of place here to explain, I conclude
that the prismatic spectrum consists of three different
spectra, viz. red, yellow, and blue, all having
the same length, and all overlapping each other.
Hence red, yellow, and blue rays of the very same
refrangibility coexist at every point of the spectrum;
but the colour at any one point will be that
of the predominant ray, and will depend upon the
relative distance of the point from the maximum
ordinate of the curve which represents the intensity
of the light of each of the three spectra.
Fig. 7.
This structure of the spectrum, which harmonizes
with the old hypothesis of three simple colours,
will be understood from the annexed diagram,
where MN is the spectrum of seven colours, all
compounded of the three simple ones, red, yellow,
and blue. The ordinates of the curves R, Y, and
B will express the intensities of each colour at different
points of the spectrum. At the red extremity
M of the spectrum, the pure red is scarcely
altered by the very slight intermixture of yellow
and blue. Farther on in the red space, the yellow
begins to make the red incline to scarlet. It then
exists in sufficient quantity to form orange, and, as
the red declines, the yellow predominates over the
feeble portion of red and blue which are mixed with
it. As the yellow decreases in intensity, the increasing
blue forms with it a good green, and the
blue rising to its maximum speedily overpowers the
small portion of yellow and red. When the blue
becomes very faint, the red exhibits its influence
in converting it into violet, and the yellow ceases
to exercise a marked influence on the tint. The
influence of the red over the blue space is scarcely
perceptible, on account of the great intensity of the
blue light; but we may easily conceive it to reappear
and form the violet light, not only from the
rapid decline of the blue light, but from the greater
influence of the red rays upon the retina.
These views may, perhaps, be more clearly understood
by supposing that a certain portion of white
light is actually formed at every point of the spectrum
by the union of the requisite number of the
three coloured rays that exist at any point. The
white light thus formed will add to the brilliancy
without affecting the tint of the predominant colour.
In the violet space we may conceive the small
portion of yellow which exists there to form white
light with a part of the blue and a part of the red,
so that the resulting tint will be violet, composed
of the blue and the small remaining portion of red,
mixed with the white light. This white light will
possess the remarkable property of not being susceptible
of decomposition by the analysis of the
prism, as it is composed of red, yellow, and blue
rays of the very same refrangibility. The insulation
of this white light by the absorption of the
predominant colours I have effected in the green,
yellow, and red spaces, and by the use of new absorbing
media we may yet hope to exhibit it in some
of the other colours, particularly in the brightest
part of the blue space, where an obvious approximation
to it takes place.
Among the most important modern discoveries
respecting the spectrum we must enumerate that
of fixed dark and coloured lines, which we owe to
the sagacity of Dr. Wollaston and M. Fraunhofer.
Two or three of these lines were discovered by Dr.
Wollaston, but nearly 600 have been detected by
means of the fine prisms and the magnificent apparatus
of the Bavarian optician. These lines are
parallel to one another, and perpendicular to the
length of the spectrum. The largest occupy a
space from 5″ to 10″ in breadth. Sometimes they
occur in well-defined lines, and at other times in
groups; and in all spectra formed from solar light,
they preserve the same order and intensity, and the
same relative position to the coloured spaces, whatever
be the nature of the prism by which they are
produced. Hence these lines are fixed points, by
which the relative dispersive powers of different
media may be ascertained with a degree of accuracy
hitherto unknown in this branch of science. In
the light of the fixed stars, and in that of artificial
flames, a different system of lines is produced, and
this system remains unaltered, whatever be the nature
of the prism by which the spectrum is formed.
The most important fixed lines in the spectrum
formed by light emitted from the sun, whether it is
reflected from the sky, the clouds, or the moon, may
be easily seen by looking at a narrow slit in the
window-shutter of a dark room, through a hollow
prism formed of plates of parallel glass, and filled
with any fluid of a considerable dispersive power.
The slit should not greatly exceed the twentieth of
an inch, and the eye should look through the thinnest
edge of the prism where there is the least thickness
of fluid. These lines I have found to be the boundaries
of spaces within which the rays have particular
affinities for particular bodies.
Colours of thin Plates first studied by Boyle and Hooke—Newton determines
the Law of their Production—His Theory of Fits of Easy
Reflection and Transmission—Colours of thick Plates.
In examining the nature and origin of colours as
the component parts of white light, the attention of
Newton was directed to the curious subject of the
colours of thin plates, and to its application to explain
the colours of natural bodies. His earliest
researches on this subject were communicated, in
his Discourse on Light and Colours, to the Royal
Society, on the 9th December, 1675, and were read
at subsequent meetings of that body. This discourse
contained fuller details respecting the composition
and decomposition of light than he had given in his
letter to Oldenburg, and was concluded with nine
propositions, showing how the colours of thin transparent
plates stand related to those of all natural
bodies.
The colours of thin plates seem to have been
first observed by Mr. Boyle. Dr. Hooke afterward
studied them with some care, and gave a correct
account of the leading phenomena, as exhibited in
the coloured rings upon soap-bubbles, and between
plates of glass pressed together. He recognised
that the colour depended upon some certain thickness
of the transparent plate, but he acknowledges
that he had attempted in vain to discover the relation
between the thickness of the plate and the
colour which it produced.
Dr. Hooke succeeded in splitting a mineral substance,
called mica, into films of such extreme thinness
as to give brilliant colours. One plate, for example,
gave a yellow colour, another a blue colour,
and the two together a deep purple; but, as plates
which produced those colours were always less than
the 12,000th part of an inch thick, it was quite impracticable,
by any contrivance yet discovered, to
measure their thickness, and determine the law according
to which the colour varied with the thickness
of the film. Newton surmounted this difficulty
by laying a double convex lens, the radius of curvature
of each side of which was fifty feet, upon the
flat surface of a plano-convex object-glass, and in
this way he obtained a plate of air or of space varying
from the thinnest possible edge at the centre of
the object-glass where it touched the plane surface,
to a considerable thickness at the circumference of
the lens. When light was allowed to fall upon the
object-glass, every different thickness of the plate
of air between the object-glass gave different colours,
so that the point where the two object-glasses
touched one another was the centre of a number of
concentric coloured rings. Now, as the curvature
of the object-glass was known, it was easy to calculate
the thickness of the plate of air at which any
particular colour appeared, and thus to determine
the law of the phenomena.
In order to understand how he proceeded, let
CED be the convex surface of the one object-glass, and
AEB the flat surface of the other. Let them touch
at the point E, and let homogeneous red rays fall
upon them, as shown in the figure. At the point
of contact E, where the plate of air is inconceivably
thin, not a single ray of the pencil RE is reflected.
The light is wholly transmitted, and, consequently,
to an eye above E, there will appear at
E a black spot. At a, where the plate of air is
thicker, the red light ra is reflected in the direction
aa′, and as the air has the same thickness in a circle
round the point E, the eye above E, at a, will see
next the black spot E a ring of red light. At m,
where the thickness of the air is a little greater than
at a, the light r′m is all transmitted as at E, and not
a single ray suffers reflection, so that to an eye
above E at m′ there will be seen without the red ring
a a dark ring m. In like manner, at greater thicknesses
of the plate of air, there is a succession of
red and dark rings, diminishing in breadth as shown
in the diagram.
Fig. 8.
When the same experiment was repeated in orange,
yellow, green, blue, indigo, and violet light, the very
same phenomenon was observed; with this difference
only, that the rings were largest in red light,
and smallest in violet light, and had intermediate
magnitudes in the intermediate colours.
If the observer now places his eye below E, so
as to see the transmitted rays, he will observe a set
of rings as before, but they will have a bright spot
in their centre at E, and the luminous rings will now
correspond with those which were dark when seen
by reflection, as will be readily understood from inspecting
the preceding diagram.
When the object-glasses are illuminated by white
light, the seven systems of rings, formed by all the
seven colours which compose white light, will now
be seen at once. Had the rings in each colour been
all of the same diameter they would all have formed
brilliant white rings, separated by dark intervals;
but, as they have all different diameters, they will
overlap one another, producing rings of various
colours by their mixture. These colours, reckoning
from the centre E, are as follows:—
1st Order. Black, blue, white, yellow, orange, red.
2d Order. Violet, blue, green, yellow, orange, red.
3d Order. Purple, blue, green, yellow, red, bluish-red.
4th Order. Bluish-green, green, yellowish-green,
red.
5th Order. Greenish-blue, red.
6th Order. Greenish-blue, red.
By accurate measurements, Sir Isaac found that
the thicknesses of air at which the most luminous
parts of the first rings were produced, were in parts
of an inch 1/178000, 3/178000, 5/178000, 7/178000, 9/178000,
11/178000. If the medium or the substance of the thin
plate is water, as in the case of the soap-bubble,
which produces beautiful colours according to its
different degrees of thinness, the thicknesses at
which the most luminous parts of the rings appear
are produced at 1/1·336 of the thickness at which they
are produced in air, and in the case of glass or mica
at 1/1·525 of that thickness; the numbers 1.336, 1.525
expressing the ratio of the sines of the angles of
incidence and refraction in the substances which
produce the colours.
From the phenomena thus briefly described, Sir
Isaac Newton deduces that ingenious, though hypothetical,
property of light, called its fits of easy
reflection and transmission. This property consists in
supposing that every particle of light from its first
discharge from a luminous body possesses, at equally
distant intervals, dispositions to be reflected from,
and transmitted through, the surfaces of bodies upon
which it is incident. Hence, if a particle of light
reaches a reflecting surface of glass when it is in
its fit of reflection, or in its disposition to be reflected,
it will yield more readily to the reflecting force of
the surface; and, on the contrary, if it reaches the
same surface while in a fit of easy transmission, or
in a disposition to be transmitted, it will yield with
more difficulty to the reflecting force. Sir Isaac
has not ventured to inquire into the cause of this
property; but we may form a very intelligible idea
of it by supposing, that the particles of light have
two attractive and two repulsive poles at the extremities
of two axes at right angles to each other,
and that the particles revolve round their axes, and
at equidistant intervals bring one or other of these
axes into the line of the direction in which the particle
is moving. If the attractive axis is in the line
of the direction in which the particle moves when it
reaches the refracting surface, the particle will yield
to the attractive force of the medium, and be refracted
and transmitted; but if the repulsive axis is
in the direction of the particle’s motion when it
reaches the surface, it will yield to the repulsive
force of the medium, and be reflected from it.
The application of the theory of alternate fits of
reflection and transmission to explain the colours of
thin plates is very simple. When the light falls upon
the first surface AB, Fig. 8 of the plate of air between
AB and CED, the rays that are in a fit of reflection
are reflected, and those that are in a fit of
transmission are transmitted. Let us call F the
length of a fit, or the distance through which the
particle of light moves while it passes from the state
of being in a fit of reflection to the state of being in
a fit of transmission. Now, as all the particles of
light transmitted through AB were in a state of easy
transmission when they entered AB, it is obvious,
that, if the plate of air at E is so thin as to be less
than one-half of F, the particles of light will still
be in their disposition to be transmitted, and consequently
the light will be all transmitted, and none
reflected at the curve surface at E. When the plate
becomes thicker towards a, so that its thickness exceeds
half of F, the light will not reach the surface
CE till it has come under its fit of reflection, and
consequently at a the light will be all reflected, and
none transmitted. As the thickness increases towards
m, the light will have come under its fit of
transmission, and so on, the light being reflected at
a, l, and transmitted at E, m. This will perhaps be
still more easily understood from fig. 9, where we
may suppose AEC to be a thin wedge of glass or
any other transparent body. When light is incident
on the first surface AE, all the particles of it that
are in a fit of easy reflection will be reflected, and
all those in a fit of easy transmission will be transmitted.
As the fits of transmission all commence
at AE, let the first fit of transmission end when the
particles of light have reached ab, and the second
when they have reached ef; and let the fits of reflection
commence at cd and gh. Then, as the fit
of transmission continues from AE to ab, all the
light that falls upon the portion mE of the second
surface will be transmitted and none reflected, so
that to an eye above E the space mE will appear
black. As the fit of reflection commences at ab, and
continues to cd, all the light which falls upon the
portion nm will be reflected, and none transmitted;
and so on, the light being transmitted at mE and
pn, and reflected at nm and qp. Hence to an eye
above E the wedge-shaped film of which AEC is
a section will be covered with parallel bands or
fringes of light separated by dark fringes of the
same breadth, and they will be all parallel to the
thin edge of the plate, a dark fringe corresponding
to the thinnest edge. To an eye placed below CE,
similar fringes will be seen, but the one corresponding
to the thinnest edge mE will be luminous.
Fig. 9.
If the thickness of the plate does not vary according
to a regular law as in fig. 9, but if, like a film of
blown glass, it has numerous inequalities, then the
alternate fringes of light and darkness will vary with
the thickness of the film, and throughout the whole
length of each fringe the thickness of the film will
be the same.
We have supposed in the preceding illustration
that the light employed is homogeneous. If it is
white, then the differently coloured fringes will form
by their superposition a system of fringes analogous
to those seen between two object-glasses, as already
explained.
The same periodical colours which we have now
described as exhibited by thin plates were discovered
by Newton in thick plates, and he has explained
them by means of the theory of fits; but it
would lead us beyond the limits of a popular work
like this to enter into any details of his observations,
or to give an account of the numerous and important
additions which this branch of optics has received
from the discoveries of succeeding authors.
Newton’s Theory of the Colours of Natural Bodies explained—Objections
to it stated—New Classification of Colours—Outline of a New
Theory proposed.
If the objects of the material world had been
illuminated with white light, all the particles of
which possessed the same degree of refrangibility,
and were equally acted upon by the bodies on which
they fall, all nature would have shone with a leaden
hue, and all the combinations of external objects,
and all the features of the human countenance, would
have exhibited no other variety but that which they
possess in a pencil sketch or a China-ink drawing.
The rainbow itself would have dwindled into a narrow
arch of white light,—the stars would have shone
through a gray sky,—and the mantle of a wintry
twilight would have replaced the golden vesture of
the rising and the setting sun. But He who has exhibited
such matchless skill in the organization of
material bodies, and such exquisite taste in the forms
upon which they are modelled, has superadded that
ethereal beauty which enhances their more permanent
qualities, and presents them to us in the
ever-varying colours of the spectrum. Without this
the foliage of vegetable life might have filled the eye
and fostered the fruit which it veils,—but the youthful
green of its spring would have been blended with
the dying yellow of its autumn. Without this the
diamond might have displayed to science the beauty
of its forms, and yielded to the arts its adamantine
virtues;—but it would have ceased to shine in the
chaplet of beauty, and to sparkle in the diadem of
princes. Without this the human countenance might
have expressed all the sympathies of the heart, but
the “purple light of love” would not have risen on
the cheek, nor the hectic flush been the herald of
its decay.
The gay colouring with which the Almighty has
decked the pale marble of nature is not the result
of any quality inherent in the coloured body, or in
the particles by which it may be tinged, but is merely
a property of the light in which they happen to be
placed. Newton was the first person who placed
this great truth in the clearest evidence. He found
that all bodies, whatever were their peculiar colours,
exhibited these colours only in white light. When
they were illuminated by homogeneous red light
they appeared red, by homogeneous yellow light,
yellow, and so on, “their colours being most brisk
and vivid under the influence of their own daylight
colours.” The leaf of a plant, for example, appeared
green in the white light of day, because it
had the property of reflecting that light in greater
abundance than any other. When it was placed in
homogeneous red light, it could no longer appear
green, because there was no green light to reflect;
but it reflected a portion of red light, because there
was some red in the compound green which it had
the property of reflecting. Had the leaf originally
reflected a pure homogeneous green, unmixed with
red, and reflected no white light from its outer surface,
it would have appeared quite black in pure homogeneous
red light, as this light does not contain
a single ray which the leaf was capable of reflecting.
Hence the colours of material bodies are owing
to the property which they possess of stopping certain
rays of white light, while they reflect or transmit
to the eye the rest of the rays of which white
light is composed.
So far the Newtonian doctrine of colours is capable
of rigid demonstration; but its author was
not content with carrying it thus far: he sought to
determine the manner in which particular rays are
stopped, while others are reflected or transmitted;
and the result of this profound inquiry was his theory
of the colours of natural bodies, which was communicated
to the Royal Society on the 10th February,
1675. This theory is perhaps the loftiest of all his
speculations; and though, as a physical generalization,
it stands on a perishable basis, and must soon
be swept away in the progress of science, it yet
bears the deepest impress of the grasp of his powerful
intellect.
The principles upon which this theory is founded
are the following:—
1. Bodies that have the greatest refractive powers
reflect the greatest quantity of light; and at the
confines of equally refracting media there is no reflection.
2. The least particles of almost all natural bodies
are in some measure transparent.
3. Between the particles of bodies are many pores
or spaces, either empty or filled with media of less
density than the particles.
4. The particles of bodies and their pores, or the
spaces between the particles, have some definite
size.
Upon these principles Newton explains the origin
of transparency, opacity, and colour.
Transparency he considers as arising from the particles
and their intervals or pores being too small to
cause reflection at their common surfaces,19 so that
all the light which enters transparent bodies passes
through them without any portion of it being turned
from its path by reflection. If we could obtain, for
example, a film of mica whose thickness does not
exceed two-thirds of the millionth part of an inch,
all the light which fell upon it would pass through it,
and none would be reflected. If this film was then
cut into fragments, a number of such fragments
would constitute a bundle, which would also transmit
all the light which fell upon it, and be perfectly
transparent.
Opacity in bodies arises, he thinks, from an opposite
cause, viz. when the parts of bodies are of such
a size as to be capable of reflecting the light which
falls upon them, in which case the light is “stopped
or stifled” by the multitude of reflections.
The colours of natural bodies have, in the Newtonian
hypothesis, the same origin as the colours of
thin plates, their transparent particles, according to
their several sizes, reflecting rays of one colour, and
transmitting those of another. “For if a thinned
or plated body which, being of an uneven thickness,
appears all over of one uniform colour, should be slit
into threads, or broken into fragments of the same
thickness with the plate or film, every thread or fragment
should keep its colour, and consequently, a
heap of such threads or fragments should constitute
a mass or powder of the same colour which the
plate exhibited before it was broken: and the parts
of all natural bodies being like so many fragments
of a plate, must, on the same grounds, exhibit the
same colour.”
Such is the theory of the colours of natural
bodies, stated as clearly and briefly as we can. It
has been very generally admitted by philosophers,
both of our own and of other countries, and has been
recently illustrated and defended by a French philosopher
of distinguished eminence. That this theory
affords the true explanation of certain colours, or,
to speak more correctly, that certain colours in natural
bodies are the colours of thin plates, cannot be
doubted; but it will not be difficult to show that it is
quite inapplicable to that great class of phenomena
which may be considered as representing the colours
of natural bodies.
The first objection to the Newtonian theory is the
total absence of all reflected light from the particles
of transparent coloured media, such as coloured
gems, coloured glasses, and coloured fluids. This
objection was urged long ago by Mr. Delaval, who
placed coloured fluids on black grounds, and never
could perceive the least trace of the reflected tints.
I have repeated the experiment with every precaution,
and with every variation that I could think of,
and I consider it as an established fact, that in such
coloured bodies the complementary reflected colour
cannot be rendered visible. If the fluid, for example,
be red, the green light from which the red has been
separated ought to appear either directly by looking
into the coloured mass, or ought to be recognised
by its influence in modifying the light really reflected;
but as it cannot be seen, we must conclude
that it has not been reflected, but has been destroyed
by some other property of the coloured
body.
A similar objection may be drawn from the disappearance
of the transmitted complementary colour
in the leaves of plants and petals of flowers. I have
ascertained from numerous experiments, that the
transmitted colour is almost invariably the same
with the reflected colour, and that the same holds
true with the coloured juices expressed from them.
The complementary tints are never seen, and wherever
there has been any thing like an approximation
to two tints, I have invariably found that it arose
from there being two different coloured juices existing
in different sides of the leaf.
In the phenomena of the light transmitted by
coloured glasses, there are some peculiarities which,
we think, demonstrate that their colours are not
those of thin plates. The light, for example, transmitted
through a particular kind of blue glass, has a
blue colour of such a peculiar composition that there
is no blue in any of the orders of colours in thin
plates which has any resemblance to it. It is entirely
destitute of the red rays which form the middle of
the red space in the spectrum; so that the particles
on which the colour depends must reflect the middle
red rays, and transmit those on each side of it,—a
property which cannot be deduced from the Newtonian
doctrine.
The explanation of opacity, as arising from a
multitude of reflections, is liable to the same objection
which we have urged against the explanation
of colour. In order to appreciate its weight,
we must distinguish opacity into two kinds, namely,
the opacity of whiteness and the opacity of blackness.
Those bodies which possess the power of reflection
in the highest degree, such as white metals, chalk,
and plaster of Paris, never reflect more than one-half
of the light which falls upon them. The other
half of the incident light is, according to Newton,
lost by a multitude of reflections. But how is it
lost? Reflection merely changes the direction of the
particles of light, so that they must again emerge
from the body, unless they are reflected into fixed
returning orbits, which detain them for ever in a
state of motion within the body. In the case of
black opacity, such as that of coal, which reflects
from its first surface only 1/25th of the white light,
the difficulty is still greater, and we cannot conceive
how any system of interior reflections could so
completely stifle 24/25ths of the whole incident light,
without some of it returning to the eye in a visible
form.
In determining the constitution of bodies that produce
transparency and blackness, the Newtonian
theory encounters a difficulty which its author has
by no means surmounted. Transparency, as we
have already seen, arises from the “particles and
their interstices being too small to cause reflections
in their common surfaces,” that is, they must be
“less than any of those which exhibit colours,” or
“less than is requisite to reflect the white and very
faint blue of the first order. But this is the very same
constitution which produces blackness by reflection,
and in order to explain the cause of blackness by
transmission, or black opacity, Newton is obliged to
introduce a new principle.
“For the production of black,” says he, “the corpuscles
must be less than any of those which exhibit
colours. For at all greater sizes there is too
much light reflected to constitute this colour. But
if they be supposed a little less than is requisite to
reflect the white and very faint blue of the first order,
they will reflect so very little light as to appear
intensely black, and yet may perhaps variously refract20
it to and fro within themselves so long, until it happens
to be stifled and lost, by which means they will
appear black in all positions of the eye, without any
transparency.”
This very remarkable passage exhibits, in a striking
manner, the perplexity in which our author was involved
by the difficulties of his subject. As the particles
which produce blackness by reflection are
necessarily so small as to exclude the existence of
any reflective forces, he cannot ascribe the loss of
the intromitted light, as he does in the case of white
opacity, to “a multitude of reflections;” and therefore
he is compelled to have recourse to refracting
forces to perform the same office. The reluctance
with which he avails himself of this expedient is
well marked in the mode of expression which he
adopts; and I am persuaded that when he wrote the
above passage, he felt the full force of the objections
to this hypothesis, which cannot fail to present
themselves. As the size of the particles which
produce blackness are intermediate between those
which produce transparency and those which produce
colour, approaching closely to the latter, it is
difficult to conceive why they should refract the intromitted
light, while the greater and smaller particles,
and even those almost of the same size, should
be destitute of that property. It is, besides, not easy
to understand how a refraction can take place within
bodies which shall stifle all the light, and prevent it
from emerging. Nay, we may admit the existence
of such refractions, and yet understand how, by a
compensation in their direction, the refracted rays
may all emerge from the opaque body.
The force of these objections is tacitly recognised
in Pemberton’s View of Sir Isaac Newton’s Philosophy;21
and as Newton not only read and approved of
that work, but even perused a great part of it along
with its author, we may fairly consider the opinion
there stated to be his own.
“For producing black, the particles ought to be
smaller than for exhibiting any of the colours, viz.
of a size answering to the thickness of the bubble,
whereby reflecting little or no light, it appears colourless;
but yet they must not be too small, for that will
make them transparent through deficiency of reflections
in the inward parts of the body, sufficient to
stop the light from going through it; but they must
be of a size bordering upon that disposed to reflect
the faint blue of the first order, which affords an
evident reason why blacks usually partake a little
of that colour.” In this passage all idea of refraction
is abandoned, and that precise degree of size is
assumed for the particles which leaves a small power
of reflection, which is deemed sufficient to prevent
the body from becoming transparent; that is, sufficient
to render it opaque or black.
The last objection which we shall state to this
theory is one to which we attach great weight, and,
as it is founded on discoveries and views which have
been published since the time of Newton, we venture
to believe, that, had he been aware of them, he
would never have proposed the theory which we
are considering.
When light falls upon a thin film such as AEC,
fig. 9, p. 80, so as to produce the colours of thin
plates, it follows, from Sir Isaac Newton’s theory
of fits, that a portion of the light is, as usual, reflected
at the first surface AE,22 while the light which
forms the coloured image is that which is reflected
from the second surface EC, so that all the colours
of thin plates are diluted with the white light reflected
from the first surface. Now, in the modern
theory, which ascribes the colours of thin plates to
the interference of the light reflected from the
second surface EC, with the light reflected from the
first surface AE, the resulting tint arises from the
combination of these two pencils, and consequently
there is no white light reflected from the surface
AE. In like manner, when the thickness of the
film is such that the two interfering pencils completely
destroy one another, and produce black,
there is not a ray of light reflected from the first
surface. Here, then, we have a criterion for deciding
between the theory of fits and the theory of
interference; for if there is no white light reflected
from the first surface AE, the theory of fits must be
rejected. In a remarkable phenomenon of blackness
arising from minute fibres, which I have had
occasion to describe, there was no perceptible reflection
from the surface of the fibres;23 and M.
Fresnel describes an experiment made to determine
the same point, and states the result of it to
have been unequivocally in favour of the doctrine
of interference.
In order to apply this important fact, let us take
a piece of coal, one of the blackest and most opaque
of all substances, and which does not reflect to the
eye a single ray out of those which enter its substance.
The size of its particles is so small, that
they are incapable of reflecting light. When a number
of these particles are placed together, so as to
form a surface, and other particles behind them, so
as to form a solid, they will not acquire by this
process the power of reflection; and consequently, a
piece of coal so composed should be destitute of the
property of reflecting light from its first surface.
But this is not the case,—light is abundantly reflected
from the first surface of the coal, and consequently,
its elementary particles must possess the
same power. Hence the blackness of coal must be
ascribed to some other cause than to the minuteness
of its transparent atoms.
To transparent bodies this argument has a similar
application. As their atoms are still less than those
of black bodies, their inability to reflect light is still
greater, and hence arises their transparency. But
the particles forming the surface of such bodies do
reflect light, and, therefore, their transparency must
have another origin.
In the case of coloured bodies, too, the particles
forming their surfaces reflect white light like those
of all other bodies, so that these particles cannot
produce colour on the same principles as those of
thin plates. In many of those cases of colour which
seem to depend upon the minuteness of the particles
of the body, the reflection of white light may nevertheless
be observed, but this will be found to arise
from a thin transparent film, behind which the colorific
particles are placed.
Whatever answer may be given to these objections,
we think it will be admitted by those who
have studied the subject most profoundly, that a
satisfactory theory of the colours of natural bodies
is still a desideratum in science. How far we may
be able to approach to it in the present state of
optics the reader will judge from the following
views.
Colours may be arranged into seven classes, each
of which depends upon different principles.
1. Transparent coloured fluids—transparent coloured
gems—transparent coloured glasses—coloured
powders—and the colours of the leaves and flowers
of plants.
2. Oxidations on metals—colours of Labrador
feldspar—colours of precious and hydrophanous
opal, and other opalescences—the colours of the
feathers of birds, of the wings of insects, and of the
scales of fishes.
3. Superficial colours, as those of mother-of-pearl
and striated surfaces.
4. Opalescences and colours in composite crystals
having double refraction.
5. Colours from the absorption of common and
polarized light by doubly refracting crystals.
6. Colours at the surfaces of media of different
dispersive powers.
7. Colours at the surface of media in which the
reflecting forces extend to different distances, or follow
different laws.
The first two of these classes are the most important.
The Newtonian theory appears to be
strictly applicable to the phenomena of the second
class; but those of the first class cannot, we conceive,
be referred to the same cause.
* * * * *
The rays of solar light possess several remarkable
physical properties: They heat—they illuminate—they
promote chymical combination—they effect
chymical decompositions—they impart magnetism
to steel—they alter the colours of bodies—they
communicate to plants and flowers their peculiar
colours, and are in many cases necessary to the
development of their characteristic qualities. It is
impossible to admit for a moment that these varied
effects are produced by a mere mechanical action,
or that they arise from the agitation of the particles
of bodies by the vibration of the ether which is considered
to be the cause of light. Whatever be the
difficulties which attach to the theory which supposes
light to consist of material particles, we are
compelled, by its properties, to admit that light acts
as if it were material, and that it enters into combinations
with bodies, in order to produce the effects
which we have enumerated.
When a beam of light falls upon a body, and the
whole or a part of that which enters its substance
totally disappears, we are entitled to say, that it is
detained by some power exercised by the particles
of the body over the particles of light. When this
light is said to be lost by a multitude of reflections
or refractions, the statement is not only hypothetical,
but it is an hypothesis incompatible with optical
principles. That the light detained within bodies
has been stopped by the attractive force of the particles
seems to be highly probable, and the mind
will not feel any repugnance to admit that the particles
of all bodies, whether solid, fluid, or aëriform,
have a specific affinity for the particles of light.
Considering light, therefore, as material, it is not
difficult to comprehend how it should, like other
elementary substances, enter into combination with
bodies, and produce many chymical and physical
effects, but particularly the phenomena of transparency,
opacity, and colour.
In transparent colourless bodies, such as water
and glass, the intromitted light experiences a considerable
loss, because a certain number of its particles
are attracted and detained by the atoms of the
water or glass, and the light which emerges is
colourless, because the particles exercise a proportional
action over all the simple colours which
compose white light.
When the transparent body has any decided
colour, such as those enumerated in Class I., then
the particles of the body have exercised a specific
attraction over those rays of white light which are
complementary to those which compose the colour
of the transmitted light. If the transparent body,
for example, is red, then its particles have detained
the green rays which entered into the incident light,
or certain other rays, which with the red are necessary
to compose white light. In compound bodies,
like some of the artificial glasses, the particles will
attract and detain rays of light of different colours,
as may be seen by analyzing the transmitted light
with a prism, which will exhibit a spectrum deprived
of all the rays which have been detained. In black
bodies the particles exercise a powerful attraction
over light, and detain all the intromitted rays.
When coloured bodies are opaque, so as to exhibit
their colours principally by reflection, the light
which is reflected back to the observer has received
its colour from transmission through part of the
thickness of the body, or, what is the same thing,
the colour reflected to the eye is complementary to
that which has been detained by the particles of the
body while the light is passing and repassing
through a thickness terminated by the reflecting
surfaces; and as only a part of this light is reflected,
as in the case of leaves and flowers, the transmitted
light must have the same colour as the reflected
light.
When coloured bodies exhibit two different colours
complementary to each other, the one seen by reflection
and the other by transmission, it is then
highly probable that the colours are those of thin
plates, though there are still other optical principles
to which they may be referred. As the particles of
bodies, and the medium which unites them, or, as
the different atoms of a compound body may have
different dispersive powers, while they exercise the
same refractive force over a particular part of the
spectrum, the rays for which this compensation
takes place will be transmitted, while part of the
complementary light is reflected.24 Or in cases
where the refractive and dispersive powers are the
same, the reflective forces of the particles may vary
according to a different law, so that at the separating
surfaces either white or coloured light may be
reflected.25
In those cases of colour where the reflected and
the transmitted tints are not complementary, as in
leaf-gold, where the former is yellow and the latter
green;—in leaf-silver, where they are white and blue,
and in certain pieces of fir-wood, where the reflected
light is whitish yellow, and the transmitted light a
brilliant homogeneous red, we may explain the separation
of the colours either by the principles we
have already laid down or by the doctrine of thin
plates. On the first principle, the colour of the reflected
light, which is supposed to be the same as
that of the transmitted light, will be modified by the
law according to which the particles of the body
attract different rays out of the beam of white light.
In pitch, for example, the blue rays are first absorbed,
so that at small thicknesses the transmitted
light is a fine yellow, while, by the action of a
greater thickness, the yellow itself is absorbed, and
the transmitted light is a bright homogeneous red.
Now in leaf-gold the transmitted colour of thinner
films than we can obtain may be yellow, and, consequently,
the light reflected from the first strata of
interrupting faces will be yellow, and will determine
the predominant tint of the reflected light. On the
Newtonian doctrine, Mr. Herschel has explained it
by saying, “that the transmitted rays have traversed
the whole thickness of the medium, and therefore
undergo many more times the action of its atoms
than those reflected, especially those near the first
surface to which the brighter part of the reflected
colour is due.”
The phenomena of the absorption of common
and polarized light, which I have described in another
place,26 throw much light on the subject of
coloured bodies. The relation of the absorbent action
to the axes of double refraction, and, consequently,
to the poles of the molecules of the crystal,
shows how the particles of light attracted by the
molecules of the body will vary, both in their nature
and number, according to the direction in which
they approach the molecules; and explains how the
colour of a body may be changed, either temporarily
or permanently, by heat, according as it produces
a temporary or a permanent change in the
relative position of the molecules. This is not the
place to enlarge on this subject; but we may be
permitted to apply the idea to the curious experiment
of Thenard on phosphorus. When this substance
is rendered pure by repeated distillation, it
is transparent, and transmits yellow light; but when
it is thrown in a melted state into cold water, it
becomes jet black. When again melted, it resumes
its original colour and transparency. According to
the Newtonian theory, we must suppose that the
atoms of the phosphorus have been diminished in
size by sudden cooling,—an effect which it is not
easy to comprehend; but, according to the preceding
views, we may suppose that the atoms of
the phosphorus have been forced by sudden cooling
into relative positions quite different from those
which they take when they slowly assume the solid
state, and their poles of maximum attraction, in
place of being turned to one another, are turned in
different directions, and then allowed to exercise
their full action in attracting the intromitted light,
and detaining it wholly within the body.27
Before concluding this chapter, there is one topic
peculiarly deserving our notice, namely, the change
of colour produced in bodies by continued exposure
to light. The general effect of light is to diminish
or dilute the colours of bodies, and in many cases
to deprive them entirely of their colour. Now, it
is not easy to understand how repeated undulations
propagated through a body could diminish the size
of its particles, or how the same effect could be
produced by a multitude of reflections from particle
to particle. But if light is attracted by the particles
of bodies, and combines with them, it is easy to
conceive that, when the molecules of a body have
combined with a great number of particles of a
green colour, for example, their power of combination
with others will be diminished, and, consequently,
the number of particles of any colour
absorbed or detained must diminish with the time
that the body has been exposed to light; that is,
these particles must enter into the transmitted and
reflected pencils, and diminish the intensity of their
colour. If the body, for example, absorbs red light,
and transmits and reflects green, then if the quantity
of absorbed red light is diminished, it will enter
into the reflected and transmitted pencils, and, forming
white light by its mixture with a portion of the
green rays, will actually dilute them in the same
manner as if a portion of white light had been
added.28
Newton’s Discoveries respecting the Inflection or Diffraction of Light—Previous
Discoveries of Grimaldi and Dr. Hooke—Labours of succeeding
Philosophers—Law of Interference of Dr. Young—Fresnel’s
Discoveries—New Theory of Inflection on the Hypothesis of the Materiality
of Light.
Although the discoveries of Newton respecting
the Inflection of Light were first published in his
Optics in 1704, yet there is reason to think that
they were made at a much earlier period. Sir Isaac,
indeed, informs us, in his preface to that great work,
that the third book, which contains these discoveries,
“was put together out of scattered papers;”
and he adds at the end of his observations, that “he
designed to repeat most of them with more care and
exactness, and to make some new ones for determining
the manner how the rays of light are bent in their
passage by bodies, for making the fringes of colours
with the dark lines between them. But I was then
interrupted, and cannot now think of taking these
things into consideration.” On the 18th March, 1674,
Dr. Hooke had read a valuable memoir on the phenomena
of diffraction; and, as Sir Isaac makes no
allusion whatever to this work, it is the more probable
that his “scattered papers” had been written
previous to the communication of Dr. Hooke’s experiments.
The phenomena of the inflection of light were first
discovered by Francis Maria Grimaldi, a learned
Jesuit, who has described them in a posthumous
work published in 1665, two years after his death.29
Having admitted a beam of the sun’s light through
a small pin-hole in a piece of lead or card into a
dark chamber, he found that the light diverged from
this aperture in the form of a cone, and that the
shadows of all bodies placed in this light were not
only larger than might have been expected, but were
surrounded with three coloured fringes, the nearest
being the widest, and the most remote the narrowest.
In strong light he discovered analogous fringes
within the shadows of bodies, which increased in
number with the breadth of the body, and became
more distinct when the shadow was received obliquely
and at a greater distance. When two small apertures
or pin-holes were placed so near each other
that the cones of light formed by each of them
intersected one another, Grimaldi observed, that a
spot common to the circumference of each, or, which
is the same thing, illuminated by rays from each
cone, was darker than the same spot when illuminated
by either of the cones separately; and he announces
this remarkable fact in the following paradoxical
proposition, “that a body actually illuminated
may become more dark by adding a light to that which
it already receives.”
Without knowing what had been done by the
Italian philosopher, our countryman, Dr. Robert
Hooke, had been diligently occupied with the same
subject. In 1672, he communicated his first observations
to the Royal Society, and he then spoke of
his paper as “containing the discovery of a new
property of light not mentioned by any optical writers
before him.” In his paper of 1674, already
mentioned, and which is no doubt the one to which
he alludes, he has not only described the leading
phenomena of the inflection, or the deflection of
light, as he calls it, but he has distinctly announced
the doctrine of interference, which has performed so
great a part in the subsequent history of optics.30
Such was the state of the subject when Newton
directed to it his powers of acute and accurate observation.
His attention was turned only to the
enlargement of the shadow, and to the three fringes
which surrounded it; and he begins his observations
by ascribing the discovery of these facts to Grimaldi.
After taking exact measures of the diameter
of the shadow of a human hair, and of the breadth
of the fringes at different distances behind it, he
discovered the remarkable fact that these diameters
and breadths were not proportional to the distances
from the hair at which they were measured.
In order to explain these phenomena, Newton supposed
that the rays which passed by the edge of the
hair are deflected or turned aside from it, as if by a
repulsive force, the nearest rays suffering the greatest,
and those more remote a less degree of deflection.
Fig. 10.
Thus, if X, fig. 10, represents a section of the
hair, and AB, CD, EF, GH, &c. rays passing at different
distances from X, the ray AB will be more
deflected than CD, and will cross it at m, the ray
CD will for the same reason cross EF at n, and
EF will cross GH at o. Hence the curve or caustic
formed by the intersections m, n, o, &c. will be convex
outward, its curvature diminishing as it recedes
from the vertex. As none of the passing light can
possibly enter within this curve, it will form the
boundary of the shadow of X.
The explanation given by Sir Isaac of the coloured
fringes is less precise, and can be inferred only from
the two following queries.
1. “Do not the rays which differ in refrangibility
differ also in flexibility, and are they not, by these
different inflections separated from one another, so
as after separation to make the colours in the three
fringes above described? And after what manner
are they inflected to make those fringes?
2. “Are not the rays of light in passing by the
edges and sides of bodies bent several times backwards
and forwards with a motion like that of an
eel? And do not the three fringes of light above
mentioned arise from three such bendings?”
The idea thus indistinctly thrown out in the preceding
queries has been ingeniously interpreted by
Mr. Herschel in the manner represented in fig. 11,
where SS are two rays passing by the edge of the
body MN. These rays are supposed to undergo
several bendings, as at a, b, c, and the particles of
light are thrown off at one or other of the points
of contrary flexure, according to the state of their
fits or other circumstances. Those that are thrown
outwards in the direction aA, bB, cC, dD, will
produce as many caustics by their intersections as
there are deflected rays; and each caustic, when received
on a screen at a distance, will depict on it
the brightest part or maximum of a fringe.
Fig. 11.
In this unsatisfactory state was the subject of the
inflection of light left by Sir Isaac. His inquiries
were interrupted, and never again renewed; and
though he himself found that the phenomena were
the same, “whether the hair was encompassed with
air or with any other pellucid substance,” yet this
important result does not seem to have shaken his
conviction, that the phenomena had their origin in
the action of bodies upon light.
During two sets of experiments which I made on
the inflection of light, the first in 1798, and the
second in 1812 and 1813, I was desirous of examining
the influence of density and refractive power
over the fringes produced by inflection. I compared
the fringes formed by gold-leaf with those
formed by masses of gold,—and those produced by
films which gave the colours of thin plates with
those formed by masses of the same substance. I
examined the influence of platinum, diamond, and
cork in inflecting light, the effect of non-reflecting
grooves and spaces in polished metals, and of cylinders
of glass immersed in a mixture of oil of cassia
and oil of olives of the same refractive power; and,
as the fringes had the same magnitude and character
under all these circumstances, I concluded that
they were not produced by any force inherent in
the bodies themselves, but arose from a property
of the light itself, which always showed itself when
light was stopped in its progress.
Dr. Thomas Young, who had supported with great
ingenuity and force of argument the undulatory
theory of light, as maintained by Hooke and Huygens,
was the first who gave a plausible explanation
of the inflection of light. By interposing a
small screen at B, fig. 10, and intercepting the
rays that passed near the hair X, he was surprised
to find that all the fringes within the shadow disappeared.
The same effect took place when the screen
intercepted the rays on the other side; and hence
he concluded, that the rays on each side of the hair
were necessary to the production of the inner fringes,
and that the fringes were produced by the interference
of the rays that passed on one side of the
hair with those that passed on the other side. In
order to account for the coloured fringes without the
shadow, Dr. Young conceived that the rays which
pass near the edge of the hair interfere with others,
which he supposes may be reflected after falling
very obliquely upon its edge,—a supposition which,
if correct, would certainly produce fringes very
similar to those actually observed.
In pursuing these researches so successfully begun
by Dr. Young, M. Fresnel had the good fortune to
explain all the phenomena of inflection by means of
the undulatory doctrine combined with the principle
of interference. In place of transmitting the light
through a small aperture, he caused it to diverge
from the focus of a deep convex lens, and instead
of receiving the shadow and its fringes upon a
smooth white surface, as was done by Newton, he
viewed them directly with his eye through a lens
placed behind the shadow; and by means of a microscope
he was able to measure the dimensions of
the fringes with the greatest exactness. By this
mode of observation he made the remarkable discovery,
that the inflection of the light depended on
the distance of the inflecting body from the aperture or
from the focus of divergence;31 the fringes being observed
to dilate as the body approached that focus,
and to contract as it receded from it, their relative
distances from each other, and from the margin of
the shadow continuing invariable. In attempting to
account for the formation of the exterior fringes, M.
Fresnel found it necessary to reject the supposition
of Dr. Young, that they were owing to light reflected
from the edge of the body. He not only
ascertained that the real place of the fringe was the
17/100th of a millimetre different from what it should
be on that supposition, but he found that the fringes
preserved the same intensity of light, whether the
inflecting body had a round or a sharp edge, and
even when the edge was such as not to afford sufficient
light for their production. From this difficulty
the undulatory theory speedily released him, and he
was led by its indications to consider the exterior
fringes, as produced by an infinite number of elementary
waves of light emanating from a primitive
wave when partly interrupted by an opaque body.
The various phenomena of inflection, which had
so long resisted every effort to generalize them,
having thus received so beautiful and satisfactory an
explanation from the undulatory doctrine, they must
of course be regarded as affording to that doctrine
the most powerful support, while the Newtonian
hypothesis of the materiality of light is proportionally
thrown into the shade. It is impossible, indeed,
even for national partiality to consider the views of
Newton as furnishing any explanation of the facts
discovered by Fresnel; and, as no attempt has been
made by the small though able phalanx of his disciples
to stay the decision with which, on this count
at least, the doctrine of emission has been threatened,
we shall venture to suggest some principles
by which the refractory phenomena may perhaps
be yet brought within the pale of the Newtonian
theory.
That the particles of light, like those of heat,
are endowed with a repulsive force which prevents
them from accumulating when in a state of condensation,
or when they are detained by the absorptive
action of opaque bodies, will be readily admitted.
By this power a beam of light radiating from a
luminous point has, in every azimuth, the same degree
of intensity at the same distance from its centre
of divergence; but if we intercept a portion of such
a beam by an opaque body, the repulsive force of the
light which formerly occupied its shadow is withdrawn,
and consequently the rays which pass near
the body will be repelled into the shadow, and will
form, by their interference with those similarly repelled
on the other side, the interior fringes, which
are parallel to the edges of the body. The rays
which pass at a greater distance will in like manner
be bent towards the body, but with less force, and,
interfering with those rays which retain their primitive
direction, from the state of their fits or the
position of their poles, they will form the exterior
fringes. When the inflecting body is placed near
the point of divergence, the greater proximity of
the rays will produce a greater repulsive force, and
consequently a greater inflection of the passing
light; while the removal of the body from the point
of divergence will be accompanied with an increased
distance of the particles, an inferior repulsive force,
and a feebler inflection. As the phenomena of inflection,
considered under this aspect, arise from a
property of the light itself, it follows that they will
remain invariable, whatever be the nature or density
of the body, or the form of the edge which
acts upon the passing rays.
Miscellaneous Optical Researches of Newton—His Experiments on
Refraction—His Conjecture respecting the Inflammability of the
Diamond—His Law of Double Refraction—His Observations on the
Polarization of Light—Newton’s Theory of Light—His “Optics.”
Before concluding our account of Newton’s optical
discoveries, it is necessary to notice some of
his minor researches, which, though of inferior importance
in the science of light, have either exercised
an influence over the progress of discovery,
or been associated with the history of other branches
of knowledge.
One of the most curious of these inquiries related
to the connexion between the refractive powers and
the chymical composition of bodies. Having measured
the refractive powers and the densities of twenty-two
substances, he found that the forces which
reflect and refract light are very nearly proportional
to the densities of the same bodies. In this law,
however, he noticed a remarkable exception in the
case of unctuous and sulphureous bodies, such as
camphire, olive oil, linseed oil, spirit of turpentine,
and diamond, which have their refractive powers
two or three times greater in respect of their densities
than the other substances in the table, while
among themselves their refractive powers are proportional
to their densities, without any considerable
variation. Hence he concluded that diamond “is
an unctuous substance coagulated,”—a sagacious
prediction, which has been verified in the discoveries
of modern chymistry. The connexion between a
high degree of inflammability and a great refracting
force has been still more strongly established by the
high refractive power which I detected in phosphorus,
and which was discovered in hydrogen by MM.
Biot and Arago.
There is no part of the optical labours of Newton
which is less satisfactory than that which relates to
the double refraction of light. In 1690, Huygens,
published his admirable treatise on light, in which
he has given the law of double refraction in calcareous
spar, as deduced from his theory of light, and
as confirmed by direct experiment. Viewing it
probably as a theoretical deduction, Newton seems
to have regarded it as incorrect, and though he has
given Huygens the credit of describing the phenomena
more exactly than Bartholinus, yet, without
assigning any reason, he rejected the law of the
Dutch philosopher, and substituted another in its
place. These observations of our author form the
subject of the twenty-fifth and twenty-sixth queries at
the end of his Optics, which was published fourteen
years after the appearance of Huygens’s work. The
law adopted by Newton is not accompanied with any
of the experiments from which it was deduced; and
though he has given it without expressing any doubt
of its accuracy, it is, nevertheless, entirely incompatible
with observation, and has been rejected by
all succeeding philosophers.
In his speculations respecting the successive disappearance
and reappearance of two of the four
images which are formed when a luminous object
is viewed through two rhombs of calcareous spar,
one of which is made to revolve upon the other,
Newton has been more successful. He concluded
from these phenomena that every ray of light has
two opposite sides originally endued with the property
on which the unusual refraction depends, and
other two opposite sides not endued with that property;
and he suggested it as a subject for future
inquiry, whether there are not more properties of
light by which the sides of the rays differ, and are
distinguished from one another. This is the first
occasion on which the idea of a polarity in the rays
of light has been suggested.32
From the various optical inquiries in which Newton
was engaged, he was strongly impressed with
the belief that light consists of small material particles
emitted from shining substances, and that
these particles could be again recombined into solid
matter, so that “gross bodies and light were convertible
into one another.” He conceived also that
the particles of solid bodies and of light exerted a
mutual action upon each other, the former being
agitated and heated by the latter, and the latter
being attracted and repelled by the former, with
forces depending on the inertia of the luminous particles.
These forces he regarded as insensible at
all measurable distances, and he conceived that the
distances between the particles of bodies were very
small when compared with the extent of their sphere
of attraction and repulsion.
With the exception of Hooke, Huygens, and
Euler, almost all the contemporaries and successors
of Newton maintained the doctrine of the materiality
of light. It was first successfully assailed by
Dr. Thomas Young, and since that time it has been
shaken to its foundation by those great discoveries
which have illustrated the commencement of the
present century. The undulatory theory, which has
thus triumphed in its turn, is still subject to grave
difficulties, and we fear another century must elapse
before a final decision can be pronounced on this
long-agitated question.
The most important of the optical discoveries of
Newton, of which we have given a general history,
were communicated to the Royal Society in detached
papers; but the disputes in which they had
involved their author made him hesitate about the
publication of his other discoveries. Although he
had drawn up a connected view of his labours under
the title of “Opticks, or a Treatise on the Reflexions,
Refractions, Inflexions, and Colours of Light,”
yet he resolved not to publish this work during the
life of Hooke, by whose rival jealousy his tranquillity
had been so frequently interrupted. Hooke, however,
died in 1702, and the Optics of Newton appeared
in English in 1704. Dr. Samuel Clark proposed
a Latin edition of it, which appeared in 1706,
and he was generously presented by Sir Isaac with
500l. (or 100l. for each of his five children), as a
token of the approbation and gratitude of the author.
Both the English and the Latin editions have been
frequently reprinted both in England and on the
Continent,33 and there perhaps never was a work of
profound science so widely circulated.
Astronomical Discoveries of Newton—Necessity of combined Exertion
to the Completion of great Discoveries—Sketch of the History of Astronomy
previous to the Time of Newton—Copernicus, 1473–1543—Tycho
Brahe, 1546–1601—Kepler, 1571–1631—Galileo, 1564–1642.
From the optical labours of Newton we now proceed
to the history of his astronomical discoveries—those
transcendent deductions of human reason
by which he has secured to himself an immortal
name, and vindicated the intellectual dignity of his
species. Pre-eminent as his triumphs have been, it
would be unjust to affirm that they were achieved
by his single arm. The torch of many a preceding
age had thrown its light into the strongholds of
the material universe, and the grasp of many a powerful
hand had pulled down the most impregnable of
its defences. An alliance, indeed, of many kindred
spirits had been long struggling in this great cause,
and Newton was but the leader of their mighty
phalanx,—the director of their combined genius,—the
general who won the victory, and therefore
wears its laurels.
The history of science presents us with no example
of an individual mind throwing itself far in
advance of its contemporaries. It is only in the
career of crime and ambition that reckless man
takes the start of his species, and, uncurbed by
moral and religious restraint, erects an unholy dynasty
upon the ruins of ancient and venerable institutions.
The achievements of intellectual power,
though often begun by one mind and completed by
another, have ever been the results of combined exertions.
Slow in their growth, they gradually approximate
to a more perfect condition:—the variety
in the phenomena of nature call forth a variety of
intellectual gifts;—the powers of analysis and combination
are applied to the humbler labours of observation
and experiment, and in the ordeal of rival
inquiry truth is finally purified from error. How
different is it with those systems which the imagination
rears,—those theories of wild import which
are directed against the consciences and hopes of
man. The fatal upas-tree distils its poison in the
spring as well as the autumn of its growth, but the
fruit which sustains life must have its bud prepared
before the approach of winter, its blossom expanded
in the spring, and its juices elaborated by the light
and heat of the summer and the autumnal sun.
In the century which preceded the birth of Newton
the science of astronomy advanced with the
most rapid steps. Emerging from the darkness of
the middle ages, the human mind seemed to rejoice
in its new-born strength, and to apply itself with
elastic vigour to unfold the mechanism of the heavens.
The labours of Hipparchus and Ptolemy had indeed
furnished many important epochs and supplied many
valuable data; but the cumbrous appendages of
cycles and epicycles with which they explained the
stations and retrogradations of the planets, and the
vulgar prejudices which a false interpretation of
Scripture had excited against a belief in the motion
of the earth, rendered it difficult even for great
minds to escape from the trammels of authority,
and appeal to the simplicity of nature.
The sovereign of Castile, the generous and noble-minded
Alphonso, had long before proscribed the
rude expedients of his predecessors; and when he
declared that if the heavens were thus constituted,
he could have given the Deity good advice, he must
not only have felt the absurdity of the prevailing
system, but must have obtained some foresight of a
more simple arrangement. But neither he nor the
astronomers whom he so liberally protected seem to
have established a better system, and it was left
to Copernicus to enjoy the dignity of being the
restorer of astronomy.
This great man, a native of Thorn in Prussia, following
his father’s profession, began his career as a
doctor of medicine, but an accidental attendance on
the mathematical lectures of Brudzevius excited a
love for astronomy, which became the leading passion
of his life. Quitting a profession uncongenial
to such pursuits, he went to Bologna to study
astronomy under Dominic Maria; and after having
enjoyed the friendship and instruction of that able
philosopher, he established himself at Rome in the
humble situation of a teacher of mathematics. Here
he made numerous astronomical observations which
served him as the basis of future researches; but
an event soon occurred which, though it interrupted
for a while his important studies, placed him in a
situation for pursuing them with new zeal. The
death of one of the canons enabled his uncle, who
was Bishop of Ermeland, to appoint him to a canonry
in the chapter of Frauenburg, where, in a
house situated on the brow of a mountain, he continued,
in peaceful seclusion, to carry on his astronomical
observations. During his residence at Rome
his talents had been so well appreciated, that the
Bishop of Fossombrona, who presided over the
council for reforming the calendar, solicited the aid
of Copernicus in this desirable undertaking. At first
he entered warmly into the views of the council,
and charged himself with the determination of the
length of the year and of the month, and of the
other motions of the sun and moon that seemed to
be required; but he found the task too irksome, and
probably felt that it would interfere with those
interesting discoveries which had already begun to
dawn upon his mind.
Copernicus is said to have commenced his inquiries
by an historical examination of the opinions of
ancient authors on the system of the universe; but
it is more likely that he sought for the authority of
their great names to countenance his peculiar views,
and that he was more desirous to present his own
theory as one that he had received, rather than as
one which he had invented. His mind had been
long imbued with the idea that simplicity and harmony
should characterize the arrangements of the
planetary system, and, in the complication and disorder
which reigned in the hypothesis of Ptolemy,
he saw insuperable objections to its being regarded
as a representation of nature. In the opinions of
the Egyptian sages, in those of Pythagoras, Philolaus,
Aristarchus, and Nicetas, he recognised his
own earliest conviction that the earth was not the
centre of the universe; but he appears to have considered
it as still possible that our globe might perform
some function in the system more important
than that of the other planets; and his attention
was much occupied with the speculation of Martianus
Capella, who placed the sun between Mars and
the moon, and made Mercury and Venus revolve
round him as a centre; and with the system of
Apollonius Pergæus, who made all the planets revolve
round the sun, while the sun and moon were
carried round the earth in the centre of the universe.
The examination, however, of these hypotheses
gradually dispelled the difficulties with which the
subject was beset; and after the labours of more
than thirty years, he was permitted to see the true
system of the heavens. The sun he considered as
immoveable in the centre of the system, while the
earth revolved between the orbits of Venus and
Mars, and produced by its rotation about its axis all
the diurnal phenomena of the celestial sphere. The
precession of the equinoxes was thus referred to a
slight motion of the earth’s axis, and the stations
and retrogradations of the planets were the necessary
consequence of their own motions combined
with that of the earth about the sun. These remarkable
views were supported by numerous astronomical
observations; and in 1530 Copernicus
brought to a close his immortal work on the Revolutions
of the Heavenly Bodies.
But while we admire the genius which triumphed
over so many difficulties, we cannot fail to commend
the extraordinary prudence with which he ushered
his new system into the world. Aware of the prejudices,
and even of the hostility with which such a
system would be received, he resolved neither to
startle the one nor provoke the other. He allowed
his opinions to circulate in the slow current of personal
communication. The points of opposition
which they presented to established doctrines were
gradually worn down, and they insinuated themselves
into reception among the ecclesiastical circles
by the very reluctance of their author to bring them
into notice. In the year 1534, Cardinal Schonberg,
Bishop of Capua, and Gyse, Bishop of Culm, exerted
all their influence to induce Copernicus to lay his
system before the world; but he resisted their solicitations;
and it was not till 1539 that an accidental
circumstance contributed to alter his resolution.
George Rheticus, professor of mathematics at Wirtemberg,
having heard of the labours of Copernicus,
resigned his chair, and repaired to Frauenberg to
make himself master of his discoveries. This zealous
disciple prevailed upon his master to permit the
publication of his system; and they seem to have
arranged a plan for giving it to the world without
alarming the vigilance of the church, or startling
the prejudices of individuals. Under the disguise
of a student of mathematics, Rheticus published in
1540 an account of the manuscript volume of Copernicus.
This pamphlet was received without any
disapprobation, and its author was encouraged to
reprint it at Basle, in 1541, with his own name.
The success of these publications, and the flattering
manner in which the new astronomy was received
by several able writers, induced Copernicus to place
his MSS. in the hands of Rheticus. It was accordingly
printed at the expense of Cardinal Schonberg,
and appeared at Nuremberg in 1543. Its illustrious
author, however, did not live to peruse it.
A complete copy was handed to him in his last
moments, and he saw and touched it a few hours
before his death. This great work was dedicated
to the Holy Pontiff, in order, as Copernicus himself
says, that the authority of the head of the church
might silence the calumnies of individuals who had
attacked his views by arguments drawn from religion.
Thus introduced, the Copernican system met
with no ecclesiastical opposition, and gradually made
its way in spite of the ignorance and prejudices
of the age.
Among the astronomers who provided the materials
of the Newtonian philosophy the name of
Tycho Brahe merits a conspicuous place. Descended
from an ancient Swedish family, he was
born at Knudstorp, in Norway, in 1546, three years
after the death of Copernicus. The great eclipse
of the sun which happened on the 26th August,
1560, while he was at the University of Copenhagen,
attracted his notice: and when he found that all
its phenomena had been accurately predicted, he
was seized with the most irresistible passion to acquire
the knowledge of a science so infallible in its
results. Destined for the profession of the law, his
friends discouraged the pursuit which now engrossed
his thoughts; and such were the reproaches and
even persecutions to which he was exposed, that he
quitted his country with the design of travelling
through Germany. At the very commencement of
his journey, however, an event occurred in which
the impetuosity of his temper had nearly cost him
his life. At a wedding-feast in Rostock, a questionable
point in geometry involved him in a dispute
with a Danish nobleman of the same temperament
with himself; and the two mathematicians resolved
to settle the difference by the sword. Tycho,
however, seems to have been second in the conflict,
for he lost the greater part of his nose, and was
obliged to supply its place by a substitute of gold
and silver, which a cement of glue attached to his
face. During his stay at Augsburg he inspired the
burgomaster of the city, Peter Hainzell, with a love
of astronomy. This public-spirited citizen erected
an excellent observatory at his own expense, and
here Tycho began that distinguished career which
has placed him in the first rank of practical astronomers.
Upon his return to Copenhagen in 1570, he was
received with every mark of respect. The king invited
him to court, and persons of all ranks harassed
him with their attentions. At Herritzvold, near his
native place, the house of his maternal uncle afforded
him a retreat from the gayeties of the capital, and
he was there offered every accommodation for the
prosecution of his astronomical studies. Here,
however, the passion of love and the pursuits of
alchymy distracted his thoughts; but though the
peasant girl of whom he was enamoured was of
easier attainment than the philosopher’s stone, the
marriage produced an open quarrel with his relations,
which it required the interference of the king to allay.
In the tranquillity of domestic happiness, Tycho resumed
his study of the heavens, and in 1572 he
enjoyed the singular good fortune of observing,
through all its variations, the new star in Cassiopeia,
which appeared with such extraordinary splendour
as to be visible in the daytime, and which gradually
disappeared in the following year.
Dissatisfied with his residence in Denmark, Tycho
resolved to settle in some distant country; and having
gone as far as Venice in search of a suitable
residence, he at last fixed upon Basle, in Switzerland.
The King of Denmark, however, had learned
his intention from the Prince of Hesse; and when
Tycho returned to Copenhagen to remove his family
and his instruments, his sovereign announced to him
his resolution to detain him in his kingdom. He
presented him with the canonry of Roschild, with
an income of 2000 crowns per annum. To this he
added a pension of 1000 crowns; and he promised
to give him the island of Huen, with a complete
observatory erected under his own eye. This generous
offer was instantly accepted. The celebrated
observatory of Uraniburg was established at the
expense of about 20,000l.; and in this magnificent
retreat Tycho continued for twenty-one years to enrich
astronomy with the most valuable observations.
Admiring disciples crowded to this sanctuary of the
sciences to acquire the knowledge of the heavens;
and kings34 and princes felt themselves honoured
by becoming the guests of the great astronomer of
the age.
One of the principal discoveries of Tycho was
that of the inequality of the moon’s motion, called
the variation. He detected, also, the annual equation
which affects the place of her apogee and nodes,
and he determined the greatest and the least inclination
of the lunar orbit. His observations on the
planets were numerous and precise, and have formed
the data of the present generalizations in astronomy.
Though thus skilful in the observation of phenomena,
his mind was but little suited to investigate their
cause, and it was probably owing to this defect that
he rejected the system of Copernicus. The vanity
of giving his own name to another system was not
likely to actuate a mind such as his, and it was more
probable that he was led to adopt the immobility of
the earth, and to make the sun, with all his attendant
planets, circulate round it, from the great difficulty
which still presented itself by comparing the apparent
diameter of the stars with the annual parallax of the
earth’s orbit.
The death of Frederick in 1588 proved a severe
calamity to Tycho, and to the science which he cultivated.
During the first years of the minority of
Christian IV. the regency continued the royal patronage
to the observatory of Uraniburg; and in 1592
the young king paid a visit of some days to Tycho,
and left him a gold chain in token of his favour.
The astronomer, however, had made himself enemies
at court, and the envy of his high reputation had
probably added fresh malignity to the irritation of
personal feelings. Under the ministry of Wolchendorf,
a name for ever odious to science, Tycho’s
pension was stopped;—he was in 1597 deprived of
the canonry of Roschild, and was thus forced, with
his wife and children, to seek an asylum in a foreign
land. His friend, Henry Rantzau, of Wansbeck,
under whose roof he found a hospitable shelter, was
fortunately acquainted with the emperor Rodolph II.,
who, to his love of science, added a passion for
alchymy and astrology. The reputation of Tycho
having already reached the imperial ear, the recommendation
of Rantzau was scarcely necessary to ensure
him his warmest friendship. Invited by the emperor,
he repaired in 1599 to Prague, where he met
with the kindest reception. A pension of three
thousand crowns was immediately settled upon him,
and a commodious observatory erected for his use
in the vicinity of that city. Here the exiled astronomer
renewed with delight his interrupted labours,
and the gratitude which he cherished for the royal
favour increased the satisfaction which he felt in
having so unexpectedly found a resting-place for
approaching age. These prospects of better days
were enhanced by the good fortune of receiving two
such men as Kepler and Longomontanus for his
pupils; but the fallacy of human anticipation was
here, as in so many other cases, strikingly displayed.
Tycho was not aware of the inroads which both his
labours and his disappointments had made upon his
constitution. Though surrounded with affectionate
friends and admiring disciples, he was still an exile
in a foreign land. Though his country had been
base in its ingratitude, it was yet the land which he
loved,—the scene of his earliest affection,—the
theatre of his scientific glory. These feelings continually
preyed upon his mind, and his unsettled
spirit was ever hovering among his native mountains.
In this condition he was attacked with a disease of
the most painful kind, and though the paroxysms of
its agonies had lengthened intermissions, yet he saw
that death was approaching. He implored his pupils
to persevere in their scientific labours. He conversed
with Kepler on some of the profoundest points of
astronomy, and with these secular occupations he
mingled frequent acts of piety and devotion. In
this happy condition he expired without pain at the
age of fifty-five, the unquestionable victim of the
councils of Christian IV.
Notwithstanding the accessions which astronomy
had received from the labours of Copernicus and
Tycho, no progress was yet made in developing
the general laws of the system, and scarcely an idea
had been formed of the power by which the planets
were retained in their orbits. The labours of assiduous
observers had supplied the materials for this
purpose, and Kepler arose to lay the foundations of
physical astronomy.
John Kepler was born at Wiel, in Wirtemberg, in
1571. He was educated for the church, and discharged
even some of the clerical functions; but his
devotion to science withdrew him from the study of
theology. Having received mathematical instruction
from the celebrated Mæstlinus, he had made
such progress in the science, that he was invited in
1594 to fill the mathematical chair of Gratz in Styria.
Endowed with a fertile imagination, his mind
was ever intent upon subtle and ingenious speculations.
In the year 1596 he published his peculiar
views in a work on the Harmonies and Analogies of
Nature. In this singular production, he attempts to
solve what he calls the great cosmographical mystery
of the admirable proportion of the planetary
orbits; and by means of the six regular geometrical
solids,35 he endeavours to assign a reason why there
are six planets, and why the dimensions of their
orbits and the time of their periodical revolutions
were such as Copernicus had found them. If a
cube, for example, were inserted in a sphere, of which
Saturn’s orbit was one of the great circles, it would,
he supposed, touch by its six planes the lesser
sphere of Jupiter; and, in like manner, he proposes
to determine, by the aid of the other geometrical
solids, the magnitude of the spheres of the other
planets. A copy of this work was presented by its
author to Tycho Brahe, who had been too long
versed in the severe realities of observation to attach
any value to such wild theories. He advised
his young friend “first to lay a solid foundation for
his views by actual observation, and then, by ascending
from these, to strive to reach the causes of
things;” and there is reason to think that, by the aid
of the whole Baconian philosophy, thus compressed
by anticipation into a single sentence, he abandoned
for a while his visionary inquiries.
In the year 1598 Kepler suffered persecution for
his religious principles, and was compelled to quit
Gratz; but though he was recalled by the States of
Styria, he felt his situation insecure, and accepted of
a pressing invitation from Tycho to settle at Prague,
and assist him in his calculations. Having arrived
in Bohemia in 1600, he was introduced by his friends
to the Emperor Rodolph, from whom he ever afterward
received the kindest attention. On the death
of Tycho in 1601, he was appointed mathematician
to the emperor,—a situation in which he was continued
during the successive reigns of Matthias and
Ferdinand; but what was of more importance to
science, he was put in possession of the valuable
collection of Tycho’s observations. These observations
were remarkably numerous; and as the orbit
of Mars was more oval than that of any of the other
planets, they were peculiarly suitable for determining
its real form. The notions of harmony and
symmetry in the construction of the solar system,
which had filled the mind of Kepler, necessarily led
him to believe that the planets revolved with a uniform
motion in circular orbits. So firm, indeed, was
this conviction, that he made numerous attempts to
represent the observations of Tycho by this hypothesis.
The deviations were too great to be ascribed
to errors of observation; and in trying various
other curves, he was led to the discovery that Mars
revolved round the sun in an elliptical orbit, in one
of the foci of which the sun itself was placed. The
same observations enabled him to determine the
dimensions of the planet’s orbit, and by comparing
together the times in which Mars passed over
different portions of its orbit, he found that they
were to one another as the areas described by the
lines drawn from the centre of the planet to the
centre of the sun, or, in more technical terms, that
the radius vector describes equal areas in equal
times. These two remarkable discoveries, the first
that were ever made in physical astronomy, were
extended to all the other planets of the system, and
were communicated to the world in 1609, in his
“Commentaries on the Motions of the Planet Mars,
as deduced from the observations of Tycho Brahe.”
Although our author was conducted to these great
laws by the patient examination of well-established
facts, his imagination was ever hurrying him among
the wilds of conjecture. Convinced that the mean
distances of the planets from the sun bore to one
another some mysterious relation, he not only compared
them with the regular geometrical solids, but
also with the intervals of musical tones; an idea
which the ancient Pythagoreans had suggested, and
which had been adopted by Archimedes himself.
All these comparisons were fruitless; and Kepler
was about to abandon an inquiry of about seventeen
years’ duration, when, on the 8th March, 1618, he
conceived the idea of comparing the powers of the
different members which express the planetary distances,
in place of the numbers themselves. He
compared the squares and the cubes of the distances
with the same powers of the periodic times; nay, he
tried even the squares of the times with the cubes
of the distances; but his hurry and impatience led
him into an error of calculation, and he rejected this
law as having no existence in nature! On the 15th
May, his mind again reverted to the same notion,
and upon making the calculations anew, and free from
error, he discovered the great law, that the squares
of the periodic times of any two planets are to one
another as the cubes of their distances from the sun.
Enchanted with this unexpected result, he could
scarcely trust his calculations; and, to use his own
language, he at first believed that he was dreaming,
and had taken for granted the very truth of which
he was in search. This brilliant discovery was published
in 1619, in his “Harmony of the World;” a
work dedicated to James VI. of Scotland. Thus
were established what have been called the three
laws of Kepler,—the motion of the planets in elliptical
orbits,—the proportionality between the areas
described and their times of description,—and the
relations between the squares of the periodic times
and the cubes of the distances.
The relation of the movements of the planets to
the sun, as the general centre of all their orbits,
could not fail to suggest to Kepler that some power
resided in that luminary by which these various motions
were produced; and he went so far as to conjecture
that this power diminishes as the square of
the distance of the body on which it was exerted;
but he immediately rejects this law, and prefers that
of the simple distances. In his work on Mars, he
speaks of gravity as a mutual and corporeal affection
between similar bodies. He maintained that
the tides were occasioned by the moon’s attraction,
and that the irregularities of the lunar motions, as
detected by Tycho, were owing to the joint actions
of the sun and the earth; but the relation between
gravity, as exhibited on the earth’s surface, and as
conducting the planets in their orbits, required
more patience of thought than he could command,
and was accordingly left for the exercise of higher
powers.
The misery in which Kepler lived forms a painful
contrast with the services which he performed to
science. The pension on which he subsisted was
always in arrears, and though the three emperors
whose reigns he adorned directed their ministers
to be more punctual in its payment, the disobedience
of their commands was a source of continued
vexation to Kepler. When he retired to Sagan, in
Silesia, to spend in retirement the remainder of his
days, his pecuniary difficulties became still more
harassing. Necessity at last compelled him to apply
personally for the arrears which were due; and he
accordingly set out in 1630 for Ratisbon; but in
consequence of the great fatigue which so long a
journey on horseback produced, he was seized with
a fever, which carried him off on the 30th November,
1630, in the 59th year of his age.
While Kepler was thus laying the foundation of
physical astronomy, Galileo was busily employed in
extending the boundaries of the solar system. This
distinguished philosopher was born at Pisa in 1564.
He was the son of a Florentine nobleman, and was
educated for the medical profession; but a passion
for geometry took possession of his mind, and called
forth all his powers. Without the aid of a master,
he studied the writings of Euclid and of Archimedes;
and such were his acquirements, that he was appointed
by the Grand-duke of Tuscany to the mathematical
chair of Pisa in the twenty-fifth year of his
age. His opposition to the Aristotelian philosophy
gained him many enemies, and at the end of three
years he quitted Pisa, and accepted of an invitation
to the professorship of mathematics at Padua. Here
he continued for eighteen years adorning the university
by his name, and diffusing around him a
taste for the physical sciences. With the exception
of some contrivances of inferior importance,
Galileo had distinguished himself by no discovery
till he had reached the forty-fifth year of his age.
In the year 1609, the same year in which Kepler
published his celebrated commentary on Mars, Galileo
paid a visit to Venice, where he heard, in the
course of conversation, that a Dutchman of the
name of Jansens had constructed and presented to
Prince Maurice an instrument through which he saw
distant objects magnified and rendered more distinct,
as if they had been brought nearer to the observer.
This report was credited by some and disbelieved
by others; but, in the course of a few days, Galileo
received a letter from James Badovere at Paris,
which placed beyond a doubt the existence of such
an instrument. The idea instantly filled his mind
as one of the utmost importance to science; and so
thoroughly was he acquainted with the properties
of lenses, that he not only discovered the principle
of its construction, but was able to complete a telescope
for his own use. Into one end of a leaden
tube he fitted a spectacle-glass plane on one side
and convex on the other, and in the other end he
placed another spectacle-glass concave on one side
and plane on the other. He then applied his eye
to the concave glass, and saw objects “pretty large
and pretty near him.” They appeared three times
nearer, and nine times larger in surface, than to the
naked eye. He soon after made another, which
represented objects above sixty times larger; and,
sparing neither labour nor expense, he finally constructed
an instrument so excellent, as “to show
things almost a thousand times larger, and above
thirty times nearer to the naked eye.”
There is, perhaps, no invention that science has
presented to man so extraordinary in its nature, and
so boundless in its influence, as that of the telescope.
To the uninstructed mind, the power of
seeing an object a thousand miles distant, as large
and nearly as distinct as if it were brought within
a mile of the observer, must seem almost miraculous;
and to the philosopher, even, who thoroughly
comprehends the principles upon which it acts, it
must ever appear one of the most elegant applications
of science. To have been the first astronomer
in whose hands such a gift was placed was a preference
to which Galileo owed much of his future
reputation.
No sooner had he completed his telescope than
he applied it to the heavens, and on the 7th January,
1618, the first day of its use, he saw round
Jupiter three bright little stars lying in a line parallel
to the ecliptic, two to the east, and one to the
west of the planet. Regarding them as ordinary
stars, he never thought of estimating their distances.
On the following day, when he accidentally directed
his telescope to Jupiter, he was surprised to see
the three stars to the west of the planet. To produce
this effect it was requisite that the motion of
Jupiter should be direct, though, according to calculation,
it was actually retrograde. In this dilemma
he waited with impatience for the evening of the
9th, but unfortunately the sky was covered with
clouds. On the 10th he saw only two stars to the
east—a circumstance which he was no longer able
to explain by the motion of Jupiter. He was therefore
compelled to ascribe the change to the stars
themselves; and upon repeating his observations
on the 11th, he no longer doubted that he had discovered
three planets revolving round Jupiter. On
the 13th January he for the first time saw the
fourth satellite.36
This discovery, though of the utmost importance
in itself, derived an additional value from the light
which it threw on the true system of the universe.
While the earth was the only planet enlightened
by a moon, it might naturally be supposed that it
alone was habitable, and was therefore entitled to
the pre-eminence of occupying the centre of the
system; but the discovery of four moons round a
much larger planet deprived this argument of its
force, and created a new analogy between the earth
and the other planets. When Kepler received the
“Sidereal Messenger,” the work in which Galileo
announced his discovery in 1610, he perused it with
the deepest interest; and while it confirmed and
extended his substantial discoveries, it dispelled at
the same time some of those harmonic dreams which
still hovered among his thoughts. In the “Dissertation”
which he published on the discovery of
Galileo, he expresses his hope that satellites will
be discovered round Saturn and Mars,—he conjectures
that Jupiter has a motion of rotation about
his axis,—and states his surprise, that, after what
had been written on the subject of telescopes by
Baptista Porta, they had not been earlier introduced
into observatories.
In continuing his observations, Galileo applied
his telescope to Venus, and in 1610 he discovered
the phases of that planet, which exhibited to him
the various forms of the waxing and the waning
moon. This fact established beyond a doubt that
the planet revolved round the sun, and thus gave
an additional blow to the Ptolemaic system. In his
observations on the sun, Galileo discovered his spots,
and deduced from them the rotation of the central
luminary. He observed that the body of Saturn
had handles attached to it; but he was unable to
detect the form of its ring, or render visible its
minute satellites. On the surface of the moon he
discovered her mountains and valleys, and determined
the curious fact of her libration, in virtue of
which parts of the margin of her disk occasionally
appear and disappear. In the Milky Way he descried
numerous minute stars which the unassisted
eye was unable to perceive; and as the largest fixed
stars, in place of being magnified by the telescope,
became actually minute brilliant points, he inferred
their immense distance as rendered necessary by the
Copernican hypothesis. All his discoveries, indeed,
furnished fresh arguments in favour of the new
system; and the order of the planets and their relation
to a central sun may now be considered as
established by incontrovertible evidence.
While Galileo was occupied with these noble pursuits
at Pisa, to which he had been recalled in 1611,
his generous patron, Cosmo II. Grand-duke of Tuscany,
invited him to Florence, that he might pursue
with uninterrupted leisure his astronomical observations,
and carry on his correspondence with the
German astronomers. His fame had now resounded
through all Europe;—the strongholds of prejudice
and ignorance were unbarred;—and the most obstinate
adherents of ancient systems acknowledged
the meridian power of the day-star of science.
Galileo was ambitious of propagating the great
truths which he contributed so powerfully to establish.
He never doubted that they would received
with gratitude by all,—by the philosopher as
the consummation of the greatest efforts of human
genius,—and by the Christian as the most transcendent
displays of Almighty power. But he had mistaken
the disposition of his species, and the character
of the age. That same system of the heavens
which had been discovered by the humble ecclesiastic
of Frauenberg, which had been patronised by
the kindness of a bishop, and published at the expense
of a cardinal, and which the pope himself
had sanctioned by the warmest reception, was, after
the lapse of a hundred years, doomed to the most
violent opposition, as subversive of the doctrines
of the Christian faith. On no former occasion has
the human mind exhibited such a fatal relapse into
intolerance. The age itself had improved in liberality;—the
persecuted doctrines themselves had
become more deserving of reception;—the light of
the Reformed faith had driven the Catholics from
some of their most obnoxious positions;—and yet,
under all these circumstances, the church of Rome
unfurled her banner of persecution against the pride
of Italy, against the ornament of his species, and
against truths immutable and eternal.
In consequence of complaints laid before the Holy
Inquisition, Galileo was summoned to appear at
Rome in 1615, to answer for the heretical opinions
which he had promulgated. He was charged with
“maintaining as true the false doctrine held by
many, that the sun was immoveable in the centre
of the world, and that the earth revolved with a
diurnal motion;—with having certain disciples to
whom he taught the same doctrine;—with keeping
up a correspondence on the subject with several
German mathematicians;—with having published
letters on the solar spots, in which he explained the
same doctrine as true;—and with having glossed
over with a false interpretation the passages of
Scripture which were urged against it.” The consideration
of these charges came before a meeting
of the Inquisition, which assembled on the 25th
February, 1616; and the court, declaring their disposition
to deal gently with the prisoner, pronounced
the following decree:—“That Cardinal
Bellarmine should enjoin Galileo to renounce entirely
the above-recited false opinions; that, on his
refusal to do so, he should be commanded by the
commissary of the Inquisition to abandon the said
doctrine, and to cease to teach and defend it; and
that, if he did not obey this command, he should
be thrown into prison.” On the 26th of February
Galileo appeared before Cardinal Bellarmine, and,
after receiving from him a gentle admonition, he
was commanded by the commissary, in the presence
of a notary and witnesses, to desist altogether from
his erroneous opinions; and it was declared to be
unlawful for him in future to teach them in any
way whatever, either orally or in his writings. To
these commands Galileo promised obedience, and
was dismissed from the Inquisition.
The mildness of this sentence was no doubt partly
owing to the influence of the Grand-duke of Tuscany,
and other persons of rank and influence at the
papal court, who took a deep interest in the issue
of the trial. Dreading, however, that so slight a
punishment might not have the effect of putting
down the obnoxious doctrines, the Inquisition issued
a decree denouncing the new opinions as false and
contrary to the sacred writings, and prohibiting the
sale of every book in which they should be maintained.
Thus liberated from his persecutors, Galileo returned
to Florence, where he pursued his studies
with his wonted diligence and ardour. The recantation
of his astronomical opinions was so formal
and unreserved, that ordinary prudence, if not a
sense of personal honour, should have restrained him
from unnecessarily bringing them before the world.
No anathema was pronounced against his scientific
discoveries; no interdict was laid upon the free
exercise of his genius. He was prohibited merely
from teaching a doctrine which the church of Rome
considered to be injurious to its faith. We might
have expected, therefore, that a philosopher so conspicuous
in the eyes of the world would have respected
the prejudices, however base, of an institution
whose decrees formed part of the law of the
land, and which possessed the power of life and
death within the limits of its jurisdiction. Galileo,
however, thought otherwise. A sense of degradation37
seems to have urged him to retaliate, and before
six years had elapsed, he began to compose his
“Cosmical System, or Dialogues on the two greatest
Systems of the World, the Ptolemean and the Copernican,”
the concealed object of which is to
establish the opinions which he had promised to
abandon. In this work the subject is discussed by
three speakers, Sagredo, Salviatus, and Simplicius,
a peripatetic philosopher, who defends the system of
Ptolemy with much skill against the overwhelming
arguments of the rival disputants. Galileo hoped to
escape notice by this indirect mode of propagating
the new system, and he obtained permission to publish
his work, which appeared at Florence in 1632.
The Inquisition did not, as might have been expected,
immediately summon Galileo to their presence.
Nearly a year elapsed before they gave any
indication of their design; and, according to their
own statement, they did not even take the subject
under consideration till they saw that the obnoxious
tenets were every day gaining ground, in consequence
of the publication of the Dialogues. They
then submitted the work to a careful examination,
and having found it to be a direct violation of the
injunction which had been formerly intimated to its
author, they again cited him before their tribunal in
1633. The venerable sage, now in his seventieth
year, was thus compelled to repair to Rome, and
when he arrived he was committed to the apartments
of the Fiscal of the Inquisition. The unchangeable
friendship, however, of the Grand-duke
of Tuscany obtained a remission of this severity,
and Galileo was allowed to reside at the house of
the Tuscan ambassador during the two months
which the trial occupied. When brought before
the Inquisition, and examined upon oath, he acknowledged
that the Dialogues were written by himself,
and that he obtained permission to publish them
without notifying to the person who gave it that he
had been prohibited from holding, defending, or
teaching the heretical opinions. He confessed also
that the Dialogues were composed in such a manner,
that the arguments in favour of the Copernican system,
though given as partly false, were yet managed
in such a manner that they were more likely to confirm
than overturn its doctrines; but that this error,
which was not intentional, arose from the natural
desire of making an ingenious defence of false propositions,
and of opinions that had the semblance of
probability.
After receiving these confessions and excuses, the
Inquisition allowed Galileo a proper time for giving
in his defence; but this seems to have consisted
solely in bringing forward the certificate of Cardinal
Bellarmine already mentioned, which made no allusion
to the promise under which Galileo had come
never to defend, nor teach in any way whatever, the
Copernican doctrines. The court held this defence
to be an aggravation of the crime rather than an
excuse for it, and proceeded to pronounce a sentence
which will be ever memorable in the history of the
human mind.
Invoking the name of our Saviour, they declare,
that Galileo had made himself liable to the suspicion
of heresy, by believing the doctrine, contrary to
Scripture, that the sun was the centre of the earth’s
orbit, and did not move from east to west; and by
defending as probable the opinion that the earth
moved, and was not the centre of the world; and
that he had thus incurred all the censures and penalties
which were enacted by the church against such
offences;—but that he should be absolved from these
penalties, provided he sincerely abjured and cursed
all the errors and heresies contained in the formula
of the church, which should be submitted to him.
That so grave and pernicious a crime should not
pass altogether unpunished, that he might become
more cautious in future, and might be an example
to others to abstain from such offences, they decreed
that his Dialogues should be prohibited by a formal
edict,—that he should be condemned to the prison
of the Inquisition during pleasure,—and that, during
the three following years, he should recite once a
week the seven penitential psalms.
This sentence was subscribed by seven cardinals;
and on the 22d June, 1633, Galileo signed an abjuration
humiliating to himself and degrading to philosophy.
At the age of seventy, on his bended knees,
and with his right hand resting on the Holy Evangelists,
did this patriarch of science avow his present
and his past belief in all the dogmas of the Romish
Church, abandon as false and heretical the doctrine
of the earth’s motion and of the sun’s immobility,
and pledge himself to denounce to the Inquisition
any other person who was even suspected of heresy.
He abjured, cursed, and detested those eternal and
immutable truths which the Almighty had permitted
him to be the first to establish. What a mortifying
picture of moral depravity and intellectual weakness!
If the unholy zeal of the assembly of cardinals has
been branded with infamy, what must we think of
the venerable sage whose gray hairs were entwined
with the chaplet of immortality, quailing under the
fear of man, and sacrificing the convictions of his
conscience and the deductions of his reason at the
altar of a base superstition? Had Galileo but added
the courage of the martyr to the wisdom of the
sage,—had he carried the glance of his indignant
eye round the circle of his judges,—had he lifted
his hands to heaven, and called the living God to
witness the truth and immutability of his opinions,
the bigotry of his enemies would have been disarmed,
and science would have enjoyed a memorable
triumph.
The great truths of the Copernican system, instead
of being considered as heretical, had been actually
adopted by many pious members of the Catholic
church, and even some of its dignitaries did not
scruple to defend it openly. Previous to the first
persecution of Galileo in 1615, a Neapolitan nobleman,
Vincenzio Caraffa, a person equally distinguished
by his piety and birth, had solicited Paul
Anthony Foscarinus, a learned Carmelite monk, to
illustrate and defend the new system of the universe.
With this request the ecclesiastic speedily complied;
and in the pamphlet which he completed on the 6th
January, 1615, he defends the Copernican system
with much boldness and ingenuity; he reconciles
the various passages of Scripture with the new doctrine,
and he expresses the hope that such an attempt,
now made for the first time, will prove agreeable to
philosophers, but particularly to those very learned
men, Galileo Galilei, John Kepler, and all the members
of the Lyncean Academy, who, he believes,
entertain the same opinion. This remarkable production,
written from the convent of the Carmelites
at Naples, is dedicated to the very Reverend Sebastian
Fantoni, general of the order of Carmelites, and
was published at Florence, with the sanction of the
ecclesiastical authorities, in 1630; three years before
the second persecution of Galileo.
It would be interesting to know the state of public
feeling in Italy when Galileo was doomed to the
prisons of the Inquisition. No appeal seems to have
been made against so cruel a sentence; and neither
in remonstrance nor in derision does an individual
voice seem to have been raised. The master spirits
of the age looked with sullen indifference on the
persecution of exalted genius; and Galileo lay in
chains, deserted and unpitied. This unrebuked triumph
of his enemies was perhaps favourable to the
object of their vengeance. Resistance might have
heightened the rigour of a sentence, which submission
seems to have alleviated. The interference
of some eminent individuals of Rome, among whom
we have no doubt that the Grand-duke of Tuscany
was the most influential, induced Pope Urban VIII.,
not only to shorten the period, but to soften the
rigour of Galileo’s imprisonment. From the dungeon
of the Inquisition, where he had remained only
four days, he was transported to the ambassador’s
palace in the Garden de Medici at Rome; and when
his health had begun to suffer, he was permitted to
leave the metropolis; and would have been allowed
to return to Florence, but as the plague raged in
that city, he was sent, in July, 1633, to the archiepiscopal
palace of Sienna, the residence of the Archbishop
Piccolimini, where he carried on and completed
his valuable investigations respecting the
resistance of solids. Here he continued five months,
when, in consequence of the disappearance of the
plague at Florence, he was allowed to retire to his
villa at Bellosguardo, and afterward to that of Arcetri
in the vicinity of Florence.
Though Galileo was now, to a certain degree,
liberated from the power of man, yet the afflicting
dispensations of Providence began to fall thickly
around him. No sooner had he returned to Arcetri,
than his favourite daughter, Maria, was seized with
a dangerous illness, which soon terminated in her
death. He was himself attacked with hernia, palpitation
of the heart, loss of appetite, and the most
oppressive melancholy; and though he solicited
permission to repair to Florence for medical assistance,
yet this deed of mercy was denied him. In
1638, however, the pope permitted him to pay a visit
to Florence, and his friend, Father Castelli, was
allowed to visit him in the company of an officer of
the Inquisition. But this indulgence was soon withdrawn,
and at the end of a few months he was remanded
to Arcetri. The sight of his right eye had
begun to fail in 1636, from an opacity of the cornea.
In 1637 his left eye was attacked with the same
complaint; so that in a few months he was affected
with total and incurable blindness. Before this calamity
had supervened, he had noticed the curious
phenomenon of the moon’s libration, in consequence
of which, parts of her visible disk that are exposed
to view at one time are withdrawn at another. He
succeeded in explaining two of the causes of this
curious phenomenon, viz. the different distances of
the observer from the line joining the centre of the
earth and the moon, which produces the diurnal
libration, and the unequal motion of the moon in her
orbit, which produces the libration in longitude. It
was left, however, to Hevelius to discover the libration
in latitude, which arises from the inclination of
her axis being a little less than a right angle to the
ecliptic; and to Lagrange to discover the spheroidal
libration, or that which arises from the action of the
earth upon the lunar spheroid.
The sorrows with which Galileo was now beset,
seemed to have disarmed the severity of the Inquisition.
He was freely permitted to enjoy the society
of his friends, who now thronged around him to
express their respect and their sympathy. The
Grand-duke of Tuscany was his frequent visiter,
and Gassendi, Deodati, and our countryman Milton
went to Italy for the purpose of visiting him. He
entertained his friends with the warmest hospitality,
and though simple and abstemious in his diet, yet he
was fond of good wine, and seems even in his last
days to have paid particular attention to the excellence
of his cellar.
Although Galileo had nearly lost his hearing as
well as his sight, yet his intellectual faculties were
unimpaired; and while his mind was occupied in
considering the force of percussion, he was seized
with fever and palpitation of the heart, which, after
two months’ illness, terminated his life on the 8th
of January, 1642.
Among the predecessors of Newton in astronomical
research we must not omit the names of
Bouillaud (Bullialdus), Borelli, and Dr. Hooke.
Ismael Bouillaud, a native of Laon in France, and
the author of several valuable astronomical works,
has derived more reputation from a single sentence
in his Astronomica Philolaica, published in 1645, than
from all the rest of his labours. He was not a believer
in the doctrine of attraction, which, as we
have already seen, had been broached by Copernicus,
and discovered by Kepler; but in speaking of that
power as the cause of the planetary motions, he
remarks, “that if attraction existed, it would decrease
as the square of the distance.” The influence
of gravity was still more distinctly developed
by Borelli, a Neapolitan philosopher, who published
in 1666 a work on Jupiter’s satellites.38 In this work
he maintains, that all the planets perform their motions
round the sun according to a general law; that
the satellites of Jupiter and of Saturn move round
their primary planets in the same manner as the
moon does round the earth, and that they all revolve
round the sun, which is the only source of
any virtue, and that this virtue attaches them, and
unites them so that they cannot recede from their
centre of action.39
Our countryman Dr. Robert Hooke seems to
have devoted much of his attention to the cause of
the planetary motions. On the 21st March, 1666,
he read to the Royal Society an account of a series
of experiments for determining if bodies experience
any variation in their weight at different distances
from the centre of the earth. His experiments, as
Hooke himself saw, were by no means satisfactory,
and hence he was led to the ingenious idea of
measuring the force of gravity by observing, at different
altitudes, the rate of a pendulum clock.
About two months afterward, he exhibited to the
Society an approximate representation of the forces
which retain the planets in their orbits, in the paths
described by a circular pendulum impelled with different
degrees of force; but though this experiment
illustrated the production of a curvilineal motion, by
combining a tangential force with a central power
of attraction, yet it was only an illustration, and
could not lead to the true cause of the planetary motions.
At a later period, however, viz. in 1674,
Hooke resumed the subject in a dissertation entitled
“An Attempt to prove the Motion of the Earth from
Observation,” which contains the following remarkable
observations upon gravity:—
“I shall hereafter explain a system of the world
differing in many particulars from any yet known,
answering in all things to the common rules of mechanical
motions. This depends upon three suppositions:—first,
that all celestial bodies whatsoever
have an attraction or gravitating power towards
their own centres, whereby they attract, not only
their own parts, and keep them from flying from
them, as we may observe the earth to do, but that
they also do attract all the other celestial bodies
that are within the sphere of their activity, and consequently,
that not only the sun and moon have an
influence upon the body and motion of the earth,
and the earth upon them, but that Mercury, Venus,
Mars, Jupiter, and Saturn, also, by their attractive
powers, have a considerable influence upon its motion,
as in the same manner the corresponding attractive
power of the earth hath a considerable influence
upon every one of their motions also. The
second supposition is this, that all bodies whatsoever
that are put into a direct and simple motion
will so continue to move forward in a straight line,
till they are, by some other effectual powers, deflected,
and sent into a motion describing a circle,
ellipsis, or some other more compounded curve line.
The third supposition is, that those attractive powers
are so much the more powerful in operating by
how much the nearer the body wrought upon is to their
own centres. Now, what these several degrees are I
have not yet experimentally verified; but it is a notion
which, if fully prosecuted, as it ought to be, will
mightily assist the astronomers to reduce all the
celestial motions to a certain rule, which I doubt
will never be done without it. He that understands
the nature of the circular pendulum and circular
motion will easily understand the whole of this
principle, and will know where to find directions in
nature for the true stating thereof. This I only
hint at present to such as have ability and opportunity
of prosecuting this inquiry, and are not wanting
of industry for observing and calculating, wishing
heartily such may be found, having myself many
other things in hand, which I would first complete,
and therefore cannot so well attend it. But this I
do not promise the undertaker, that he will find all
the great motions of the world to be influenced by
this principle, and that the true understanding
thereof will be the true perfection of astronomy.”
This passage, which has been considered as a remarkable
one by the philosophers of every country,
has, we think, been misapprehended by M. Delambre,
when he asserts that every thing which it contains
“is to be found expressly in Kepler.”40
The first Idea of Gravity occurs to Newton in 1666—His first Speculations
upon it—Interrupted by his Optical Experiments—He resumes
the Subject in consequence of a Discussion with Dr. Hooke—He
discovers the true Law of Gravity and the Cause of the Planetary
Motions—Dr. Halley urges him to publish his Principia—His Principles
of Natural Philosophy—Proceedings of the Royal Society on
this Subject—The Principia appears in 1687—General Account of it,
and of the Discoveries it contains—They meet with great Opposition,
owing to the Prevalence of the Cartesian System—Account of the Reception
and Progress of the Newtonian Philosophy in foreign Countries—Account
of its Progress and Establishment in England.
Such is a brief sketch of the labours and lives of
those illustrious men who prepared the science of
astronomy for the application of Newton’s genius.
Copernicus had determined the arrangement and
general movements of the planetary bodies: Kepler
had proved that they moved in elliptical orbits;
that their radii vectores described arcs proportional
to the times; and that their periodic times were
related to their distances. Galileo had added to the
universe a whole system of secondary planets; and
several astronomers had distinctly referred the motion
of the heavenly bodies to the power of attraction.
In the year 1666, when the plague had driven
Newton from Cambridge, he was sitting alone in
the garden at Woolsthorpe, and reflecting on the
nature of gravity,—that remarkable power which
causes all bodies to descend towards the centre of
the earth. As this power is not found to suffer any
sensible diminution at the greatest distance from
the earth’s centre to which we can reach, being as
powerful at the tops of the highest mountains as at
the bottom of the deepest mines, he conceived it
highly probable, that it must extend much farther
than was usually supposed. No sooner had this
happy conjecture occurred to his mind, than he considered
what would be the effect of its extending as
far as the moon. That her motion must be influenced
by such a power he did not for a moment
doubt; and a little reflection convinced him that it
might be sufficient for retaining that luminary in her
orbit round the earth. Though the force of gravity
suffers no sensible diminution at those small distances
from the earth’s centre at which we can
place ourselves, yet he thought it very possible,
that, at the distance of the moon, it might differ
much in strength from what it is on the earth. In
order to form some estimate of the degree of its
diminution, he considered that, if the moon be retained
in her orbit by the force of gravity, the primary
planets must also be carried round the sun by
the same power; and by comparing the periods of
the different planets with their distances from the
sun, he found, that if they were retained in their
orbits by any power like gravity, its force must decrease
in the duplicate proportion,41 or as the squares
of their distances from the sun. In drawing this
conclusion, he supposed the planets to move in orbits
perfectly circular, and having the sun in their
centre. Having thus obtained the law of the force
by which the planets were drawn to the sun, his
next object was to ascertain if such a force, emanating
from the earth and directed to the moon, was
sufficient, when diminished in the duplicate ratio of
the distance, to retain her in her orbit. In performing
this calculation, it was necessary to compare
the space through which heavy bodies fall in a second
at a given distance from the centre of the earth, viz.
at its surface, with the space through which the
moon, as it were, falls to the earth in a second of
time while revolving in a circular orbit. Being at
a distance from books when he made this computation,
he adopted the common estimate of the earth’s
diameter then in use among geographers and navigators,
and supposed that each degree of latitude
contained sixty English miles. In this way he
found that the force which retains the moon in her
orbit, as deduced from the force which occasions the
fall of heavy bodies to the earth’s surface, was one-sixth
greater than that which is actually observed in
her circular orbit. This difference threw a doubt
upon all his speculations; but, unwilling to abandon
what seemed to be otherwise so plausible, he endeavoured
to account for the difference of the two forces,
by supposing that some other cause42 must have been
united with the force of gravity in producing so
great a velocity of the moon in her circular orbit.
As this new cause, however, was beyond the reach
of observation, he discontinued all further inquiries
into the subject, and concealed from his friends the
speculations in which he had been employed.
After his return to Cambridge in 1666, his attention
was occupied with those optical discoveries of
which we have given an account in a preceding
chapter; but he had no sooner brought them to a
close than his mind reverted to the great subject of
the planetary motions. Upon the death of Oldenburg
in August, 1678, Dr. Hooke was appointed
secretary to the Royal Society; and as this learned
body had requested the opinion of Newton about a
system of physical astronomy, he addressed a letter
to Dr. Hooke on the 28th November, 1679. In this
letter he proposed a direct experiment for verifying
the motion of the earth, viz. by observing whether
or not bodies that fall from a considerable height
descend in a vertical direction, for if the earth were
at rest the body would describe exactly a vertical
line, whereas if it revolved round its axis, the falling
body must deviate from the vertical line towards the
east. The Royal Society attached great value to
the idea thus casually suggested; and Dr. Hooke was
appointed to put it to the test of experiment. Being
thus led to consider the subject more attentively, he
wrote to Newton, that wherever the direction of
gravity was oblique to the axis on which the earth
revolved, that is, in every part of the earth except
the equator, falling bodies should approach
to the equator, and the deviation from the vertical,
in place of being exactly to the east, as
Newton maintained, should be to the south-east of
the point from which the body began to move.
Newton acknowledged that this conclusion was correct
in theory, and Dr. Hooke is said to have given
an experimental demonstration of it before the Royal
Society in December, 1679.43 Newton had erroneously
concluded that the path of the falling body
would be a spiral; but Dr. Hooke, on the same
occasion on which he made the preceding experiment,
read a paper to the Society, in which he proved
that the path of the body would be an eccentric
ellipse in vacuo, and an ellipti-spiral, if the body
moved in a resisting medium.44
This correction of Newton’s error, and the discovery
that a projectile would move in an elliptical
orbit when under the influence of a force varying in
the inverse ratio of the square of the distance, led
Newton, as he himself informs us in his letter to
Halley,45 to discover “the theorem by which he afterward
examined the ellipsis,” and to demonstrate
the celebrated proposition, that a planet acted upon
by an attractive force varying inversely as the
squares of the distances will describe an elliptical
orbit, in one of whose foci the attractive force resides.
But though Newton had thus discovered the true
cause of all the celestial motions, he did not yet
possess any evidence that such a force actually resided
in the sun and planets. The failure of his
former attempt to identify the law of falling bodies
at the earth’s surface with that which guided the
moon in her orbit threw a doubt over all his speculations,
and prevented him from giving any account
of them to the public.
An accident, however, of a very interesting nature
induced him to resume his former inquiries, and
enabled him to bring them to a close. In June,
1682, when he was attending a meeting of the Royal
Society of London, the measurement of a degree of
the meridian, executed by M. Picard in 1679, became
the subject of conversation. Newton took a memorandum
of the result obtained by the French astronomer,
and having deduced from it the diameter of the
earth, he immediately resumed his calculation of
1665, and began to repeat it with these new data.
In the progress of the calculation he saw that the
result which he had formerly expected was likely to
be produced, and he was thrown into such a state of
nervous irritability that he was unable to carry on
the calculation. In this state of mind he intrusted
it to one of his friends, and he had the high satisfaction
of finding his former views amply realized.
The force of gravity which regulated the fall of
bodies at the earth’s surface, when diminished as
the square of the moon’s distance from the earth,
was found to be almost exactly equal to the centrifugal
force of the moon as deduced from her observed
distance and velocity.
The influence of such a result upon such a mind
may be more easily conceived than described. The
whole material universe was spread out before him;—the
sun with all his attending planets;—the planets
with all their satellites;—the comets wheeling in
every direction in their eccentric orbits;—and the
systems of the fixed stars stretching to the remotest
limits of space. All the varied and complicated
movements of the heavens, in short, must have been
at once presented to his mind, as the necessary result
of that law which he had established in reference to
the earth and the moon.
After extending this law to the other bodies of
the system, he composed a series of propositions
on the motion of the primary planets about the sun,
which were sent to London about the end of 1683,
and were soon afterward communicated to the
Royal Society.46
About this period other philosophers had been
occupied with the same subject. Sir Christopher
Wren had many years before endeavoured to explain
the planetary motions “by the composition
of a descent towards the sun, and an impressed
motion; but he at length gave it over, not finding
the means of doing it.” In January, 1683–4, Dr.
Halley had concluded, from Kepler’s Law of the
Periods and Distances, that the centripetal force decreased
in the reciprocal proportion of the squares
of the distances, and having one day met Sir Christopher
Wren and Dr. Hooke, the latter affirmed
that he had demonstrated upon that principle all
the laws of the celestial motions. Dr. Halley confessed
that his attempts were unsuccessful, and
Sir Christopher, in order to encourage the inquiry,
offered to present a book of forty shillings’ value to
either of the two philosophers who should, in the
space of two months, bring him a convincing demonstration
of it. Hooke persisted in the declaration
that he possessed the method, but avowed it
to be his intention to conceal it for some time. He
promised, however, to show it to Sir Christopher;
but there is every reason to believe that this promise
was never fulfilled.
In August, 1684, Dr. Halley went to Cambridge
for the express purpose of consulting Newton on
this interesting subject. Newton assured him that
he had brought this demonstration to perfection,
and promised him a copy of it. This copy was received
in November by the doctor, who made a
second visit to Cambridge, in order to induce its
author to have it inserted in the register book of
the society. On the 10th of December, Dr. Halley
announced to the society, that he had seen at Cambridge
Mr. Newton’s treatise De Motu Corporum,
which he had promised to send to the society to be
entered upon their register; and Dr. Halley was desired
to unite with Mr. Paget, master of the mathematical
school in Christ’s Hospital, in reminding
Mr. Newton of his promise “for securing the invention
to himself till such time as he can be at leisure
to publish it.” On the 25th February Mr. Aston,
the secretary, communicated a letter from Mr.
Newton, in which he expressed his willingness “to
enter in the register his notions about motion, and
his intentions to fit them suddenly for the press.”
The progress of his work was, however, interrupted
by a visit of five or six weeks which he made in
Lincolnshire; but he proceeded with such diligence
on his return, that he was able to transmit the manuscript
to London before the end of April. This
manuscript, entitled Philosophiæ Naturalis Principia
Mathematica, and dedicated to the society, was presented
by Dr. Vincent on the 28th April, 1686, when
Sir John Hoskins, the vice-president, and the particular
friend of Dr. Hooke, was in the chair. Dr.
Vincent passed a just encomium on the novelty and
dignity of the subject; and another member added,
that “Mr. Newton had carried the thing so far, that
there was no more to be added.” To these remarks
the vice-president replied, that the method “was so
much the more to be prized as it was both invented
and perfected at the same time.” Dr. Hooke took
offence at these remarks, and blamed Sir John for
not having mentioned “what he had discovered to
him;” but the vice-president did not seem to recollect
any such communication, and the consequence
of this discussion was, that “these two, who till
then were the most inseparable cronies, have since
scarcely seen one another, and are utterly fallen
out.” After the breaking up of the meeting, the
society adjourned to the coffee-house, where Dr.
Hooke stated that he not only had made the same
discovery, but had given the first hint of it to Newton.
An account of these proceedings was communicated
to Newton through two different channels.
In a letter dated May 22d, Dr. Halley wrote to him
“that Mr. Hooke has some pretensions upon the
invention of the rule of the decrease of gravity being
reciprocally as the squares of the distances from
the centre. He says you had the notion from him,
though he owns the demonstration of the curves
generated thereby to be wholly your own. How
much of this is so you know best, as likewise what
you have to do in this matter. Only Mr. Hooke
seems to expect you would make some mention of
him in the preface, which it is possible you may
see reason to prefix.”
This communication from Dr. Halley induced
our author, on the 20th June, to address a long
letter to him, in which he gives a minute and able
refutation of Hooke’s claims; but before this letter
was despatched, another correspondent, who had
received his information from one of the members
that were present, informed Newton “that Hooke
made a great stir, pretending that he had all from
him, and desiring they would see that he had justice
done him.” This fresh charge seems to have ruffled
the tranquillity of Newton; and he accordingly
added an angry and satirical postscript, in which he
treats Hooke with little ceremony, and goes so far
as to conjecture that Hooke might have acquired
his knowledge of the law from a letter of his own
to Huygens, directed to Oldenburg, and dated January
14th, 1672–3. “My letter to Hugenius was
directed to Mr. Oldenburg, who used to keep the
originals. His papers came into Mr. Hooke’s possession.
Mr. Hooke, knowing my hand, might have
the curiosity to look into that letter, and there take
the notion of comparing the forces of the planets
arising from their circular motion; and so what he
wrote to me afterward about the rate of gravity
might be nothing but the fruit of my own garden.”
In replying to this letter, Dr. Halley assured him
that Hooke’s “manner of claiming the discovery
had been represented to him in worse colours than
it ought, and that he neither made public application
to the society for justice, nor pretended that you
had all from him.” The effect of this assurance
was to make Newton regret that he had written the
angry postscript to his letter; and in replying to
Halley on the 14th July, 1686, he not only expresses
his regret, but recounts the different new ideas
which he had acquired from Hooke’s correspondence,
and suggests it as the best method “of compromising
the present dispute,” to add a scholium,
in which Wren, Hooke, and Halley are acknowledged
to have independently deduced the law of gravity
from the second law of Kepler.47
At the meeting of the 28th April, at which the
manuscript of the Principia was presented to the
Royal Society, it was agreed that the printing of it
should be referred to the council; that a letter of
thanks should be written to its author; and at a
meeting of the council on the 19th May, it was
resolved that the MSS. should be printed at the
society’s expense, and that Dr. Halley should superintend
it while going through the press. These
resolutions were communicated by Dr. Halley in a
letter dated the 22d May; and in Newton’s reply on
the 20th June already mentioned, he makes the following
observations: “The proof you sent me I
like very well. I designed the whole to consist of
three books; the second was finished last summer,
being short, and only wants transcribing, and drawing
the cuts fairly. Some new propositions I have
since thought on, which I can as well let alone.
The third wants the theory of comets. In autumn
last I spent two months in calculation to no purpose
for want of a good method, which made me afterward
return to the first book, and enlarge it with
diverse propositions, some relating to comets, others
to other things found out last winter. The third I
now design to suppress. Philosophy is such an impertinently
litigious lady, that a man had as good be
engaged in lawsuits as have to do with her. I
found it so formerly, and now I can no sooner come
near her again but she gives me warning. The first
two books without the third will not so well bear
the title of Philosophiæ Naturalis Principia Mathematica;
and therefore I had altered it to this, De
Motu Corporum Libri duo. But after second thoughts
I retain the former title. It will help the sale of the
book, which I ought not to diminish now ’tis yours.”
In replying to this letter on the 29th June, Dr.
Halley regrets that our author’s tranquillity should
have been thus disturbed by envious rivals; and
implores him in the name of the society not to
suppress the third book. “I must again beg you,”
says he, “not to let your resentments run so high
as to deprive us of your third book, wherein your
applications of your mathematical doctrine to the
theory of comets, and several curious experiments,
which, as I guess by what you write ought to compose
it, will undoubtedly render it acceptable to
those who will call themselves philosophers without
mathematics, which are much the greater number.”
To these solicitations Newton seems to have
readily yielded. His second book was sent to the
society, and presented on the 2d March, 1686–7.
The third book was also transmitted, and presented
on the 6th April, and the whole work was completed
and published in the month of May, 1687.
Such is a brief account of the publication of a
work which is memorable, not only in the annals of
one science or of one country, but which will form
an epoch in the history of the world, and will ever
be regarded as the brightest page in the records of
human reason. We shall endeavour to convey to
the reader some idea of its contents, and of the brilliant
discoveries which it disseminated over Europe.
The Principia consists of three books. The first
and second, which occupy three-fourths of the work,
are entitled, On the Motion of Bodies; and the third
bears the title, On the System of the World. The
first two books contain the mathematical principles
of philosophy, namely, the laws and conditions of
motions and forces; and they are illustrated with
several philosophical scholia, which treat of some of
the most general and best established points in philosophy,
such as the density and resistance of bodies,
spaces void of matter, and the motion of sound and
light. The object of the third book is to deduce
from these principles the constitution of the system
of the world; and this book has been drawn up in
as popular a style as possible, in order that it may
be generally read.
The great discovery which characterizes the
Principia is that of the principle of universal gravitation,
as deduced from the motion of the moon,
and from the three great facts or laws discovered by
Kepler. This principle is, that every particle of
matter is attracted by, or gravitates to, every other
particle of matter, with a force inversely proportional
to the squares of their distances. From the first law
of Kepler, namely, the proportionality of the areas
to the times of their description, Newton inferred
that the force which kept the planet in its orbit was
always directed to the sun; and from the second
law of Kepler, that every planet moves in an ellipse
with the sun in one of its foci, he drew the still more
general inference, that the force by which the planet
moves round that focus varies inversely as the
square of its distance from the focus. As this law
was true in the motion of satellites round their primary
planets, Newton deduced the equality of gravity
in all the heavenly bodies towards the sun, upon the
supposition that they are equally distant from its
centre; and in the case of terrestrial bodies, he succeeded
in verifying this truth by numerous and accurate
experiments.
By taking a more general view of the subject,
Newton demonstrated that a conic section was the
only curve in which a body could move when acted
upon by a force varying inversely as the square of
the distance; and he established the conditions depending
on the velocity and the primitive position
of the body, which were requisite to make it describe
a circular, an elliptical, a parabolic, or a
hyperbolic orbit.
Notwithstanding the generality and importance
of these results, it still remained to be determined
whether the force resided in the centres of the
planets, or belonged to each individual particle of
which they were composed. Newton removed this
uncertainty by demonstrating, that if a spherical
body acts upon a distant body with a force varying
as the distance of this body from the centre of the
sphere, the same effect will be produced as if each
of its particles acted upon the distant body according
to the same law. And hence it follows that the
spheres, whether they are of uniform density, or
consist of concentric layers, with densities varying
according to any law whatever, will act upon each
other in the same manner as if their force resided
in their centres alone. But as the bodies of the
solar system are very nearly spherical, they will all
act upon one another, and upon bodies placed on
their surface, as if they were so many centres of
attraction; and therefore we obtain the law of gravity
which subsists between spherical bodies, namely,
that one sphere will act upon another with a force
directly proportional to the quantity of matter, and
inversely as the square of the distance between the
centres of the spheres. From the equality of action
and reaction, to which no exception can be found,
Newton concluded that the sun gravitated to the
planets, and the planets to their satellites; and the
earth itself to the stone which falls upon its surface;
and, consequently, that the two mutually gravitating
bodies approached to one another with velocities
inversely proportional to their quantities of matter.
Having established this universal law, Newton
was enabled, not only to determine the weight which
the same body would have at the surface of the sun
and the planets, but even to calculate the quantity
of matter in the sun, and in all the planets that had
satellites, and even to determine the density or
specific gravity of the matter of which they were
composed. In this way he found that the weight of
the same body would be twenty-three times greater
at the surface of the sun than at the surface of the
earth, and that the density of the earth was four times
greater than that of the sun, the planets increasing
in density as they receded from the centre of the
system.
If the peculiar genius of Newton has been displayed
in his investigation of the law of universal
gravitation, it shines with no less lustre in the patience
and sagacity with which he traced the consequences
of this fertile principle.
The discovery of the spheroidal form of Jupiter
by Cassini had probably directed the attention of
Newton to the determination of its cause, and consequently
to the investigation of the true figure of
the earth. The spherical form of the planets have
been ascribed by Copernicus to the gravity or natural
appetency of their parts; but upon considering the
earth as a body revolving upon its axis, Newton
quickly saw that the figure arising from the mutual
attraction of its parts must be modified by another
force arising from its rotation. When a body revolves
upon an axis, the velocity of rotation increases
from the poles, where it is nothing, to the
equator, where it is a maximum. In consequence
of this velocity the bodies on the earth’s surface
have a tendency to fly off from it, and this tendency
increases with the velocity. Hence arises a centrifugal
force which acts in combination with a force
of gravity, and which Newton found to be the 289th
part of the force of gravity at the equator, and decreasing,
as the cosine of the latitude, from the
equator to the poles. The great predominance of
gravity over the centrifugal force prevents the latter
from carrying off any bodies from the earth’s surface,
but the weight of all bodies is diminished by
the centrifugal force, so that the weight of any body
is greater at the poles than it is at the equator. If
we now suppose the waters at the pole to communicate
with those at the equator by means of a canal,
one branch of which goes from the pole to the
centre of the earth, and the other from the centre
of the earth to the equator, then the polar branch
of the canal will be heavier than the equatorial
branch, in consequence of its weight not being diminished
by the centrifugal force, and, therefore, in
order that the two columns may be in equilibrio, the
equatorial one must be lengthened. Newton found
that the length of the polar must be to that of the
equatorial canal as 229 to 230, or that the earth’s polar
radius must be seventeen miles less than its equatorial
radius; that is, that the figure of the earth is
an oblate spheroid, formed by the revolution of an
ellipse round its lesser axis. Hence it follows, that
the intensity of gravity at any point of the earth’s
surface is in the inverse ratio of the distance of that
point from the centre, and, consequently, that it diminishes
from the equator to the poles,—a result
which he confirmed by the fact, that clocks required
to have their pendulums shortened in order to beat
true time when carried from Europe towards the
equator.
The next subject to which Newton applied the
principle of gravity was the tides of the ocean.
The philosophers of all ages have recognised the
connexion between the phenomena of the tides and
the position of the moon. The College of Jesuits
at Coimbra, and subsequently Antonio de Dominis
and Kepler, distinctly referred the tides to the attraction
of the waters of the earth by the moon, but so
imperfect was the explanation which was thus given
of the phenomena, that Galileo ridiculed the idea of
lunar attraction, and substituted for it a fallacious
explanation of his own. That the moon is the
principal cause of the tides is obvious from the well-known
fact, that it is high water at any given place
about the time when she is in the meridian of that
place; and that the sun performs a secondary part
in their production may be proved from the circumstance,
that the highest tides take place when the
sun, the moon, and the earth are in the same straight
line, that is, when the force of the sun conspires
with that of the moon, and that the lowest tides
take place when the lines drawn from the sun and
moon to the earth are at right angles to each other,
that is, when the force of the sun acts in opposition
to that of the moon. The most perplexing phenomenon
in the tides of the ocean, and one which is
still a stumbling-block to persons slightly acquainted
with the theory of attraction, is the existence of
high water on the side of the earth opposite to the
moon, as well as on the side next the moon. To
maintain that the attraction of the moon at the same
instant draws the waters of the ocean towards herself,
and also draws them from the earth in an opposite
direction, seems at first sight paradoxical; but
the difficulty vanishes when we consider the earth,
or rather the centre of the earth, and the water on
each side of it as three distinct bodies placed at different
distances from the moon, and consequently
attracted with forces inversely proportional to the
squares of their distances. The water nearest the
moon will be much more powerfully attracted than
the centre of the earth, and the centre of the earth
more powerfully than the water farthest from the
moon. The consequence of this must be, that the
waters nearest the moon will be drawn away from
the centre of the earth, and will consequently rise
from their level, while the centre of the earth will
be drawn away from the waters opposite the moon,
which will, as it were, be left behind, and consequently
be in the same situation as if they were
raised from the earth in a direction opposite to
that in which they are attracted by the moon.
Hence the effect of the moon’s action upon the
earth is to draw its fluid parts into the form of an
oblong spheroid, the axis of which passes through
the moon. As the action of the sun will produce
the very same effect, though in a smaller degree,
the tide at any place will depend on the relative position
of these two spheroids, and will be always
equal either to the sum or to the difference of the
effects of the two luminaries. At the time of new
and full moon the two spheroids will have their axes
coincident, and the height of the tide, which will
then be a spring one, will be equal to the sum of the
elevations produced in each spheroid considered
separately, while at the first and third quarters the
axes of the spheroids will be at right angles to each
other, and the height of the tide, which will then be
a neap one, will be equal to the difference of the
elevations produced in each separate spheroid. By
comparing the spring and neap tides, Newton found
that the force with which the sun acted upon the
waters of the earth was to that with which the sun
acted upon them as 4.48 to 1;—that the force of the
moon produced a tide of 8.63 feet;—that of the sun
one of 1.93 feet;—and both of them combined, one
of 10½ French feet,—a result which in the open sea
does not deviate much from observation. Having
thus ascertained the force of the moon on the waters
of our globe, he found that the quantity of matter
in the moon was to that in the earth as 1 to 40, and
the density of the moon to that of the earth as 11
to 9.
The motions of the moon, so much within the
reach of our own observation, presented a fine field
for the application of the theory of universal gravitation.
The irregularities exhibited in the lunar
motions had been known in the time of Hipparchus
and Ptolemy. Tycho had discovered the great inequality
called the variation, amounting to 37′, and
depending on the alternate acceleration and retardation
of the moon in every quarter of a revolution,
and he had also ascertained the existence of the
annual equation. Of these two inequalities Newton
gave a most satisfactory explanation. The action
of the sun upon the moon may be always resolved
into two, one acting in the direction of the line joining
the moon and earth, and consequently tending
to increase or diminish the moon’s gravity to the
earth, and the other in a direction at right angles to
this, and consequently tending to accelerate or retard
the motion in her orbit. Now, it was found by
Newton that this last force was reduced to nothing,
or vanished at the syzigies or quadratures, so that
at these four points the moon described areas proportional
to the times. The instant, however, that
the moon quits these positions, the force under consideration,
which we may call the tangential force,
begins, and it reaches its maximum in the four octants.
The force, therefore, compounded of these
two elements of the solar force, or the diagonal of
the parallelogram which they form, is no longer
directed to the earth’s centre, but deviates from it at
a maximum about 30 minutes, and therefore affects
the angular motion of the moon, the motion being
accelerated in passing from the quadratures to the
syzigies, and retarded in passing from the syzigies
to the quadratures. Hence the velocity is in its
mean state in the octants, a maximum in the syzigies,
and a minimum in the quadratures.
Upon considering the influence of the solar force
in diminishing or increasing the moon’s gravity to
the earth, Newton saw that her distance and her
periodic time must from this cause be subject to
change, and in this way he accounted for the annual
equation observed by Tycho. By the application
of similar principles, he explained the cause of the
motion of the apsides, or of the greater axis of the
moon’s orbit, which has an angular progressive motion
of 3° 4′ nearly in the course of one lunation;
and he showed that the retrogradation of the nodes,
amounting to 3′ 10″ daily, arose from one of the elements
of the solar force being exerted in the plane
of the ecliptic, and not in the plane of the moon’s
orbit, the effect of which was to draw the moon
down to the plane of the ecliptic, and thus cause the
line of the nodes, or the intersection of these two
planes, to move in a direction opposite to that of the
moon. The lunar theory thus blocked out by Newton,
required for its completion the labours of another
century. The imperfections of the fluxionary calculus
prevented him from explaining the other inequalities
of the moon’s motions, and it was reserved
to Euler, D’Alembert, Clairaut, Mayer, and Laplace
to bring the lunar tables to a high degree of perfection,
and to enable the navigator to determine his
longitude at sea with a degree of precision which
the most sanguine astronomer could scarcely have
anticipated.
By the consideration of the retrograde motion of
the moon’s nodes, Newton was led to discover the
cause of the remarkable phenomenon of the precession
of the equinoctial points, which moved 50″ annually,
and completed the circuit of the heavens in
25,920 years. Kepler had declared himself incapable
of assigning any cause for this motion, and we
do not believe that any other astronomer ever made
the attempt. From the spheroidal form of the earth,
it may be regarded as a sphere with a spheroidal
ring surrounding its equator, one-half of the ring
being above the plane of the ecliptic and the other
half below it. Considering this excess of matter
as a system of satellites adhering to the earth’s surface,
Newton saw that the combined actions of the
sun and moon upon these satellites tended to produce
a retrogradation in the nodes of the circles
which they described in their diurnal rotation, and
that the sum of all the tendencies being communicated
to the whole mass of the planet, ought to produce
a slow retrogradation of the equinoctial points.
The effect produced by the motion of the sun he
found to be 40″, and that produced by the action of
the moon 10″.
Although there could be little doubt that the
comets were retained in their orbits by the same
laws which regulated the motions of the planets,
yet it was difficult to put this opinion to the test of
observation. The visibility of comets only in a
small part of their orbits rendered it difficult to ascertain
their distance and periodic times, and as their
periods were probably of great length, it was impossible
to correct approximate results by repeated observation.
Newton, however, removed this difficulty,
by showing how to determine the orbit of a
comet, namely, the form and position of the orbit
and the periodic time, by three observations. By
applying this method to the comet of 1680, he calculated
the elements of its orbit, and from the agreement
of the computed places with those which
were observed, he justly inferred that the motions
of comets were regulated by the same laws as those
of the planetary bodies. This result was one of
great importance; for as the comets enter our system
in every possible direction, and at all angles
with the ecliptic, and as a great part of their orbits
extend far beyond the limits of the solar system, it
demonstrated the existence of gravity in spaces far
removed beyond the planet, and proved that the law
of the inverse ratio of the squares of the distance
was true in every possible direction, and at very remote
distances from the centre of our system.48
Such is a brief view of the leading discoveries
which the Principia first announced to the world.
The grandeur of the subjects of which it treats, the
beautiful simplicity of the system which it unfolds,
the clear and concise reasoning by which that system
is explained, and the irresistible evidence by
which it is supported might have ensured it the
warmest admiration of contemporary mathematicians,
and the most welcome reception in all the
schools of philosophy throughout Europe. This,
however, is not the way in which great truths are
generally received. Though the astronomical discoveries
of Newton were not assailed by the class
of ignorant pretenders who attacked his optical
writings, yet they were every where resisted by the
errors and prejudices which had taken a deep hold
even of the strongest minds. The philosophy of
Descartes was predominant throughout Europe.
Appealing to the imagination, and not to the reason
of mankind, it was quickly received into popular
favour, and the same causes which facilitated its introduction
extended its influence, and completed its
dominion over the human mind. In explaining all
the movements of the heavenly bodies by a system
of vortices in a fluid medium diffused through the
universe, Descartes had seized upon an analogy of
the most alluring and deceitful kind. Those who
had seen heavy bodies revolving in the eddies of a
whirlpool, or in the gyrations of a vessel of water
thrown into a circular motion, had no difficulty in
conceiving how the planets might revolve round the
sun by analogous movements. The mind instantly
grasped at an explanation of so palpable a character,
and which required for its development neither the
exercise of patient thought nor the aid of mathematical
skill. The talent and perspicuity with which
the Cartesian system was expounded, and the show
of experiments with which it was sustained, contributed
powerfully to its adoption, while it derived a
still higher sanction from the excellent character
and the unaffected piety of its author.
Thus intrenched, as the Cartesian system was, in
the strongholds of the human mind, and fortified by
its most obstinate prejudices, it was not to be wondered
at that the pure and sublime doctrines of the
Principia were distrustfully received and perseveringly
resisted. The uninstructed mind could not
readily admit the idea, that the great masses of the
planets were suspended in empty space, and retained
in their orbits by an invisible influence residing in
the sun; and even those philosophers who had been
accustomed to the rigour of true scientific research,
and who possessed sufficient mathematical skill for
the examination of the Newtonian doctrines, viewed
them at first as reviving the occult qualities of the
ancient physics, and resisted their introduction with
a pertinacity which it is not easy to explain. Prejudiced,
no doubt, in favour of his own metaphysical
views, Leibnitz himself misapprehended the principles
of the Newtonian philosophy, and endeavoured
to demonstrate the truths in the Principia by the application
of different principles. Huygens, who above all
other men was qualified to appreciate the new philosophy,
rejected the doctrine of gravitation as existing
between the individual particles of matter, and received
it only as an attribute of the planetary masses.
John Bernouilli, one of the first mathematicians of
his age, opposed the philosophy of Newton. Mairan,
in the early part of his life, was a strenuous defender
of the system of vortices. Cassini and Maraldi
were quite ignorant of the Principia, and occupied
themselves with the most absurd methods of
calculating the orbits of comets long after the Newtonian
method had been established on the most
impregnable foundation; and even Fontenelle, a man
of liberal views and extensive information, continued,
throughout the whole of his life, to maintain the
doctrines of Descartes.
The Chevalier Louville of Paris had adopted the
Newtonian philosophy before 1720. S’Gravesande
had introduced it into the Dutch universities at a
somewhat earlier period, and Maupertuis, in consequence
of a visit which he paid to England in 1728,
became a zealous defender of it; but notwithstanding
these and some other examples that might be
quoted, we must admit the truth of the remark of
Voltaire, that though Newton survived the publication
of the Principia more than forty years, yet at
the time of his death he had not above twenty followers
out of England.
With regard to the progress of the Newtonian
philosophy in England, some difference of opinion
has been entertained. Professor Playfair gives the
following account of it. “In the universities of
England, though the Aristotelian physics had made
an obstinate resistance, they had been supplanted
by the Cartesian, which became firmly established
about the time when their foundation began to be
sapped by the general progress of science, and particularly
by the discoveries of Newton. For more
than thirty years after the publication of these discoveries,
the system of vortices kept its ground; and
a translation from the French into Latin of the Physics
of Rohault, a work entirely Cartesian, continued
at Cambridge to be the text for philosophical
instruction. About the year 1718, a new and more
elegant translation of the same book was published
by Dr. Samuel Clarke, with the addition of notes, in
which that profound and ingenious writer explained
the views of Newton on the principal objects of
discussion, so that the notes contained virtually a
refutation of the text; they did so, however, only
virtually, all appearance of argument and controversy
being carefully avoided. Whether this escaped
the notice of the learned doctor or not is uncertain,
but the new translation, from its better Latinity, and
the name of the editor, was readily admitted to all
the academical honours which the old one had enjoyed.
Thus the stratagem of Dr. Clarke completely
succeeded; the tutor might prelect from the
text, but the pupil would sometimes look into the
notes; and error is never so sure of being exposed
as when the truth is placed close to it, side by side,
without any thing to alarm prejudice, or awaken
from its lethargy the dread of innovation. Thus,
therefore, the Newtonian philosophy first entered
the university of Cambridge under the protection of
the Cartesian.” To this passage Professor Playfair
adds the following as a note:—
“The universities of St. Andrew’s and Edinburgh
were, I believe, the first in Britain where the Newtonian
philosophy was made the subject of the academical
prelections. For this distinction they are
indebted to James and David Gregory, the first in
some respects the rival, but both the friends of
Newton. Whiston bewails, in the anguish of his
heart, the difference, in this respect, between those
universities and his own. David Gregory taught in
Edinburgh for several years prior to 1690, when he
removed to Oxford; and Whiston says, ‘He had
already caused several of his scholars to keep acts,
as we call them, upon several branches of the Newtonian
philosophy, while we at Cambridge, poor
wretches, were ignominiously studying the fictitious
hypotheses of the Cartesians.’49 I do not, however,
mean to say, that from this date the Cartesian philosophy
was expelled from those universities; the
Physics of Rohault were still in use as a text-book,—at
least occasionally, to a much later period than this,
and a great deal, no doubt, depended on the character
of the individual. Professor Keill introduced the
Newtonian philosophy in his lectures at Oxford in
1697; but the instructions of the tutors, which constitute
the real and efficient system of the university,
were not cast in that mould till long afterward.”
Adopting the same view of the subject, Mr. Dugald
Stewart has stated, “that the philosophy of Newton
was publicly taught by David Gregory at Edinburgh,
and by his brother, James Gregory, at St. Andrew’s,50
before it was able to supplant the vortices of Descartes
in that very university of which Newton
was a member. It was in the Scottish universities
that the philosophy of Locke, as well as that of
Newton, was first adopted as a branch of academical
education.”
Anxious as we should have been to have awarded
to Scotland the honour of having first adopted the
Newtonian philosophy, yet a regard for historical
truth compels us to take a different view of the subject.
It is well known that Sir Isaac Newton delivered
lectures on his own philosophy from the
Lucasian chair before the publication of the Principia;
and in the very page of Whiston’s life quoted
by Professor Playfair, he informs us that he had
heard him read such lectures in the public schools,
though at that time he did not at all understand
them. Newton continued to lecture till 1699, and
occasionally, we presume, till 1703, when Whiston
became his successor, having been appointed his
deputy in 1699. In both of these capacities Whiston
delivered in the public schools a course of lectures
on astronomy, and a course of physico-mathematical
lectures, in which the mathematical philosophy
of Newton was explained and demonstrated,
and both these courses were published, the one in
1707, and the other in 1710, “for the use of the
young men in the university.” In 1707, the celebrated
blind mathematician Nicholas Saunderson
took up his residence in Christ’s College without
being admitted a member of that body. The society
not only allotted to him apartments, but gave him
the free use of their library. With the concurrence
of Whiston he delivered a course of lectures “on
the Principia, Optics, and Universal Arithmetic of
Newton,” and the popularity of these lectures was
so great, that Sir Isaac corresponded on the subject
of them with their author; and on the ejection of
Whiston from the Lucasian chair in 1711, Saunderson
was appointed his successor. In this important office
he continued to teach the Newtonian philosophy till
the time of his death, which took place in 1739.
But while the Newtonian philosophy was thus
regularly taught in Cambridge, after the publication
of the Principia, there were not wanting other exertions
for accelerating its progress. About 1694, the
celebrated Dr. Samuel Clarke, while an under-graduate,
defended, in the public schools, a question taken
from the Newtonian philosophy; and his translation
of Rohault’s Physics, which contains references in
the notes to the Principia, and which was published
in 1697 (and not in 1718, as stated by Professor
Playfair), shows how early the Cartesian system
was attacked by the disciples of Newton. The
author of the Life of Saunderson informs us, that
public exercises or acts founded on every part of the
Newtonian system were very common about 1707,
and so general were such studies in the university,
that the Principia rose to four times its original
price.51 One of the most ardent votaries of the
Newtonian philosophy was Dr. Laughton, who had
been tutor in Clare Hall from 1694, and it is probable
that during the whole, or at least a greater part, of
his tutorship he had inculcated the same doctrines.
In 1709–10, when he was proctor of that college, instead
of appointing a moderator, he discharged the
office himself, and devoted his most active exertions
to the promotion of mathematical knowledge. Previous
to this, he had even published a paper of questions
on the Newtonian philosophy, which appear to
have been used as theses for disputations; and such
was his ardour and learning that they powerfully
contributed to the popularity of his college. Between
1706 and 1716, the year of his death, the celebrated
Roger Cotes, the friend and disciple of Newton,
filled the Plumian chair of astronomy and experimental
philosophy at Cambridge. During this
period he edited the second edition of the Principia,
which he enriched with an admirable preface, and
thus contributed, by his writings as well as by his
lectures, to advance the philosophy of his master.
About the same time, the learned Dr. Bentley, who
first made known the philosophy of his friend to the
readers of general literature, filled the high office of
master of Trinity College, and could not fail to have
exerted his utmost influence in propagating doctrines
which he so greatly admired. Had any opposition
been offered to the introduction of the true system
of the universe, the talents and influence of these
individuals would have immediately suppressed it;
but no such opposition seems to have been made;
and though there may have been individuals at Cambridge
ignorant of mathematical science, who adhered
to the system of Descartes, and patronised
the study of the Physics of Rohault, yet it is probable
that similar persons existed in the universities
of Edinburgh and St. Andrew’s; and we cannot regard
their adherence to error as disproving the general
fact, that the philosophy of Newton was quickly
introduced into all the universities of Great Britain.
But while the mathematical principles of the Newtonian
system were ably expounded in our seats of
learning, its physical truths were generally studied,
and were explained and communicated to the public
by various lecturers on experimental philosophy.
The celebrated Locke, who was incapable of understanding
the Principia from his want of mathematical
knowledge, inquired of Huygens if all the mathematical
propositions in that work were true. When
he was assured that he might depend upon their certainty,
he took them for granted, and carefully examined
the reasonings and corollaries deduced from
them. In this manner he acquired a knowledge of
the physical truths in the Principia, and became a
firm believer in the discoveries which it contained.
In the same manner he studied the treatise on Optics,
and made himself master of every part of it
which was not mathematical.52 From a manuscript
of Sir Isaac Newton’s, entitled “A demonstration
that the planets, by their gravity towards the sun,
may move in ellipses,53 found among the papers of
Mr. Locke, and published by Lord King,” it would
appear that he himself had been at considerable
trouble in explaining to his friend that interesting
doctrine. This manuscript is endorsed, “Mr. Newton,
March, 1689.” It begins with three hypotheses
(the first two being the two laws of motion, and the
third the parallelogram of motion), which introduce
the proposition of the proportionality of the areas
to the times in motions round an immoveable centre
of attraction.54 Three lemmas, containing properties
of the ellipse, then prepare the reader for the celebrated
proposition, that when a body moves in an
ellipse,55 the attraction is reciprocally as the square
of the distance of the body from the focus to which
it is attracted. These propositions are demonstrated
in a more popular manner than in the Principia, but
there can be no doubt that, even in their present
modified form, they were beyond the capacity of
Mr. Locke.
Dr. John Keill was the first person who publicly
taught natural philosophy by experiments. Desaguliers
informs us that this author “laid down very
simple propositions, which he proved by experiments,
and from these he deduced others more compound,
which he still confirmed by experiments, till he had
instructed his auditors in the laws of motion, the
principles of hydrostatics and optics, and some of
the chief propositions of Sir Isaac Newton concerning
light and colours. He began these courses in
Oxford about the year 1704 or 1705, and in that way
introduced the love of the Newtonian philosophy.”
When Dr. Keill left the university, Desaguliers began
to teach the Newtonian philosophy by experiments.
He commenced his lectures at Harthall in
Oxford, in 1710, and delivered more than a hundred
and twenty courses; and when he went to settle in
London in 1713, he informs us that he found “the
Newtonian philosophy generally received among
persons of all ranks and professions, and even
among the ladies by the help of experiments.”
Such were the steps by which the Newtonian philosophy
was established in Great Britain. From
the time of the publication of the Principia, its
mathematical doctrines formed a regular part of academical
education; and before twenty years had
elapsed, its physical truths were communicated to
the public in popular lectures illustrated by experiments,
and accommodated to the capacities of those
who were not versed in mathematical knowledge.
The Cartesian system, though it may have lingered
for a while in the recesses of our universities, was
soon overturned; and long before his death, Newton
enjoyed the high satisfaction of seeing his philosophy
triumphant in his native land.
Doctrine of Infinite Quantities—Labours of Pappus—Kepler—Cavaleri—Roberval—Fermat—Wallis—Newton
discovers the Binomial Theorem—and
the Doctrine of Fluxions in 1666—His Manuscript Work
containing this Doctrine communicated to his Friends—His Treatise
on Fluxions—His Mathematical Tracts—His Universal Arithmetic—His
Methodus Differentialis—His Geometria Analytica—His Solution
of the Problems proposed by Bernouilli and Leibnitz—Account
of the celebrated Dispute respecting the Invention of Fluxions—Commercium
Epistolicum—Report of the Royal Society—General View
of the Controversy.
Previous to the time of Newton, the doctrine of
infinite quantities had been the subject of profound
study. The ancients made the first step in this
curious inquiry by a rude though ingenious attempt
to determine the area of curves. The method of
exhaustions which was used for this purpose consisted
in finding a given rectilineal area to which the
inscribed and circumscribed polygonal figures continually
approached by increasing the number of
their sides. This area was obviously the area
of the curve, and in the case of the parabola it was
found by Archimedes to be two-thirds of the area
formed by multiplying the ordinate by the abscissa.
Although the synthetical demonstration of the results
was perfectly conclusive, yet the method itself
was limited and imperfect.
The celebrated Pappus of Alexandria followed
Archimedes in the same inquiries; and in his demonstration
of the property of the centre of gravity
of a plane figure, by which we may determine the
solid formed by its revolution, he has shadowed
forth the discoveries of later times.
In his curious tract on Stereometry, published in
1615, Kepler made some advances in the doctrine
of infinitesimals. Prompted to the task by a dispute
with the seller of some casks of wine, he
studied the measurement of solids formed by the
revolution of a curve round any line whatever.
In solving some of the simplest of these problems,
he conceived a circle to be formed of an infinite
number of triangles having all their vertices in the
centre, and their infinitely small bases in the circumference
of the circle, and by thus rendering familiar
the idea of quantities infinitely great and infinitely
small, he gave an impulse to this branch of mathematics.
The failure of Kepler, too, in solving some
of the more difficult of the problems which he himself
proposed roused the attention of geometers,
and seems particularly to have attracted the notice
of Cavaleri.
This ingenious mathematician was born at Milan
in 1598, and was Professor of Geometry at Bologna.
In his method of Indivisibles, which was published
in 1635, he considered a line as composed of an infinite
number of points, a surface of an infinite
number of lines, and a solid of an infinite number
of surfaces; and he lays it down as an axiom that
the infinite sums of such lines and surfaces have the
same ratio when compared with the linear or superficial
unit, as the surfaces and solids which are to
be determined. As it is not true that an infinite
number of infinitely small points can make a line,
or an infinite number of infinitely small lines a surface,
Pascal removed this verbal difficulty by considering
a line as composed of an infinite number
of infinitely short lines, a surface as composed of
an infinite number of infinitely narrow parallelograms,
and a solid of an infinite number of infinitely
thin solids. But, independent of this correction,
the conclusions deduced by Cavaleri are rigorously
true, and his method of ascertaining the ratios of
areas and solids to one another, and the theorems
which he deduced from it may be considered as
forming an era in mathematics.
By the application of this method, Roberval and
Toricelli showed that the area of the cycloid is three
times that of its generating circle, and the former
extended the method of Cavaleri to the case where
the powers of the terms of the arithmetical progression
to be summed were fractional.
In applying the doctrine of infinitely small quantities
to determine the tangents of curves, and the
maxima and minima of their ordinates, both Roberval
and Fermat made a near approach to the
invention of fluxions—so near indeed that both
Lagrange and Laplace56 have pronounced the latter
to be the true inventer of the differential calculus.
Roberval supposed the point which describes a
curve to be actuated by two motions, by the composition
of which it moves in the direction of a tangent;
and had he possessed the method of fluxions,
he could, in every case, have determined the relative
velocities of these motions, which depend on
the nature of the curve, and consequently the
direction of the tangent which he assumed to be in
the diagonal of a parallelogram whose sides had the
same ratio as the velocities. But as he was able
to determine these velocities only in the conic sections,
&c. his ingenious method had but few applications.
The labours of Peter Fermat, a counsellor of the
parliament of Toulouse, approached still nearer to
the fluxionary calculus. In his method of determining
the maxima and minima of the ordinates of
curves, he substitutes x + e for the independent
variable x in the function which is to become a
maximum, and as these two expressions should be
equal when e becomes infinitely small or 0, he frees
this equation from surds and radicals, and after dividing
the whole by e, e is made = 0, and the equation
for the maximum is thus obtained. Upon a similar
principle he founded his method of drawing tangents
to curves. But though the methods thus used by
Fermat are in principle the same with those which
connect the theory of tangents and of maxima
and minima with the analytical method of exhibiting
the differential calculus, yet it is a singular example
of national partiality to consider the inventer
of these methods as the inventer of the method of
fluxions.
“One might be led,” says Mr. Herschel, “to suppose
by Laplace’s expression that the calculus of
finite differences had then already assumed a systematic
form, and that Fermat had actually observed
the relation between the two calculi, and derived
the one from the other. The latter conclusion
would scarcely be less correct than the former. No
method can justly be regarded as bearing any analogy
to the differential calculus which does not lay
down a system of rules (no matter on what considerations
founded, by what names called, or by what
extraneous matter enveloped) by means of which
the second term of the development of any function
of x + e in powers of e, can be correctly calculated,
‘quæ extendet se,’ to use Newton’s expression,
‘citra ullum molestum calculum in terminis surdis
æque ac in integris procedens.’ It would be strange
to suppose Fermat or any other in possession of
such a method before any single surd quantity had
ever been developed in a series. But, in point of
fact, his writings present no trace of the kind; and
this, though fatal to his claim, is allowed by both the
geometers cited. Hear Lagrange’s candid avowal.
‘Il fait disparaitre dans cette equation,’ that of the
maximum between x and e, ‘les radicaux et les fractions
s’il y en à.’ Laplace, too, declares that ‘il savoit
etendre son calcul aux fonctions irrationelles
en se debarrassant des irrationalités par l’elevation
des radicaux aux puissances.’ This is at once giving
up the point in question. It is allowing unequivocally
that Fermat in these processes only took
a circuitous route to avoid a difficulty which it is
one of the most express objects of the differential
calculus to face and surmount. The whole claim
of the French geometer arises from a confusion (too
often made) of the calculus and its applications, the
means and the end, under the sweeping head of
‘nouveaux calculs’ on the one hand, and an assertion
somewhat too unqualified, advanced in the
warmth and generality of a preface, on the other.”57
The discoveries of Fermat were improved and
simplified by Hudde, Huygens, and Barrow; and by
the publication of the Arithmetic of Infinites by Dr.
Wallis, Savilian professor of geometry at Oxford,
mathematicians were conducted to the very entrance
of a new and untrodden field of discovery. This
distinguished author had effected the quadrature of
all curves whose ordinates can be expressed by any
direct integral powers; and though he had extended
his conclusions to the cases where the ordinates are
expressed by the inverse or fractional powers, yet
he failed in its application. Nicolas Mercator (Kauffman)
surmounted the difficulty by which Wallis
had been baffled, by the continued division of the
numerator by the denominator to infinity, and then
applying Wallis’s method to the resulting positive
powers. In this way he obtained, in 1667, the first
general quadrature of the hyperbola, and, at the
same time, gave the regular development of a function
in series.
In order to obtain the quadrature of the circle, Dr.
Wallis considered that if the equations of the curves
of which he had given the quadrature were arranged
in a series, beginning with the most simple, these
areas would form another series. He saw also that
the equation of the circle was intermediate between
the first and second terms of the first series, or
between the equation of a straight line and that of
a parabola, and hence he concluded, that by interpolating
a term between the first and second term of
the second series, he would obtain the area of the
circle. In pursuing this singularly beautiful thought,
Dr. Wallis did not succeed in obtaining the indefinite
quadrature of the circle, because he did not employ
general exponents; but he was led to express the
entire area of the circle by a fraction, the numerator
and denominator of which are each obtained by
the continued multiplication of a certain series of
numbers.
Such was the state of this branch of mathematical
science, when Newton, at an early age, directed to
it the vigour of his mind. At the very beginning
of his mathematical studies, when the works of Dr.
Wallis fell into his hands, he was led to consider
how he could interpolate the general values of the
areas in the second series of that mathematician.
With this view he investigated the arithmetical law
of the coefficients of the series, and obtained a
general method of interpolating, not only the series
above referred to, but also other series. These
were the first steps taken by Newton, and, as he
himself informs us, they would have entirely escaped
from his memory if he had not, a few weeks
before,58 found the notes which he made upon the
subject. When he had obtained this method, it occurred
to him that the very same process was applicable
to the ordinates, and, by following out this
idea, he discovered the general method of reducing
radical quantities composed of several terms into
infinite series, and was thus led to the discovery of
the celebrated Binomial Theorem. He now neglected
entirely his methods of interpolation, and employed
that theorem alone as the easiest and most direct
method for the quadratures of curves, and in the solution
of many questions which had not even been
attempted by the most skilful mathematicians.
After having applied the Binomial theorem to the
rectification of curves, and to the determination of
the surfaces and contents of solids, and the position
of their centres of gravity, he discovered the general
principle of deducing the areas of curves from the
ordinate, by considering the area as a nascent quantity,
increasing by continual fluxion in the proportion
of the length of the ordinate, and supposing
the abscissa to increase uniformly in proportion to
the time. In imitation of Cavalerius, he called the
momentary increment of a line a point, though it is
not a geometrical point, but an infinitely short line;
and the momentary increment of an area or surface
he called a line, though it is not a geometrical line,
but an infinitely narrow surface. By thus regarding
lines as generated by the motion of points, surfaces
by the motions of lines, and solids by the motion of
surfaces, and by considering that the ordinates, abscissæ,
&c. of curves thus formed, vary according
to a regular law depending on the equation of the
curve, he deduces from this equation the velocities
with which these quantities are generated; and by
the rules of infinite series he obtains the ultimate
value of the quantity required. To the velocities
with which every line or quantity is generated,
Newton gave the name of Fluxions, and to the lines
or quantities themselves that of Fluents. This
method constitutes the doctrine of fluxions which
Newton had invented previous to 1666, when the
breaking out of the plague at Cambridge drove him
from that city, and turned his attention to other
subjects.
But though Newton had not communicated this
great invention to any of his friends, he composed
his treatise, entitled Analysis per equationes numero
terminorum infinitas, in which the principle of fluxions
and its numerous applications are clearly pointed
out. In the month of June, 1669, he communicated
this work to Dr. Barrow, who mentions it in a letter
to Mr. Collins, dated the 20th June, 1669, as the production
of a friend of his residing at Cambridge, who
possesses a fine genius for such inquiries. On the
31st July, he transmitted the work to Collins; and
having received his approbation of it, he informs him
that the name of the author of it was Newton, a
fellow of his own college, and a young man who
had only two years before taken his degree of M.A.
Collins took a copy of this treatise, and returned the
original to Dr. Barrow; and this copy having been
found among Collins’s papers by his friend Mr. William
Jones, and compared with the original manuscript
borrowed from Newton, it was published with
the consent of Newton in 1711, nearly fifty years
after it was written.
Though the discoveries contained in this treatise
were not at first given to the world, yet they were
made generally known to mathematicians by the
correspondence of Collins, who communicated them
to James Gregory; to MM. Bertet and Vernon in
France; to Slusius in Holland; to Borelli in Italy;
and to Strode, Townsend, and Oldenburg, in letters
dated between 1669 and 1672.
Hitherto the method of fluxions was known only
to the friends of Newton and their correspondents;
but, in the first edition of the Principia, which appeared
in 1687, he published, for the first time, the
fundamental principle of the fluxionary calculus, in
the second lemma of the second book. No information,
however, is here given respecting the algorithm
or notation of the calculus; and it was not till
1693–5[?] that it was communicated to the mathematical
world in the second volume of Dr. Wallis’s works,
which were published in that year. This information
was extracted from two letters of Newton
written in 1692.
About the year 1672, Newton had undertaken to
publish an edition of Kinckhuysen’s Algebra, with
notes and additions. He therefore drew up a treatise,
entitled, A Method of Fluxions, which he proposed
as an introduction to that work; but the fear
of being involved in disputes about this new discovery,
or perhaps the wish to render it more complete,
or to have the sole advantage of employing
it in his physical researches, induced him to abandon
this design. At a later period of his life he again
resolved to give it to the world; but it did not appear
till after his death, when it was translated into
English, and published in 1736, with a commentary
by Mr. John Colson, Professor of Mathematics in
Cambridge.59
To the first edition of Newton’s Optics, which
appeared in 1704, there were added two mathematical
treatises, entitled, Tractatus duo de speciebus et magnitudine
figurarum curvilinearum, the one bearing the
title of Tractatus de Quadratura Curvarum, and the
other Enumeratio linearum tertii ordinis. The first
contains an explanation of the doctrine of fluxions,
and of its application to the quadrature of curves;
and the second a classification of seventy-two curves
of the third order, with an account of their properties.
The reason for publishing these two tracts in
his Optics (in the subsequent editions of which they
are omitted) is thus stated in the advertisement:—“In
a letter written to M. Leibnitz in the year 1679,
and published by Dr. Wallis, I mentioned a method
by which I had found some general theorems about
squaring curvilinear figures on comparing them with
the conic sections, or other the simplest figures with
which they might be compared. And some years
ago I lent out a manuscript containing such theorems;
and having since met with some things copied
out of it, I have on this occasion made it public, prefixing
to it an introduction, and joining a scholium
concerning that method. And I have joined with it
another small tract concerning the curvilineal figures
of the second kind, which was also written many
years ago, and made known to some friends, who
have solicited the making it public.”
In the year 1707, Mr. Whiston published the algebraical
lectures which Newton had, during nine years,
delivered at Cambridge, under the title of Arithmetica
Universalis, sive de Compositione et Resolutione Arithmetica
Liber. We are not accurately informed how
Mr. Whiston obtained possession of this work; but
it is stated by one of the editors of the English
edition, that “Mr. Whiston thinking it a pity that so
noble and useful a work should be doomed to a college
confinement, obtained leave to make it public.”
It was soon afterward translated into English by
Mr. Ralphson; and a second edition of it, with improvements
by the author, was published at London
in 1712, by Dr. Machin, secretary to the Royal Society.
With the view of stimulating mathematicians
to write annotations on this admirable work, the
celebrated S’Gravesande published a tract, entitled,
Specimen Commentarii in Arithmeticam Universalem;
and Maclaurin’s Algebra seems to have been drawn
up in consequence of this appeal.
Among the mathematical works of Newton we
must not omit to enumerate a small tract entitled,
Methodus Differentialis, which was published with
his consent in 1711. It consists of six propositions,
which contain a method of drawing a parabolic curve
through any given number of points, and which are
useful for constructing tables by the interpolation of
series, and for solving problems depending on the
quadrature of curves.
Another mathematical treatise of Newton’s was
published for the first time in 1779, in Dr. Horsley’s
edition of his works.60 It is entitled, Artis Analyticæ
Specimina, vel Geometria Analytica. In editing this
work, which occupies about 130 quarto pages, Dr.
Horsley used three manuscripts, one of which was
in the handwriting of the author; another, written
in an unknown hand, was given by Mr. William
Jones to the Honourable Charles Cavendish; and a
third, copied from this by Mr. James Wilson, the
editor of Robins’s works, was given to Dr. Horsley
by Mr. John Nourse, bookseller to the king. Dr.
Horsley has divided it into twelve chapters, which
treat of infinite series; of the reduction of affected
equations; of the specious resolution of equations;
of the doctrine of fluxions; of maxima and minima;
of drawing tangents to curves; of the radius of curvature;
of the quadrature of curves; of the area of
curves which are comparable with the conic sections;
of the construction of mechanical problems,
and on finding the lengths of curves.
In enumerating the mathematical works of our
author, we must not overlook his solutions of the
celebrated problems proposed by Bernouilli and
Leibnitz. On the Kalends of January, 1697, John
Bernouilli addressed a letter to the most distinguished
mathematicians in Europe,61 challenging
them to solve the two following problems:
1. To determine the curve line connecting two
given points which are at different distances from
the horizon, and not in the same vertical line, along
which a body passing by its own gravity, and beginning
to move at the upper point, shall descend to the
lower point in the shortest time possible.
2. To find a curve line of this property that the
two segments of a right line drawn from a given
point through the curve, being raised to any given
power, and taken together, may make every where
the same sum.
On the day after he received these problems,
Newton addressed to Mr. Charles Montague, the
President of the Royal Society, a solution of them
both. He announced that the curve required in the
first problem must be a cycloid, and he gave a
method of determining it. He solved also the
second problem, and he showed that by the same
method other curves might be found which shall cut
off three or more segments having the like properties.
Leibnitz, who was struck with the beauty of
the problem, requested Bernouilli, who had allowed
six months for its solution, to extend the period to
twelve months. This delay was readily granted,
solutions were obtained from Newton, Leibnitz, and
the Marquis de L’Hopital; and although that of
Newton was anonymous, yet Bernouilli recognised
in it his powerful mind, “tanquam,” says he, “ex
ungue leonem,” as the lion is known by his claw.
The last mathematical effort of our author was
made with his usual success, in solving a problem
which Leibnitz proposed in 1716, in a letter to the
Abbé Conti, “for the purpose, as he expressed it,
of feeling the pulse of the English analysts.” The
object of this problem was to determine the curve
which should cut at right angles an infinity of curves
of a given nature, but expressible by the same equation.
Newton received this problem about five
o’clock in the afternoon, as he was returning from
the Mint; and though the problem was extremely
difficult, and he himself much fatigued with business,
yet he finished the solution of it before he went
to bed.
Such is a brief account of the mathematical writings
of Sir Isaac Newton, not one of which were
voluntarily communicated to the world by himself.
The publication of his Universal Arithmetic is said
to have been a breach of confidence on the part of
Whiston; and, however this may be, it was an unfinished
work, never designed for the public. The
publication of his Quadrature of Curves, and of his
Enumeration of Curve Lines, was rendered necessary,
in consequence of plagiarisms from the manuscripts
of them which he had lent to his friends, and
the rest of his analytical writings did not appear till
after his death. It is not easy to penetrate into the
motives by which this great man was on these
occasions actuated. If his object was to keep possession
of his discoveries till he had brought them
to a higher degree of perfection, we may approve of
the propriety, though we cannot admire the prudence
of such a step. If he wished to retain to himself
his own methods, in order that he alone might have
the advantage of them in prosecuting his physical
inquiries, we cannot reconcile so selfish a measure
with that openness and generosity of character
which marked the whole of his life. If he withheld
his labours from the world in order to avoid the disputes
and contentions to which they might give rise,
he adopted the very worst method of securing his
tranquillity. That this was the leading motive under
which he acted, there is little reason to doubt. The
early delay in the publication of his method of fluxions,
after the breaking out of the plague at Cambridge,
was probably owing to his not having completed
the algorithm of that calculus; but no apology
can be made for the imprudence of withholding it
any longer from the public. Had he published this
noble discovery even previous to 1673, when his
great rival had not even entered upon those studies
which led him to the same method, he would have
secured to himself the undivided honour of the
invention, and Leibnitz could have aspired to no other
fame but that of an improver of the doctrine of fluxions.
But he unfortunately acted otherwise. He
announced to his friends that he possessed a method
of great generality and power; he communicated to
them a general account of its principles and applications;
and the information which was thus conveyed
directed the attention of mathematicians to subjects
to which they might not have otherwise applied their
powers. In this way the discoveries which he had
previously made were made subsequently by others;
and Leibnitz, in place of appearing in the theatre of
science as the disciple and the follower of Newton,
stood forth with all the dignity of a rival; and, by
the early publication of his discoveries had nearly
placed himself on the throne which Newton was
destined to ascend.
It would be inconsistent with the popular nature
of a work like this, to enter into a detailed history
of the dispute between Newton and Leibnitz respecting
the invention of fluxions. A brief and
general account of it, however, is indispensable.
In the beginning of 1673, Leibnitz came to London
in the suite of the Duke of Hanover, and he became
acquainted with the great men who then adorned
the capital of England. Among these was Oldenburg,
a countryman of his own, who was then secretary
to the Royal Society. About the beginning
of March, in the same year, Leibnitz went to Paris,
where, with the assistance of Huygens, he devoted
himself to the study of the higher geometry. In
the month of July he renewed his correspondence
with Oldenburg, and he communicated to him some of
the discoveries which he had made relative to series,
particularly the series for a circular arc in terms of
the tangent. Oldenburg informed him in return of
the discoveries on series which had been made by
Newton and Gregory; and in 1676 Newton communicated
to him, through Oldenburg, a letter of fifteen
closely printed quarto pages, containing many of his
analytical discoveries, and stating that he possessed
a general method of drawing tangents, which he
thought it necessary to conceal in two sentences of
transposed characters. In this letter neither the
method of fluxions nor any of its principles are
communicated; but the superiority of the method
over all others is so fully described, that Leibnitz
could scarcely fail to discover that Newton possessed
that secret of which geometers had so long
been in quest.
Had Leibnitz at the time of receiving this letter
been entirely ignorant of his own differential method,
the information thus conveyed to him by Newton
could not fail to stimulate his curiosity, and excite
his mightiest efforts to obtain possession of so great
a secret. That this new method was intimately
connected with the subject of series was clearly indicated
by Newton; and as Leibnitz was deeply
versed in this branch of analysis, it is far from improbable
that a mind of such strength and acuteness
might attain his object by direct investigation. That
this was the case may be inferred from his letter to
Oldenburg (to be communicated to Newton) of the
21st June, 1677, where he mentions that he had for
some time been in possession of a method of drawing
tangents more general than that of Slusius,
namely, by the differences of ordinates. He then
proceeds with the utmost frankness to explain this
method, which was no other than the differential
calculus. He describes the algorithm which he had
adopted, the formation of differential equations, and
the application of the calculus to various geometrical
and analytical questions. No answer seems to have
been returned to this letter either by Newton or
Oldenburg, and, with the exception of a short letter
from Leibnitz to Oldenburg, dated 12th July, 1677,
no further correspondence seems to have taken
place. This, no doubt, arose from the death of Oldenburg
in the month of August, 1677,62 when the
two rival geometers pursued their researches with
all the ardour which the greatness of the subject
was so well calculated to inspire.
In the hands of Leibnitz the differential calculus
made rapid progress. In the Acta Eruditorum, which
was published at Leipsic in November, 1684, he gave
the first account of it, describing its algorithm in the
same manner as he had done in his letter to Oldenburg,
and pointing out its application to the drawing
of tangents, and the determination of maxima and
minima. He makes a remote reference to the similar
calculus of Newton, but lays no claim to the sole
invention of the differential method. In the same
work for June, 1686, he resumes the subject; and
when Newton had not published a single word upon
fluxions, and had not even made known his notation,
the differential calculus was making rapid advances
on the Continent, and in the hands of James and
John Bernouilli had proved the means of solving
some of the most important and difficult problems.
The silence of Newton was at last broken, and in
the second lemma of the second book of the Principia,
he explained the fundamental principle of the
fluxionary calculus. His explanation, which occupied
only three pages, was terminated with the following
scholium:—“In a correspondence which
took place about ten years ago between that very
skilful geometer, G. G. Leibnitz, and myself, I announced
to him that I possessed a method of determining
maxima and minima, of drawing tangents,
and of performing similar operations which was
equally applicable to rational and irrational quantities,
and concealed the same in transposed letters
involving this sentence, (data equatione quotcunque
fluentes quantitates involvente, fluxiones invenire et vice
versa). This illustrious man replied that he also
had fallen on a method of the same kind, and he
communicated to me his method which scarcely
differed from mine except in the notation [and in the
idea of the generation of quantities.”]63 This celebrated
scholium, which is so often referred to in the
present controversy, has, in our opinion, been much
misapprehended. While M. Biot considers it as
“eternalizing the rights of Leibnitz by recognising
them in the Principia,” Professor Playfair regards it
as containing “a highly favourable opinion on the
subject of the discoveries of Leibnitz.” To us it
appears to be nothing more than the simple statement
of the fact, that the method communicated by
Leibnitz was nearly the same as his own; and this
much he might have said, whether he believed that
Leibnitz had seen the fluxionary calculus among the
papers of Collins, or was the independent inventor
of his own. It is more than probable, indeed, that
when Newton wrote this scholium he regarded
Leibnitz as a second inventor; but when he found
that Leibnitz and his friends had showed a willingness
to believe, and had even ventured to throw out
the suspicion, that he himself had borrowed the doctrine
of fluxions from the differential calculus, he
seems to have altered the opinion which he had
formed of his rival, and to have been willing in his
turn to retort the charge.
This change of opinion was brought about by a
series of circumstances over which he had no control.
M. Nicolas Fatio de Duillier, a Swiss mathematician,
resident in London, communicated to the
Royal Society, in 1699, a paper on the line of quickest
descent, which contains the following observations:—“Compelled
by the evidence of facts, I hold
Newton to have been the first inventor of this calculus,
and the earliest by several years; and whether
Leibnitz, the second inventor, has borrowed any thing
from the other, I would prefer to my own judgment
that of those who have seen the letters and other
copies of the same manuscripts of Newton.” This
imprudent remark, which by no means amounts to a
charge of plagiarism, for Leibnitz is actually designated
the second inventor, may be considered as
showing that the English mathematicians had been
cherishing suspicions unfavourable to Leibnitz, and
there can be no doubt that a feeling had long prevailed
that this mathematician either had, or might
have seen, among the papers of Collins, the “Analysis
per Equationes, &c.,” which contained the principles
of the fluxionary method. Leibnitz replied to
the remark of Duillier with much good feeling.
He appealed to the facts as exhibited in his correspondence
with Oldenburg; he referred to Newton’s
scholium as a testimony in his favour; and, without
disputing or acknowledging the priority of Newton’s
claim, he asserted his own right to the invention of
the differential calculus. Fatio transmitted a reply to
the Leipsic Acts; but the editor refused to insert it.
The dispute, therefore, terminated, and the feelings
of the contending parties continued for some time
in a state of repose, though ready to break out on
the slightest provocation.
When Newton’s Optics appeared in 1704, accompanied
by his Treatise on the Quadrature of Curves,
and his enumeration of lines of the third order, the
editor of the Leipsic Acts (whom Newton supposed
to be Leibnitz himself) took occasion to review the
first of these tracts. After giving an imperfect
analysis of its contents, he compared the method
of fluxions with the differential calculus, and, in a
sentence of some ambiguity, he states that Newton
employed fluxions in place of the differences of Leibnitz,
and made use of them in his Principia in the
same manner as Honoratus Fabri, in his Synopsis
of Geometry, had substituted progressive motion in
place of the indivisibles of Cavaleri.64 As Fabri,
therefore, was not the inventor of the method
which is here referred to, but borrowed it from Cavaleri,
and only changed the mode of its expression,
there can be no doubt that the artful insinuation
contained in the above passage was intended to convey
the impression that Newton had stolen his method
of fluxions from Leibnitz. The indirect character
of this attack, in place of mitigating its severity,
renders it doubly odious; and we are persuaded that
no candid reader can peruse the passage without a
strong conviction that it justifies, in the fullest manner,
the indignant feelings which it excited among
the English philosophers. If Leibnitz was the author
of the review, or if he was in any way a party to it,
he merited the full measure of rebuke which was
dealt out to him by the friends of Newton, and deserved
those severe reprisals which doubtless imbittered
the rest of his days. He who dared to accuse
a man like Newton, or indeed any man holding
a fair character in society, with the odious crime of
plagiarism, placed himself without the pale of the
ordinary courtesies of life, and deserved to have
the same charge thrown back upon himself. The
man who conceives his fellow to be capable of such
intellectual felony, avows the possibility of himself
committing it, and almost substantiates the weakest
evidence of the worst accusers.
Dr. Keill, as the representative of Newton’s
friends, could not brook this base attack upon his
countryman. In a letter printed in the Philosophical
Transactions for 1708, he maintained that Newton
was “beyond all doubt” the first inventor of fluxions.
He referred for a direct proof of this to his letters
published by Wallis; and he asserted “that the same
calculus was afterward published by Leibnitz, the
name and the mode of notation being changed.”
If the reader is disposed to consider this passage
as retorting the charge of plagiarism upon Leibnitz,
he will readily admit that the mode of its expression
is neither so coarse nor so insidious as that
which is used by the writer in the Leipsic Acts.
In a letter to Hans Sloane, dated March, 1711, Leibnitz
complained to the Royal Society of the treatment
he had received. He expressed his conviction
that Keill had erred more from rashness of judgment
than from any improper motive, and that he did not
regard the accusation as a calumny; and he requested
that the society would oblige Mr. Keill to
disown publicly the injurious sense which his words
might bear. When this letter was read to the
society, Keill justified himself to Sir Isaac Newton
and the other members by showing them the obnoxious
review of the Quadrature of Curves in the
Leipsic Acts. They all agreed in attaching the same
injurious meaning to the passage which we formerly
quoted, and authorized Keill to explain and defend
his statement. He accordingly addressed a letter
to Sir Hans Sloane, which was read at the society
on the 24th May, 1711, and a copy of which was
ordered to be sent to Leibnitz. In this letter, which
is one of considerable length, he declares that he
never meant to state that Leibnitz knew either the
name of Newton’s method or the form of notation,
and that the real meaning of the passage was, “that
Newton was the first inventor of fluxions or of the
differential calculus, and that he had given, in two
letters to Oldenburg, and which he had transmitted
to Leibnitz, indications of it sufficiently intelligible
to an acute mind, from which Leibnitz derived, or at
least might derive, the principles of his calculus.”
The charge of plagiarism which Leibnitz thought
was implied in the former letter of his antagonist
is here greatly modified, if not altogether denied.
Keill expresses only an opinion that the letter seen
by Leibnitz contained intelligible indications of the
fluxionary calculus. Even if this opinion were correct,
it is no proof that Leibnitz either saw these indications
or availed himself of them, or if he did perceive
them, it might have been in consequence of his
having previously been in possession of the differential
calculus, or having enjoyed some distant view of it.
Leibnitz should, therefore, have allowed the dispute
to terminate here; for no ingenuity on his part, and
no additional facts, could affect an opinion which
any other person as well as Keill was entitled to
maintain.
Leibnitz, however, took a different view of the
subject, and wrote a letter to Sir Hans Sloane,
dated December 19, 1711, which excited new feelings,
and involved him in new embarrassments. Insensible
to the mitigation which had been kindly impressed
upon the supposed charge against his honour, he
alleges that Keill had attacked his candour and sincerity
more openly than before;—that he acted
without any authority from Sir Isaac Newton, who
was the party interested;—and that it was in vain
to justify his proceedings by referring to the provocation
in the Leipsic Acts, because in that journal
no injustice had been done to any party, but every one
had received what was his due. He branded Keill with
the odious appellation of an upstart, and one little
acquainted with the circumstances of the case;65 he
called upon the society to silence his vain and unjust
clamours,66 which, he believed, were disapproved
by Newton himself, who was well acquainted with
the facts, and who, he was persuaded, would willingly
give his opinion on the matter.
This unfortunate letter was doubtless the cause
of all the rancour and controversy which so speedily
followed, and it placed his antagonist in a new and a
more favourable position. It may be correct, though
few will admit it, that Keill’s second letter was more
injurious than the first; but it was not true that
Keill acted without the authority of Newton, because
Keill’s letter was approved of and transmitted
by the Royal Society, of which Newton was
the president, and therefore became the act of that
body. The obnoxious part, however, of Leibnitz’s
letter consisted in his appropriating to himself the
opinions of the reviewer in the Leipsic Acts, by
declaring that, in a review which charged Newton
with plagiarism, every person had got what was
his due. The whole character of the controversy
was now changed: Leibnitz places himself in the
position of the party who had first disturbed the
tranquillity of science by maligning its most distinguished
ornament; and the Royal Society was imperiously
called upon to throw all the light they
could upon a transaction which had exposed their
venerable president to so false a charge. The society,
too, had become a party to the question, by
their approbation and transmission of Keill’s second
letter, and were on that account alone bound to vindicate
the step which they had taken.
When the letter of Leibnitz, therefore, was read,
Keill appealed to the registers of the society for
the proofs of what he had advanced; Sir Isaac also
expressed his displeasure at the obnoxious passage
in the Leipsic Review, and at the defence of it by
Leibnitz, and he left it to the society to act as they
thought proper. A committee was therefore appointed
on the 11th March, consisting of Dr. Arbuthnot,
Mr. Hill, Dr. Halley, Mr. Jones, Mr. Machin,
and Mr. Burnet, who were instructed to examine
the ancient registers of the society, to inquire into
the dispute, and to produce such documents as they
should find, together with their own opinions on the
subject. On the 24th April the committee produced
the following report:—
“We have consulted the letters and letter-books
in the custody of the Royal Society, and those
found among the papers of Mr. John Collins, dated
between the years 1669 and 1677, inclusive; and
showed them to such as knew and avouched the
hands of Mr. Barrow, Mr. Collins, Mr. Oldenburg,
and Mr. Leibnitz; and compared those of Mr.
Gregory with one another, and with copies of some
of them taken in the hand of Mr. Collins; and have
extracted from them what relates to the matter referred
to us; all which extracts herewith delivered
to you we believe to be genuine and authentic. And
by these letters and papers we find,—
“I. Mr. Leibnitz was in London in the beginning
of the year 1673; and went thence, in or about
March, to Paris, where he kept a correspondence
with Mr. Collins by means of Mr. Oldenburg, till
about September, 1676, and then returned by London
and Amsterdam to Hanover: and that Mr. Collins
was very free in communicating to able mathematicians
what he had received from Mr. Newton and
Mr. Gregory.
“II. That when Mr. Leibnitz was the first time in
London, he contended for the invention of another
differential method properly so called; and, notwithstanding
that he was shown by Dr. Pell that it was
Newton’s method, persisted in maintaining it to be
his own invention, by reason that he had found it by
himself without knowing what Newton had done
before, and had much improved it. And we find no
mention of his having any other differential method
than Newton’s before his letter of the 21st of June,
1677, which was a year after a copy of Mr. Newton’s
letter of the 10th of December, 1672, had been sent
to Paris to be communicated to him; and above four
years after, Mr. Collins began to communicate that
letter to his correspondent; in which letter the
method of fluxions was sufficiently described to any
intelligent person.
“III. That by Mr. Newton’s letter of the 13th of
June, 1676, it appears that he had the method of
fluxions above five years before the writing of that
letter. And by his Analysis per Æquationes numero
Terminorum Infinitas, communicated by Dr. Barrow
to Mr. Collins in July, 1669, we find that he had invented
the method before that time.
“IV. That the differential method is one and the
same with the method of fluxions, excepting the
name and mode of notation; Mr. Leibnitz calling
those quantities differences which Mr. Newton calls
moments or fluxions; and marking them with the
letter d—a mark not used by Mr. Newton.
“And therefore we take the proper question to be
not who invented this or that method, but who was
the first inventor of the method. And we believe
that those who have reputed Mr. Leibnitz the first
inventor knew little or nothing of his correspondence
with Mr. Collins and Mr. Oldenburg long before, nor
of Mr. Newton’s having that method above fifteen
years before Mr. Leibnitz began to publish it in the
Acta Eruditorum of Leipsic.
“For which reason we reckon Mr. Newton the
first inventor; and are of opinion that Mr. Keill, in
asserting the same, has been no ways injurious to
Mr. Leibnitz. And we submit to the judgment of
the society whether the extract and papers now presented
to you, together with what is extant to the
same purpose in Dr. Wallis’s third volume, may not
deserve to be made public.”
This report being read, the society unanimously
ordered the collection of letters and manuscripts to
be printed, and appointed Dr. Halley, Mr. Jones, and
Mr. Machin to superintend the press. Complete
copies of it, under the title of Commercium Epistolicum
D. Johannis Collins et aliorum de analysi promota,
were laid before the society on the 8th January, 1713,
and Sir Isaac Newton, as president, ordered a copy
to be delivered to each person of the committee appointed
for that purpose, to examine it before its
publication.
Leibnitz received information of the appearance
of the Commercium Epistolicum when he was at
Vienna; and “being satisfied,” as he expresses it,
“that it must contain malicious falsehoods, I did not
think proper to send for it by post, but wrote to M.
Bernouilli to give me his sentiments. M. Bernouilli
wrote me a letter dated at Basle, June 7th, 1713, in
which he said that it appeared probable that Sir Isaac
Newton had formed his calculus after having seen
mine.”67 This letter was published by a friend of
Leibnitz, with reflections, in a loose sheet entitled
Charta Volans, and dated July 29, 1713. It was
widely circulated without either the name of the
author, printer, or place of publication, and was
communicated to the Journal Literaire by another
friend of Leibnitz, who added remarks of his own,
and stated, that when Newton published the Principia
in 1687, he did not understand the true differential
method; and that he took his fluxions from Leibnitz.
In this state of the controversy, Mr. Chamberlayne
conceived the design of reconciling the two distinguished
philosophers; and in a letter dated April 28,
1714,68 he addressed himself to Leibnitz, who was
still at Vienna. In replying to this letter, Leibnitz
declared that he had given no occasion for the dispute;
“that Newton procured a book to be published,
which was written purposely to discredit him, and
sent it to Germany, &c. as in the name of the
society;” and he stated that there was room to doubt
whether Newton knew his invention before he had it of
him. Mr. Chamberlayne communicated this letter
to Sir Isaac Newton, who replied that Leibnitz had
attacked his reputation in 1705, by intimating that he
had borrowed from him the method of fluxions;
that if Mr. C. could point out to him any thing in
which he had injured Mr. Leibnitz, he would give
him satisfaction; that he would not retract things
which he knew to be true; and that he believed that
the Royal Society had done no injustice by the publication
of the Commercium Epistolicum.
The Royal Society, having learned that Leibnitz
complained of their having condemned him unheard,
inserted a declaration in their journals on the 20th
May, 1714, that they did not pretend that the report
of their committee should pass for a decision of the
society. Mr. Chamberlayne sent a copy of this to
Leibnitz, along with Sir Isaac’s letter, and Dr. Keill’s
answer to the papers inserted in the Journal Literaire.
After perusing these documents, M. Leibnitz
replied, “that Sir Isaac’s letter was written with
very little civility; that he was not in a humour
to put himself in a passion against such people;
that there were other letters among those of Oldenburg
and Collins which should have been published;
and that on his return to Hanover, he would be able
to publish a Commercium Epistolicum which would
be of service to the history of learning.” When
this letter was read to the Royal Society, Sir Isaac
remarked, that the last part of it injuriously accused
the society of having made a partial selection of
papers for the Commercium Epistolicum; that he
did not interfere in any way in the publication of
that work, and had even withheld from the committee
two letters, one from Leibnitz in 1693, and
another from Wallis in 1695, which were highly
favourable to his cause. He stated that he did not
think it right for M. Leibnitz himself, but that, if
he had letters to produce in his favour, that they
might be published in the Philosophical Transactions,
or in Germany.
About this time the Abbé Conti, a noble Venetian,
came to England. He was a correspondent of
Leibnitz, and in a letter which he had received soon
after his arrival,69 he enters upon his dispute with
Newton. He charges the English “with wishing
to pass for almost the only inventors.” He declares
“that Bernouilli had judged rightly in saying that
Newton did not possess before him the infinitesimal
characteristic and algorithm.” He remarks that
Newton preceded him only in series; and he confesses
that during his second visit to England, “Collins
showed him part of his correspondence,” or, as
he afterward expresses it, he saw “some of the letters
of Newton at Mr. Collins’s.” He then attacks
Sir Isaac’s philosophy, particularly his opinions
about gravity and vacuum, the intervention of God
for the preservation of his creatures; and he accuses
him of reviving the occult qualities of the schools.
But the most remarkable passage in this letter is
the following: “I am a great friend of experimental
philosophy, but Newton deviates much from it when
he pretends that all matter is heavy, or that each particle
of matter attracts every other particle.”
The above letter to the Abbé Conti was generally
shown in London, and came to be much talked of at
court, in consequence of Leibnitz having been privy
counsellor to the Elector of Hanover when that
prince ascended the throne of England. Many
persons of distinction, and particularly the Abbé
Conti, urged Newton to reply to Leibnitz’s letter,
but he resisted all their solicitations. One day,
however, King George I. inquired when Sir Isaac
Newton’s answer to Leibnitz would appear; and
when Sir Isaac heard this, he addressed a long reply
to the Abbé Conti, dated February 26th, O. S. 1715–16.
This letter, written with dignified severity, is
a triumphant refutation of the allegations of his adversary;
and the following passage deserves to be
quoted, as connected with that branch of the dispute
which relates to Leibnitz’s having seen part of
Newton’s letters to Mr. Collins. “He complains
of the committee of the Royal Society, as if they
had acted partially in omitting what made against
me; but he fails in proving the accusation. For he
instances in a paragraph concerning my ignorance,
pretending that they omitted it, and yet you will
find it in the Commercium Epistolicum, p. 547, lines
2, 3, and I am not ashamed of it. He saith that he
saw this paragraph in the hands of Mr. Collins when
he was in London the second time, that is in October,
1676. It is in my letter of the 24th of October,
1676, and therefore he then saw that letter. And
in that and some other letters writ before that time,
I described my method of fluxions; and in the same
letter I described also two general methods of series,
one of which is now claimed from me by Mr. Leibnitz.”
The letter concludes with the following
paragraph: “But as he has lately attacked me with
an accusation which amounts to plagiary; if he goes
on to accuse me, it lies upon him by the laws of all
nations to prove his accusations, on pain of being
accounted guilty of calumny. He hath hitherto
written letters to his correspondents full of affirmations,
complaints, and reflections, without proving
any thing. But he is the aggressor, and it lies upon
him to prove the charge.”
In transmitting this letter to Leibnitz, the Abbé
Conti informed him that he himself had read with
great attention, and without the least prejudice, the
Commercium Epistolicum, and the little piece70 that
contains the extract; that he had also seen at the
Royal Society the original papers of the Commercium
Epistolicum, and some other original pieces
relating to it. “From all this,” says he, “I infer,
that, if all the digressions are cut off, the only point
is, whether Sir Isaac Newton had the method of
fluxions or infinitesimals before you, or whether you
had it before him. You published it first, it is true,
but you have owned also that Sir Isaac Newton had
given many hints of it in his letters to Mr. Oldenburg
and others. This is proved very largely in the
Commercium, and in the extract of it. What answer
do you give? This is still wanting to the
public, in order to form an exact judgment of the
affair.” The Abbé adds, that Mr. Leibnitz’s own
friends waited for his answer with great impatience,
and that they thought he could not dispense with
answering, if not Dr. Keill, at least Sir Isaac Newton
himself, who had given him a defiance in express
terms.
Leibnitz was not long in complying with this
request. He addressed a letter to the Abbé Conti,
dated April 9th, 1716, but he sent it through M. Ramond
at Paris, to communicate it to others. When
it was received by the Abbé Conti, Newton wrote
observations upon it, which were communicated
only to some of his friends, and which, while they
placed his defence on the most impregnable basis,
at the same time threw much light on the early history
of his mathematical discoveries.
The death of Leibnitz on the 14th November,
1716, put an end to this controversy, and Newton
some time afterward published the correspondence
with the Abbé Conti, which had hitherto been only
privately circulated among the friends of the disputants.71
In 1722, a new edition of the Commercium Epistolicum
was published, and there was prefixed to it
a general review of its contents, which has been
falsely ascribed to Newton.72 When the third edition
of the Principia was published in 1725, the
celebrated scholium which we have already quoted,
and in which Leibnitz’s differential calculus was
mentioned, was struck out either by Newton or by
the editor. This step was perhaps rash and ill-advised;
but as the scholium had been adduced by
Leibnitz and others as a proof that Newton acknowledged
him to be an independent inventor of the
calculus,—an interpretation which it does not bear,
and which Newton expressly states he never intended
it to bear,—he was justified in withdrawing
a passage which had been so erroneously interpreted,
and so greatly misapplied.
In viewing this controversy, at the distance of
more than a century, when the passions of the individual
combatants have been allayed, and national
jealousies extinguished, it is not difficult to form a
correct estimate of the conduct and claims of the
two rival analysts. By the unanimous verdict of
all nations, it has been decided that Newton invented
fluxions at least ten years before Leibnitz. Some
of the letters of Newton which bore reference to
this great discovery were perused by the German
mathematician; but there is no evidence whatever
that he borrowed his differential calculus from these
letters. Newton was therefore the first inventor,
and Leibnitz the second. It was impossible that the
former could have been a plagiarist; but it was
possible for the latter. Had the letters of Newton
contained even stronger indications than they do of
the new calculus, no evidence short of proof could
have justified any allegation against Leibnitz’s
honour. The talents which he displayed in the improvement
of the calculus showed that he was
capable of inventing it; and his character stood
sufficiently high to repel every suspicion of his integrity.
But if it would have been criminal to
charge Leibnitz with plagiarism, what must we
think of those who dared to accuse Newton of borrowing
his fluxions from Leibnitz? This odious
accusation was made by Leibnitz himself, and by
Bernouilli; and we have seen that the former repeated
it again and again, as if his own good name
rested on the destruction of that of his rival. It was
this charge against Newton that gave rise to the attack
of Keill, and the publication of the Commercium
Epistolicum; and, notwithstanding this high provocation,
the committee of the Royal Society contented
themselves with asserting Newton’s priority, without
retorting the charge of plagiarism upon his rival.
Although an attempt has been recently made to
place the conduct of Leibnitz on the same level with
that of Newton, yet the circumstances of the case
will by no means justify such a comparison. The
conduct of Newton was at all times dignified and
just. He knew his rights, and he boldly claimed
them. Conscious of his integrity, he spurned with
indignation the charge of plagiarism with which an
ungenerous rival had so insidiously loaded him; and
if there was one step in his frank and unhesitating
procedure which posterity can blame it is his omission,
in the third edition of the Principia, of the
references to the differential calculus of Leibnitz.
This omission, however, was perfectly just. The
scholium which he had left out was a mere historical
statement of the fact, that the German mathematician
had sent him a method which was the same as
his own; and when he found that this simple assertion
had been held by Leibnitz and others as a recognition
of his independent claim to the invention,
he was bound either to omit it altogether, or to
enter into explanations which might have involved
him in a new controversy.
The conduct of Leibnitz was not marked with the
same noble lineaments. That he was the aggressor
is universally allowed. That he first dared to
breathe the charge of plagiarism against Newton,
and that he often referred to it, has been sufficiently
apparent; and when arguments failed him he had
recourse to threats—declaring that he would publish
another Commercium Epistolicum, though he had
no appropriate letters to produce. All this is now
matter of history; and we may find some apology
for it in his excited feelings, and in the insinuations
which were occasionally thrown out against the
originality of his discovery; but for other parts of
his conduct we seek in vain for an excuse. When
he assailed the philosophy of Newton in his letters
to the Abbé Conti, he exhibited perhaps only the
petty feelings of a rival; but when he dared to calumniate
that great man in his correspondence with
the Princess of Wales, by whom he was respected
and beloved; when he ventured to represent the
Newtonian philosophy as physically false, and as
dangerous to religion; and when he founded these
accusations on passages in the Principia and the
Optics glowing with all the fervour of genuine
piety, he cast a blot upon his name, which all his
talents as a philosopher, and all his virtues as a man,
will never be able to efface.
James II. attacks the Privileges of the University of Cambridge—Newton
chosen one of the Delegates to resist this Encroachment—He is
elected a Member of the Convention Parliament—Burning of his
Manuscripts—His supposed Derangement of Mind—View taken of
this by foreign Philosophers—His Correspondence with Mr. Pepys
and Mr. Locke at the time of his Illness—Mr. Millington’s Letter to
Mr. Pepys on the subject of Newton’s Illness—Refutation of the
Statement that he laboured under Mental Derangement.
From the year 1669, when Newton was installed
in the Lucasian chair, till 1695, when he ceased to
reside in Cambridge, he seems to have been seldom
absent from his college more than three or four
weeks in the year. In 1675, he received a dispensation
from Charles II. to continue in his fellowship
of Trinity College without taking orders, and we
have already seen in the preceding chapter how his
time was occupied till the publication of the Principia
in 1687.
An event now occurred which drew Newton from
the seclusion of his studies, and placed him upon the
theatre of public life. Desirous of re-establishing
the Catholic faith in its former supremacy, King
James II. had begun to assail the rights and privileges
of his Protestant subjects. Among other illegal
acts, he sent his letter of mandamus to the University
of Cambridge to order Father Francis, an ignorant
monk of the Benedictine order, to be received as
master of arts, and to enjoy all the privileges of this
degree, without taking the oaths of allegiance and
supremacy. The university speedily perceived the
consequences which might arise from such a measure.
Independent of the infringement of their rights
which such an order involved, it was obvious that
the highest interests of the university were endangered,
and that Roman Catholics might soon become
a majority in the convocation. They therefore
unanimously refused to listen to the royal order, and
they did this with a firmness of purpose which irritated
the despotic court. The king reiterated his
commands, and accompanied them with the severest
threatenings in case of disobedience. The Catholics
were not idle in supporting the views of the
sovereign. The honorary degree of M.A. which
conveys no civil rights to its possessor, having been
formerly given to the secretary of the ambassador
from Morocco, it was triumphantly urged that the
University of Cambridge had a greater regard for a
Mahometan than for a Roman Catholic, and was
more obsequious to the ambassador from Morocco
than to their own lawful sovereign. Though this
reasoning might impose upon the ignorant, it produced
little effect upon the members of the university.
A few weak-minded individuals, however,
were disposed to yield a reluctant consent to the
royal wishes. They proposed to confer the degree,
and at the same time to resolve that it should not in
future be regarded as a precedent. To this it was
replied, that the very act of submission in one case
would be a stronger argument for continuing the
practice than any such resolution would be against
its repetition. The university accordingly remained
firm in their original decision. The vice-chancellor
was summoned before the ecclesiastical commission
to answer for this act of contempt. Newton was
among the number of those who resisted the wishes
of the court, and he was consequently chosen one
of the nine delegates who were appointed to defend
the independence of the university. These delegates
appeared before the High Court. They maintained
that not a single precedent could be found to
justify so extraordinary a measure; and they showed
that Charles II. had, under similar circumstances,
been pleased to withdraw his mandamus. This
representation had its full weight, and the king was
induced to abandon his design.73
The part which Newton had taken in this affair,
and the high character which he now held in the
scientific world, induced his friends to propose him
as member of parliament for the university. He
was accordingly elected in 1688, though by a very
narrow majority,74 and he sat in the Convention
Parliament till its dissolution. In the year 1688
and 1689, Newton was absent from Cambridge during
the greater part of the year, owing, we presume, to
his attendance in parliament; but it appears from
the books of the University that from 1690 to 1695
he was seldom absent, and must therefore have
renounced his parliamentary duties.
During his stay in London he had no doubt experienced
the unsuitableness of his income to the new
circumstances in which he was placed, and it is
probable that this was the cause of the limitation
of his residence to Cambridge. His income was
certainly very confined, and but little suited to the
generosity of his disposition. Demands were doubtless
made upon it by some of his less wealthy relatives;
and there is reason to think that he himself,
as well as his influential friends, had been looking
forward to some act of liberality on the part of the
government.
An event however occurred which will ever form
an epoch in his history; and it is a singular circumstance,
that this incident has been for more than a
century unknown to his own countrymen, and has
been accidentally brought to light by the examination
of the manuscripts of Huygens. This event
has been magnified into a temporary aberration of
mind, which is said to have arisen from a cause
scarcely adequate to its production.
While he was attending divine service in a winter
morning, he had left in his study a favourite little
dog called Diamond. Upon returning from chapel
he found that it had overturned a lighted taper on
his desk, which set fire to several papers on which
he had recorded the results of some optical experiments.
These papers are said to have contained the
labours of many years, and it has been stated that
when Mr. Newton perceived the magnitude of his loss,
he exclaimed, “Oh, Diamond, Diamond, little do you
know the mischief you have done me!” It is a
curious circumstance that Newton never refers to
the experiments which he is said to have lost on this
occasion, and his nephew, Mr. Conduit, makes no
allusion to the event itself. The distress, however
which it occasioned is said to have been so deep as
to affect even the powers of his understanding.
This extraordinary effect was first communicated
to the world in the Life of Newton by M. Biot, who
received the following account of it from the celebrated
M. Van Swinden.
“There is among the manuscripts of the celebrated
Huygens a small journal in folio, in which
he used to note down different occurrences. It is
side ζ, No. 8, p. 112, in the catalogue of the library
of Leyden. The following extract is written by
Huygens himself, with whose handwriting I am well
acquainted, having had occasion to peruse several
of his manuscripts and autograph letters. ‘On the
29th May, 1694, M. Colin,75 a Scotsman, informed me
that eighteen months ago the illustrious geometer, Isaac
Newton, had become insane, either in consequence of
his too intense application to his studies, or from excessive
grief at having lost, by fire, his chymical laboratory
and several manuscripts. When he came to the
Archbishop of Cambridge, he made some observations
which indicated an alienation of mind. He was immediately
taken care of by his friends, who confined him to
his house and applied remedies, by means of which he
had now so far recovered his health that he began to understand
the Principia.’” Huygens mentioned this circumstance
to Leibnitz, in a letter dated 8th June,
1694, to which Leibnitz replies in a letter dated the
23d, “I am very glad that I received information of
the cure of Mr. Newton, at the same time that I first
heard of his illness, which doubtless must have been
very alarming. ‘It is to men like you and him, sir,
that I wish a long life.’”
The first publication of the preceding statement
produced a strong sensation among the friends and
admirers of Newton. They could not easily believe
in the prostration of that intellectual strength which
had unbarred the strongholds of the universe. The
unbroken equanimity of Newton’s mind, the purity
of his moral character, his temperate and abstemious
life, his ardent and unaffected piety, and the weakness
of his imaginative powers, all indicated a mind
which was not likely to be overset by any affliction
to which it could be exposed. The loss of a few
experimental records could never have disturbed the
equilibrium of a mind like his. If they were the
records of discoveries, the discoveries themselves
indestructible would have been afterward given to
the world. If they were merely the details of experimental
results, a little time could have easily
reproduced them. Had these records contained the
first fruits of early genius—of obscure talent, on
which fame had not yet shed its rays, we might have
supposed that the first blight of such early ambition
would have unsettled the stability of an untried
mind. But Newton was satiated with fame. His
mightiest discoveries were completed and diffused
over all Europe, and he must have felt himself
placed on the loftiest pinnacle of earthly ambition.
The incredulity which such views could not fail to
encourage was increased by the novelty of the information.
No English biographer had ever alluded
to such an event. History and tradition were equally
silent, and it was not easy to believe that the Lucasian
Professor of Mathematics at Cambridge, a member
of the English parliament, and the first philosopher
in Europe could have lost his reason without
the dreadful fact being known to his own countrymen.
But if the friends of Newton were surprised by
the nature of the intelligence, they were distressed
at the view which was taken of it by foreign philosophers.
While one maintained that the intellectual
exertions of Newton had terminated with the publication
of the Principia, and that the derangement of
his mind was the cause of his abandoning the sciences,
others indirectly questioned the sincerity of
his religious views, and ascribed to the aberration
of his mind those theological pursuits which gilded
his declining age. “But the fact,” says M. Biot,
“of the derangement of his intellect, whatever may
have been the cause of it, will explain why, after the
publication of the Principia in 1687, Newton, though
only forty-five years old, never more published a
new work on any branch of science, but contented
himself with giving to the world those which he had
composed long before that epoch, confining himself
to the completion of those parts which might require
development. We may also remark, that even
these developments appear always to be derived
from experiments and observations formerly made,
such as the additions to the second edition of the
Principia, published in 1713, the experiments on
thick plates, those on diffraction, and the chymical
queries placed at the end of the Optics in 1704; for
in giving an account of these experiments Newton
distinctly says that they were taken from ancient
manuscripts which he had formerly composed; and
he adds, that though he felt the necessity of extending
them, or rendering them more perfect, he was
not able to resolve to do this, these matters being no
longer in his way. Thus it appears that though he
had recovered his health sufficiently to understand
all his researches, and even in some cases to make
additions to them, and useful alterations, as appears
from the second edition of the Principia, for which
he kept up a very active mathematical correspondence
with Mr. Cotes, yet he did not wish to undertake
new labours in those departments of science
where he had done so much, and where he so distinctly
saw what remained to be done.” Under the
influence of the same opinion, M. Biot finds “it extremely
probable that his dissertation on the scale
of heat was written before the fire in his laboratory;”
he describes Newton’s conduct about the longitude
bill as “almost puerile on so solemn an occasion,
and one which might lead to the strangest conclusions,
particularly if we refer it to the fatal accident
which Newton had suffered in 1695.”
The celebrated Marquis de la Place viewed the
illness of Newton in a light still more painful to his
friends. He maintained that he never recovered the
vigour of his intellect, and he was persuaded that
Newton’s theological inquiries did not commence
till after that afflicting epoch of his life. He even
commissioned Professor Gautier of Geneva to make
inquiries on this subject during his visit to England,
as if it concerned the interests of truth and justice
to show that Newton became a Christian and a
theological writer only after the decay of his
strength and the eclipse of his reason.
Such having been the consequences of the disclosure
of Newton’s illness by the manuscript of
Huygens, I felt it to be a sacred duty to the memory
of that great man, to the feelings of his countrymen,
and to the interests of Christianity itself, to inquire
into the nature and history of that indisposition
which seems to have been so much misrepresented
and misapplied. From the ignorance of so extraordinary
an event which has prevailed for such a long
period in England, it might have been urged with
some plausibility that Huygens had mistaken the
real import of the information that was conveyed to
him; or that the Scotchman from whom he received
it had propagated an idle and a groundless rumour.
But we are, fortunately, not confined to this very
reasonable mode of defence. There exists at Cambridge
a manuscript journal written by Mr. Abraham
de la Pryme, who was a student in the university
while Newton was a fellow of Trinity. This manuscript
is entitled “Ephemeris Vitæ, or Diary of my
own Life, containing an account likewise of the most
observable and remarkable things that I have taken
notice of from my youth up hitherto.” Mr. de la
Pryme was born in 1671, and begins the diary in
1685. This manuscript is in the possession of his
collateral descendant, George Pryme, Esq., Professor
of Political Economy at Cambridge, to whom I
have been indebted for the following extract.
“1692, February 3d.—What I heard to-day I must
relate. There is one Mr. Newton (whom I have
very oft seen), Fellow of Trinity College, that is
mighty famous for his learning, being a most excellent
mathematician, philosopher, divine, &c. He
has been Fellow of the Royal Society these many
years; and among other very learned books and
tracts, he’s written one upon the mathematical principles
of philosophy, which has got him a mighty
name, he having received, especially from Scotland,
abundance of congratulatory letters for the same;
but of all the books that he ever wrote, there was
one of colours and light, established upon thousands
of experiments which he had been twenty years of
making, and which had cost him many hundred of
pounds. This book, which he valued so much, and
which was so much talked of, had the ill luck to
perish and be utterly lost just when the learned
author was almost at putting a conclusion at the
same, after this manner: In a winter’s morning,
leaving it among his other papers on his study table
while he went to chapel, the candle, which he had
unfortunately left burning there too, catched hold
by some means of other papers, and they fired the
aforesaid book, and utterly consumed it and several
other valuable writings; and, which is most wonderful,
did no further mischief. But when Mr. Newton
came from chapel, and had seen what was done,
every one thought he would have run mad, he was
so troubled thereat that he was not himself for a
month after. A long account of this his system of
light and colours you may find in the Transactions
of the Royal Society, which he had sent up to them
long before this sad mischance happened unto him.”
From this extract we are enabled to fix the approximate
date of the accident by which Newton
lost his papers. It must have been previous to the
3d January, 1692, a month before the date of the
extract; but if we fix it by the dates in Huygens’s
manuscript, we should place it about the 29th November,
1692, eighteen months previous to the
conversation between Collins and Huygens. The
manner in which Mr. Pryme refers to Newton’s
state of mind is that which is used every day when
we speak of the loss of tranquillity which arises
from the ordinary afflictions of life; and the meaning
of the passage amounts to nothing more than that
Newton was very much troubled by the destruction
of his papers, and did not recover his serenity, and
return to his usual occupations, for a month. The
very phrase that “every person thought he would
have run mad” is in itself a proof that no such effect
was produced; and, whatever degree of indisposition
may be implied in the phrase “he was not
himself for a month after,” we are entitled to infer
that one month was the period of its duration, and
that previous to the 3d February, 1692, the date of Mr.
Pryme’s memorandum, “Newton was himself again.”
These facts and dates cannot be reconciled with
those in Huygens’s manuscript. It appears from
that document, that, so late as May, 1694, Newton
had only so far recovered his health as to begin
to again understand the Principia. His supposed
malady, therefore, was in force from the 3d of
January, 1692, till the month of May, 1694,—a
period of more than two years. Now, it is a most
important circumstance, which M. Biot ought to
have known, that in the very middle of this period,
Newton wrote his four celebrated letters to Dr.
Bentley on the Existence of a Deity,—letters which
evince a power of thought and a serenity of mind
absolutely incompatible even with the slightest obscuration
of his faculties. No man can peruse these
letters without the conviction that their author then
possessed the full vigour of his reason, and was
capable of understanding the most profound parts
of his writings. The first of these letters was written
on the 10th December, 1692, the second on the
17th January, 1693, the third on the 25th February,
and the 4th on the 11th76 February, 1693. His mind
was, therefore, strong and vigorous on these four
occasions; and as the letters were written at the
express request of Dr. Bentley, who had been appointed
to deliver the lecture founded by Mr. Boyle
for vindicating the fundamental principles of natural
and revealed religion, we must consider such a request
as showing his opinion of the strength and
freshness of his friend’s mental powers.
In 1692, Newton, at the request of Dr. Wallis,
transmitted to him the first proposition of his book
on quadratures, with examples of it in first, second,
and third fluxions.77 These examples were written
in consequence of an application from his friend;
and the author of the review of the Commercium
Epistolicum, in which this fact is quoted, draws the
conclusion, that he had not at that time forgotten
his method of second fluxions. It appears, also,
from the second book of the Optics,78 that in the
month of June, 1692, he had been occupied with the
subject of haloes, and had made accurate observations
both on the colours and the diameters of the rings
in a halo which he had then seen around the sun.
But though these facts stand in direct contradiction
to the statement recorded by Huygens, the
reader will be naturally anxious to know the real
nature and extent of the indisposition to which it
refers. The following letters,79 written by Newton
himself, Mr. Pepys, Secretary to the Admiralty, and
Mr. Millington of Magdalene College, Cambridge,
will throw much light upon the subject.
Newton, as will be presently seen, had fallen into
a bad state of health some time in 1692, in consequence
of which both his sleep and his appetite
were greatly affected. About the middle of September,
1693, he had been kept awake for five nights
by this nervous disorder, and in this condition he
wrote the following letter to Mr. Pepys:
Sept. 13, 1693.
“Sir,
“Some time after Mr. Millington had delivered
your message, he pressed me to see you the next
time I went to London. I was averse; but upon
his pressing consented, before I considered what I
did, for I am extremely troubled at the embroilment
I am in, and have neither ate nor slept well this
twelvemonth, nor have my former consistency of
mind. I never designed to get any thing by your
interest, nor by King James’s favour, but am now
sensible that I must withdraw from your acquaintance,
and see neither you nor the rest of my friends
any more, if I may but leave them quietly. I beg
your pardon for saying I would see you again, and
rest your most humble and most obedient servant,
“Is. Newton.”
From this letter we learn, on his own authority,
that his complaint had lasted for a twelvemonth,
and that during that twelvemonth he neither ate nor
slept well, nor enjoyed his former consistency of
mind. It is not easy to understand exactly what is
meant by not enjoying his former consistency of
mind; but whatever be its import, it is obvious that
he must have been in a state of mind so sound as to
enable him to compose the four letters to Bentley,
all of which were written during the twelvemonth
here referred to.
On the receipt of this letter, his friend Mr. Pepys
seems to have written to Mr. Millington of Magdalene
College to inquire after Mr. Newton’s health;
but the inquiry having been made in a vague manner,
an answer equally vague was returned. Mr.
Pepys, however, who seems to have been deeply
anxious about Newton’s health, addressed the following
more explicit letter to his friend Mr. Millington:—
Septemb. 26, 1693.
“Sir,
“After acknowledging your many old favours,
give me leave to do it a little more particularly upon
occasion of the new one conveyed to me by my
nephew Jackson. Though, at the same time, I
must acknowledge myself not at the ease I would
be glad to be at in reference to the excellent Mr.
Newton; concerning whom (methinks) your answer
labours under the same kind of restraint which (to
tell you the truth) my asking did. For I was loth
at first dash to tell you that I had lately received a
letter from him so surprising to me for the inconsistency
of every part of it, as to be put into great
disorder by it, from the concernment I have for him,
lest it should arise from that which of all mankind I
should least dread from him and most lament for,—I
mean a discomposure in head, or mind, or both. Let
me therefore beg you, sir, having now told you the true
ground of the trouble I lately gave you, to let me
know the very truth of the matter, as far at least as
comes within your knowledge. For I own too great
an esteem for Mr. Newton, as for a public good, to
be able to let any doubt in me of this kind concerning
him lie a moment uncleared, where I can have
any hopes of helping it. I am, with great truth and
respect, dear sir, your most humble, and most affectionate
servant,
“S. Pepys.”
To this letter Mr. Millington made the following
reply:—
Coll. Magd. Camb.
Sept. the 30, 1693.
“Honor’d Sir,
“Coming home from a journey on the 28th instant
at night, I met with your letter which you were
pleased to honour me with of the 26th. I am much
troubled I was not at home in time for the post,
that I might as soon as possible put you out of your
generous payne that you are in for the worthy Mr.
Newton. I was, I must confess, very much surprised
at the inquiry you were pleased to make by your
nephew about the message that Mr. Newton made
the ground of his letter to you, for I was very sure
I never either received from you or delivered to him
any such, and therefore I went immediately to wayt
upon him, with a design to discourse him about the
matter, but, he was out of town, and since I have
not seen him, till upon the 28th I met him at Huntingdon,
where, upon his own accord, and before I
had time to ask him any question, he told me that
he had writt to you a very odd letter, at which he
was much concerned; added, that it was in a distemper
that much seized his head, and that kept him
awake for above five nights together, which upon
occasion he desired I would represent to you, and
beg your pardon, he being very much ashamed, he
should be so rude to a person for whom he hath so
great an honour. He is now very well, and, though
I fear he is under some small degree of melancholy,
yet I think there is no reason to suspect it hath at
all touched his understanding, and I hope never will;
and so I am sure all ought to wish that love learning
or the honour of our nation, which it is a sign how
much it is looked after, when such a person as Mr. Newton
lyes so neglected by those in power. And thus, honoured
sir, I have made you acquainted with all I
know of the cause of such inconsistencys in the
letter of so excellent a person; and I hope it will
remove the doubts and fears you are, with so much
compassion and publickness of spirit, pleased to
entertain about Mr. Newton; but if I should have
been wanting in any thing tending to the more full
satisfaction, I shall, upon the least notice, endeavour
to amend it with all gratitude and truth.
Honored sir, your most faithfull and most obedient
servant,
“Joh. Millington.”
Mr. Pepys was perfectly satisfied with this answer,
as appears from the following letter:—
October 3d, 1693.
“Sir,
“You have delivered me from a fear that indeed
gave me much trouble, and from my very heart I
thank you for it; an evil to Mr. Newton being what
every good man must feel for his own sake as well
as his. God grant it may stopp here. And for the
kind reflection hee has since made upon his letter to
mee, I dare not take upon mee to judge what answer
I should make him to it, or whether any or no;
and therefore pray that you will bee pleased either
to bestow on mee what directions you see fitt for
my own guidance towards him in it, or to say to
him in my name, but your own pleasure, whatever
you think may be most welcome to him upon it,
and most expressive of my regard and affectionate esteem
of him, and concernment for him. * * *
Dear sir, your most humble and most faithful servant,
“S. Pepys.”
It does not appear from the memoirs of Mr.
Pepys whether he ever returned any answer to the
letter of Mr. Newton which occasioned this correspondence;
but we find that in less than two months
after the date of the preceding letter, an opportunity
occurred of introducing to him a Mr. Smith,
who wished to have his opinion on some problem in
the doctrine of chances. This letter from Pepys is
dated November 22d, 1693. Sir Isaac replied to it
on the 26th November, and wrote to Pepys again
on the 16th December, 1693; and in both these
letters he enters fully into the discussion of the
mathematical question which had been submitted to
his judgment.80
It is obvious, from Newton’s letter to Mr. Pepys,
that the subject of his receiving some favour from
the government had been a matter of anxiety with
himself, and of discussion among his friends.81 Mr.
Millington was no doubt referring to this anxiety,
when he represents Newton as an honour to the
nation, and expresses his surprise “that such a person
should lye so neglected by those in power.” And
we find the same subject distinctly referred to in
two letters written to Mr. Locke during the preceding
year. In one of these, dated January 26th,
1691–2, he says, “Being fully convinced that Mr.
Montague, upon an old grudge which I thought had
been worn out, is false to me, I have done with him,
and intend to sit still, unless my Lord Monmouth be
still my friend.” Mr. Locke seems to have assured
him of the continued friendship of this nobleman,
and Mr. Newton, still referring to the same topic,
in a letter dated February 16th, 1691–2, remarks,
“I am very glad Lord Monmouth is still my friend,
but intend not to give his lordship and you any farther
trouble. My inclinations are to sit still.” In
a later letter to Mr. Locke, dated September, 1693,
and given below, he asks his pardon for saying or
thinking that there was a design to sell him an
office. In these letters Mr. Newton no doubt referred
to some appointment in London which he was
solicitous to obtain, and which Mr. Montague and
his other friends may have failed in procuring.
This opinion is confirmed by the letter of Mr. Montague
announcing to him his appointment to the
wardenship of the mint, in which he says that he is
very glad he can at last give him good proof of his
friendship.
In the same month in which Newton wrote to Mr.
Pepys, we find him in correspondence with Mr.
Locke. Displeased with his opinions respecting
innate ideas, he had rashly stated that they struck
at the root of all morality; and that he regarded
the author of such doctrines as a Hobbist. Upon
reconsidering these opinions, he addressed the following
remarkable letter to Locke, written three
days after his letter to Mr. Pepys, and consequently
during the illness under which he then
laboured.
“Sir,
“Being of opinion that you endeavoured to embroil
me with women, and by other means, I was so
much affected with it, as that when one told me you
were sickly and would not live, I answered, ’twere
better if you were dead. I desire you to forgive me
this uncharitableness; for I am now satisfied that
what you have done is just, and I beg your pardon
for my having hard thoughts of you for it, and for
representing that you struck at the root of morality,
in a principle you laid in your book of ideas, and
designed to pursue in another book, and that I took
you for a Hobbist.82 I beg your pardon also for
saying or thinking that there was a design to sell me
an office, or to embroil me.—I am your most humble
and unfortunate servant,
“Is. Newton.
“At the Bull, in Shoreditch, London,
Sept. 16th, 1693.”
To this letter Locke returned the following answer,
so nobly distinguished by philosophical magnanimity
and Christian charity:—
Oates, Oct. 5th, 1693.
“Sir,
“I have been, ever since I first knew you, so entirely
and sincerely your friend, and thought you so
much mine, that I could not have believed what you
tell me of yourself had I had it from anybody else.
And, though I cannot but be mightily troubled that
you should have had so many wrong and unjust
thoughts of me, yet next to the return of good
offices, such as from a sincere good-will I have ever
done you, I receive your acknowledgment of the
contrary as the kindest thing you have done me,
since it gives me hopes I have not lost a friend I so
much valued. After what your letter expresses, I
shall not need to say any thing to justify myself to
you. I shall always think your own reflection on
my carriage, both to you and all mankind, will sufficiently
do that. Instead of that, give me leave to
assure you that I am more ready to forgive you than
you can be to desire it; and I do it so freely and fully,
that I wish for nothing more than the opportunity
to convince you that I truly love and esteem you,
and that I have the same good-will for you as if
nothing of this had happened. To confirm this to
you more fully, I should be glad to meet you any
where, and the rather, because the conclusion of
your letter makes me apprehend it would not be
wholly useless to you. But whether you think it
fit or not, I leave wholly to you. I shall always be
ready to serve you to my utmost, in any way you
shall like, and shall only need your commands or
permission to do it.
“My book is going to press for a second edition;
and, though I can answer for the design with which
I write it, yet, since you have so opportunely given
me notice of what you have said of it, I should take
it as a favour if you would point out to me the
places that gave occasion to that censure, that, by
explaining myself better, I may avoid being mistaken
by others, or unawares doing the least prejudice
to truth or virtue. I am sure you are so much
a friend to them both, that, were you none to me, I
could expect this from you. But I cannot doubt but
you would do a great deal more than this for my
sake, who, after all, have all the concern of a friend
for you, wish you extremely well, and am, without
compliment, &c.”83
To this letter Newton made the following reply:—
“Sir,
“The last winter, by sleeping too often by my
fire, I got an ill habit of sleeping; and a distemper,
which this summer has been epidemical, put me
farther out of order, so that when I wrote to you, I
had not slept an hour a night for a fortnight together,
and for five days together not a wink. I remember
I wrote to you, but what I said of your book I remember
not. If you please to send me a transcript
of that passage, I will give you an account of it if I
can.—I am your most humble servant,
“Is. Newton.
“Cambridge, Oct. 5th, 1693.”
Although the first of these letters evinces the
existence of a nervous irritability which could not
fail to arise from want of appetite and of rest, yet it
is obvious that its author was in the full possession
of his mental powers. The answer of Mr. Locke,
indeed, is written upon that supposition; and it deserves
to be remarked, that Mr. Dugald Stewart,
who first published a portion of these letters, never
imagines for a moment that Newton was labouring
under any mental alienation.
The opinion entertained by Laplace, that Newton
devoted his attention to theology only in the latter
part of his life, may be considered as deriving some
countenance from the fact, that the celebrated general
scholium at the end of the second edition of the
Principia, published in 1713, did not appear in the
first edition of that work. This argument has been
ably controverted by Dr. J. C. Gregory of Edinburgh,
on the authority of a manuscript of Newton, which
seems to have been transmitted to his ancestor, Dr.
David Gregory, between the years 1687 and 1698.
This manuscript, which consists of twelve folio
pages in Newton’s handwriting, contains, in the
form of additions and scholia to some propositions
in the third book of the Principia, an account of the
opinions of the ancient philosophers on gravitation
and motion, and on natural theology, with various
quotations from their works. Attached to this
manuscript are three very curious paragraphs. The
first two appear to have been the original draught
of the general scholium already referred to; and
the third relates to the subject of an ethereal medium,
respecting which he maintains an opinion
diametrically opposite to that which he afterward
published at the end of his Optics.84 The first paragraph
expresses nearly the same ideas as some
sentences in the scholium beginning “Deus summus
est ens æternum, infinitum, absolute perfectum;”85
and it is remarkable that the second paragraph is
found only in the third edition of the Principia,
which appeared in 1726, the year before Newton’s
death.
In the middle of the year 1694, about the time
when our author is said to be beginning to understand
the Principia, we find him occupied with the
difficult and profound subject of the lunar theory.
In order to procure observations for verifying the
equations which he had deduced from the theory of
gravity, he paid a visit to Flamstead, at the Royal
Observatory of Greenwich, on the 1st September,
1694, when he received from him a series of lunar
observations. On the 7th of October he wrote to
Flamstead that he had compared the observations
with his theory, and had satisfied himself that by
both together “the moon’s theory may be reduced
to a good degree of exactness, perhaps to the exactness
of two or three minutes.” He wrote him again
on the 24th October, and the correspondence was
continued till 1698, Newton making constant application
for observations to compare with his theory
of the planetary motions; while Flamstead, not sufficiently
aware of the importance of the inquiry, received
his requests as if they were idle intrusions in
which the interests of science were but slightly concerned.86
In reviewing the details which we have now given
respecting the health and occupations of Newton
from the beginning of 1692 till 1695, it is impossible
to draw any other conclusion than that he possessed
a sound mind, and was perfectly capable of carrying
on his mathematical, his metaphysical, and his astronomical
inquiries. His friend and admirer, Mr.
Pepys, residing within fifty miles of Cambridge, had
never heard of his being attacked with any illness
till he inferred it from the letter to himself written
in September, 1693. Mr. Millington, who lived in
the same university, had been equally unacquainted
with any such attack, and, after a personal interview
with Newton, for the express purpose of ascertaining
the state of his health, he assures Mr. Pepys
“that he is very well,—that he fears he is under
some small degree of melancholy, but that there is
no reason to suspect that it hath at all touched his
understanding.”
During this period of bodily indisposition, his
mind, though in a state of nervous irritability, and
disturbed by want of rest, was capable of putting
forth its highest powers. At the request of Dr.
Wallis he drew up an example of one of his propositions
on the quadrature of curves in second
fluxions. He composed, at the desire of Dr. Bentley,
his profound and beautiful letters on the existence
of the Deity. He was requested by Locke to reconsider
his opinions on the subject of innate ideas;
and we find him grappling with the difficulties of the
lunar theory.
But with all these proofs of a vigorous mind, a
diminution of his mental powers has been rashly
inferred from the cessation of his great discoveries,
and from his unwillingness to enter upon new investigations.
The facts, however, here assumed
are as incorrect as the inference which is drawn
from them. The ambition of fame is a youthful
passion, which is softened, if not subdued, by age.
Success diminishes its ardour, and early pre-eminence
often extinguishes it. Before the middle
period of life Newton was invested with all the
insignia of immortality; but endowed with a native
humility of mind, and animated with those hopes
which teach us to form an humble estimate of human
greatness, he was satisfied with the laurels which
he had won, and he sought only to perfect and complete
his labours. His mind was principally bent on
the improvement of the Principia; but he occasionally
diverged into new fields of scientific research,—he
solved problems of great difficulty which had
been proposed to try his strength,—and he devoted
much of his time to profound inquiries in chronology
and in theological literature.
The powers of his mind were therefore in full
requisition; and, when we consider that he was
called to the discharge of high official functions
which forced him into public life, and compelled
him to direct his genius into new channels, we can
scarcely be surprised that he ceased to produce any
original works on abstract science. In the direction
of the affairs of the mint, and of the Royal Society,
to which we shall now follow him, he found
ample occupation for his time; while the leisure of
his declining years was devoted to those exalted
studies in which philosophy yields to the supremacy
of faith, and hope administers to the aspirations of
genius.
No Mark of National Gratitude conferred upon Newton—Friendship
between him and Charles Montague, afterward Earl of Halifax—Mr.
Montague appointed Chancellor of the Exchequer in 1694—He resolves
upon a Recoinage—Nominates Mr. Newton Warden of the Mint in
1695—Mr. Newton appointed Master of the Mint in 1699—Notice of
the Earl of Halifax—Mr. Newton elected Associate of the Academy
of Sciences in 1699—Member for Cambridge in 1701—and President
of the Royal Society in 1703—Queen Anne confers upon him the
Honour of Knighthood in 1705—Second Edition of the Principia,
edited by Cotes—His Conduct respecting Mr. Ditton’s Method of finding
the Longitude.
Hitherto we have viewed Newton chiefly as a
philosopher leading a life of seclusion within the
walls of a college, and either engaged in the duties
of his professorship, or ardently occupied in mathematical
and scientific inquiries. He had now reached
the fifty-third year of his age, and while those of his
own standing at the university had been receiving
high appointments in the church, or lucrative offices
in the state, he still remained without any mark of
the respect or gratitude of his country. All Europe
indeed had been offering incense to his name, and
Englishmen themselves boasted of him as the pride
of their country and the ornament of their species,
but he was left in comparative poverty,87 with no
other income than the salary of his professorship,
eked out with the small rental of his paternal inheritance.
Such disregard of the highest genius,
dignified by the highest virtue, could have taken
place only in England, and we should have ascribed
it to the turbulence of the age in which he lived,
had we not seen, in the history of another century,
that the successive governments which preside over
the destinies of our country have never been able
either to feel or to recognise the true nobility of
genius.
Among his friends at Cambridge Newton had the
honour of numbering Charles Montague, grandson
of Henry Earl of Manchester, a young man of high
promise, and every way worthy of his friendship.
Though devoted to literary pursuits, and twenty
years younger than Newton, he cherished for the
philosopher all the veneration of a disciple, and his
affection for him gathered new strength as he rose
to the highest honours and offices of the state. In
the year 1684 we find him co-operating with Newton
in the establishment of a philosophical society at
Cambridge; but though both of them had made personal
application to different individuals to become
members, yet the plan failed, from the want, as
Newton expresses it, of persons willing to try experiments.
Mr. Montague sat along with Newton in the convention
parliament, and such were the powers which
he displayed in that assembly as a public speaker,
that he was appointed a commissioner of the treasury,
and soon afterward a privy counsellor. In these
situations his talents and knowledge of business
were highly conspicuous, and in 1694 he was appointed
chancellor of the exchequer. The current
coin of the nation having been adulterated and debased,
one of his earliest designs was to recoin it
and restore it to its intrinsic value. This scheme,
however, met with great opposition. It was characterized
as a wild project, unsuitable to a period
of war, as highly injurious to the interests of commerce,
and as likely to sap the foundation of the
government. But he had weighed the subject too
deeply, and had intrenched himself behind opinions
too impartial and too well-founded, to be driven from
a measure which the best interests of his country
seemed to require.
The persons whom Mr. Montague had consulted
about the recoinage were Newton, Locke, and Halley,
and in consequence of Mr. Overton, the warden
of the mint, having been appointed a commissioner
of customs, he embraced the opportunity which was
thus offered of serving his friend and his country by
recommending Newton to that important office.
The notice of this appointment was conveyed in the
following letter to Newton.
London, 19th March, 1695.
“Sir,
“I am very glad that, at last, I can give you a
good proof of my friendship, and the esteem the
king has of your merits. Mr. Overton, the warden
of the mint, is made one of the commissioners of
the customs, and the king has promised me to make
Mr. Newton warden of the mint. The office is the
most proper for you. ’Tis the chief office in the mint,
’tis worth five or six hundred pounds per annum, and
has not too much business to require more attendance
than you can spare. I desire that you will come up
as soon as you can, and I will take care of your
warrant in the mean time. Let me see you as soon
as you come to town, that I may carry you to kiss
the king’s hand. I believe you may have a lodging
near me.—I am, &c.
Charles Montague.”
In this new situation the mathematical and chymical
knowledge of our author was of great service
to the nation, and he became eminently useful in
carrying on the recoinage, which was completed in
the short space of two years. In the year 1699, he
was promoted to the mastership of the mint,—an
office which was worth twelve or fifteen hundred
pounds per annum, and which he held during the
remainder of his life. In this situation he wrote an
official report on the Coinage, which has been published;
and he drew up a table of Assays of Foreign
Coins, which is printed at the end of Dr. Arbuthnot’s
Tables of Ancient Coins, Weights, and Measures,
which appeared in 1727.
While our author filled the inferior office of warden
of the mint, he retained his professorship at Cambridge;
but upon his promotion in 1699, he appointed
Mr. Whiston to be his deputy, with all the emoluments
of the office; and when he resigned the chair
in 1703, he succeeded in getting him nominated his
successor.
The appointment of Newton to the mastership of
the mint must have been peculiarly gratifying to
the Royal Society, and it was probably from a feeling
of gratitude to Mr. Montague, as much as from
a regard for his talents, that this able statesman was
elected president of that learned body on the 30th
November, 1695. This office he held for three
years, and on the 30th January, 1697, Newton had
the satisfaction of addressing to him his solution of
the celebrated problems proposed by John Bernouilli.
This accomplished nobleman was created Earl of
Halifax in 1700, and after the death of his first wife
he conceived a strong attachment for Mrs. Catharine
Barton, the widow of Colonel Barton, and the niece
of Newton. This lady was young, gay, and beautiful,
and though she did not escape the censures of
her contemporaries, she was regarded by those who
knew her as a woman of strict honour and virtue.
We are not acquainted with the causes which prevented
her union with the Earl of Halifax, but so
great was the esteem and affection which he bore
her, that in the will in which he left 100l. to Mr.
Newton, he bequeathed to his niece a very large
portion of his fortune. This distinguished statesman
died in 1715, in the fifty-fourth year of his age.
Himself a poet and an elegant writer, he was the
liberal patron of genius, and he numbered among
his intimate friends Congreve, Halley, Prior, Tickell,
Steele, and Pope. His conduct to Newton will be
for ever remembered in the annals of science. The
sages of every nation and of every age will pronounce
with affection the name of Charles Montague, and
the persecuted science of England will continue to
deplore that he was the first and the last English
minister who honoured genius by his friendship and
rewarded it by his patronage.
The elevation of Mr. Newton to the highest offices
in the mint was followed by other marks of honour.
The Royal Academy of Sciences at Paris having
been empowered by a new charter granted in 1699,
to admit a very small number of foreign associates,
Newton was elected a member of that distinguished
body. In the year 1701, on the assembling of a new
parliament, he was re-elected one of the members
for the University of Cambridge.88 In 1703 he was
chosen President of the Royal Society of London,
and he was annually re-elected to this office during
the remaining twenty-five years of his life. On the
16th of April, 1705, when Queen Anne was living at
the royal residence of Newmarket, she went with
Prince George of Denmark and the rest of the court
to visit the University of Cambridge. After the
meeting of the Regia Consilia, her majesty held a
court at Trinity Lodge, the residence of Dr. Bentley,
then master of Trinity; where the honour of knighthood
was conferred upon Mr. Newton, Mr. John Ellis,
the vice-chancellor, and Mr. James Montague, the
university counsel.89
On the dissolution of the parliament, which took
place in 1705, Sir Isaac was again a candidate for
the representation of the University, but notwithstanding
the recent expression of the royal favour,
he lost his election by a very great majority.90
This singular result was perhaps owing to the loss
of that personal influence which his residence in the
university could not fail to command, though it is
more probable that the ministry preferred the candidates
of a more obsequious character, and that the
electors looked for advantages which Sir Isaac Newton
was not able to obtain for them.
Although the first edition of the Principia had been
for some time sold off, and copies of it had become
extremely rare, yet Sir Isaac’s attention was so
much occupied with his professional avocations that
he could not find leisure for preparing a new edition.
Dr. Bentley, who had repeatedly urged him to this
task, at last succeeded, by engaging Roger Cotes,
Plumian Professor of Astronomy at Cambridge, to
superintend its publication at the university press.
In June, 1709, Sir Isaac committed this important
trust to his young friend; and about the middle of
July he promised to send him in the course of a fortnight
his own revised copy of the work. Business,
however, seems to have intervened, and Mr. Cotes
was obliged to remind Sir Isaac of his promise, which
he did in the following letter:—
Cambridge, Aug. 18th, 1709.
“Sir,
“The earnest desire I have to see a new edition
of your Principia makes me somewhat impatient
till we receive your copy of it, which you were
pleased to promise me about the middle of last month
you would send down in about a fortnight’s time.
I hope you will pardon me for this uneasiness, from
which I cannot free myself, and for giving you this
trouble to let you know it. I have been so much
obliged by yourself and by your book, that (I desire
you to believe me) I think myself bound in gratitude
to take all the care I possibly can that it shall be
correct.—Your obliged servant,
“Roger Cotes.
“For Sir Isaac Newton, at his house in
Jermyn-street, near St. James’s
Church, Westminster.”
This was the first letter of that celebrated correspondence,
consisting of nearly three hundred letters,
in which Sir Isaac and Mr. Cotes discussed the various
improvements which were thought necessary in a
new edition of the Principia. This valuable collection
of letters is preserved in the library of Trinity
College; and we cannot refrain from repeating the
wish expressed by Dr. Monk, “that one of the many
accomplished Newtonians who are resident in that
society would favour the world by publishing the
whole collection.”
When the work was at last printed, Mr. Cotes expressed
a wish that Dr. Bentley should write the preface
to it, but it was the opinion both of Sir Isaac
and Dr. Bentley that the preface should come from
the pen of Mr. Cotes himself. This he accordingly
undertook; but previous to its execution he addressed
the following letter to Dr. Bentley, in order
to learn from Sir Isaac the particular view with
which it should be written.
March 10th, 1712–13.
“Sir,
“I received what you wrote to me in Sir Isaac’s
letter. I will set about the index in a day or two.
As for the preface, I should be glad to know from
Sir Isaac with what view he thinks proper to have
it written. You know the book has been received
abroad with some disadvantage, and the cause of it
may be easily guessed at. The Commercium Epistolicum,
lately published by order of the Royal Society,
gives such indubitable proofs of Mr. Leibnitz’s want of
candour, that I shall not scruple in the least to speak
out the full truth of the matter, if it be thought
convenient. There are some pieces of his looking
this way which deserve a censure, as his Tentamen
de motuum cælestium causis. If Sir Isaac is willing
that something of this nature may be done, I should
be glad if, while I am making the index, he would
consider of it, and put down a few notes of what he
thinks most material to be insisted on. This I say
upon supposition that I write the preface myself.
But I think it will be much more advisable that you,
or he, or both of you should write it while you are
in town. You may depend upon it I will own it,
and defend it as well as I can, if hereafter there be
occasion.—I am sir, &c.”
We are not acquainted with the instructions which
were given to Mr. Cotes in consequence of this application;
but it appears from the preface itself,
which contains a long and able summary of the Newtonian
philosophy, that Sir Isaac had prohibited any
personal reference to the conduct of Leibnitz.
The general preface is dated 12th May, 1713, and
in a subsidiary preface of only a few lines, dated
March 28th, 1713, Sir Isaac mentions the leading
alterations which had been made in this edition.
The determination of the forces by which bodies
may revolve in given orbits was simplified and enlarged.
The theory of the resistance of fluids was
more accurately investigated, and confirmed by new
experiments. The theory of the moon and the precession
of the equinoxes were more fully deduced
from their principles; and the theory of comets was
confirmed by several examples of their orbits more
accurately computed.
In the year 1714, several captains and owners of
merchant vessels petitioned the House of Commons
to consider the propriety of bringing in a bill to
reward inventions for promoting the discovery of
the longitude at sea. A committee was appointed to
investigate the subject, and Mr. Ditton and Mr.
Whiston, having thought of a new method of finding
the longitude, submitted it to the committee. Four
members of the Royal Society, viz. Sir Isaac Newton,
Dr. Halley, Mr. Cotes, and Dr. Clarke, were
examined on the subject, along with Mr. Ditton and
Mr. Whiston. The last three of these philosophers
stated their opinions verbally. Mr. Cotes considered
the proposed scheme as correct in theory and on
shore, and both he and Dr. Halley were of opinion
that expensive experiments would be requisite.
Newton, when called upon for his opinion, read the
following memorandum, which deserves to be recorded.
“For determining the longitude at sea there have
been several projects, true in theory, but difficult to
execute.
“1. One is by a watch to keep time exactly; but
by reason of the motion of the ship, the variation
of heat and cold, wet or dry, and the difference of
gravity in different latitudes, such a watch hath not
yet been made.
“2. Another is by the eclipses of Jupiter’s satellites;
but by reason of the length of telescopes
requisite to observe them, and the motion of a ship
at sea, those eclipses cannot yet be there observed.
“3. A third is by the place of the moon; but her
theory is not yet exact enough for that purpose; it
is exact enough to determine the longitude within
two or three degrees, but not within a degree.
“4. A fourth is Mr. Ditton’s project, and this is
rather for keeping an account of the longitude at
sea than for finding it, if at any time it should be
lost, as it may easily be in cloudy weather. How far
this is practicable, and with what charge, they that
are skilled in sea affairs are best able to judge. In
sailing by this method, whenever they are to pass
over very deep seas, they must sail due east or west;
they must first sail into the latitude of the next place
to which they are going beyond it, and then keep
due east or west till they come at that place. In
the first three ways there must be a watch regulated
by a spring, and rectified every visible sunrise and
sunset, to tell the hour of the day or night. In the
fourth way such a watch is not necessary. In the
first way there must be two watches, this and the
other above mentioned. In any of the first three
ways, it may be of some service to find the longitude
within a degree, and of much more service to find it
within forty minutes, or half a degree if it may, and
the success may deserve rewards accordingly. In
the fourth way, it is easier to enable seamen to
know their distance and bearing from the shore 40,
60, or 80 miles off, than to cross the seas; and some
part of the reward may be given when the first is
performed on the coast of Great Britain for the safety
of ships coming home; and the rest when seamen
shall be enabled to sail to an assigned remote harbour
without losing their longitude if it may be.”
The committee brought up their report on the 11th
June, and recommended that a bill should be introduced
into parliament for the purpose of rewarding
inventions or discoveries connected with the determination
of the longitude. The bill passed the
House of Commons on the 3d July, and was agreed
to by the Lords on the 8th of the same month.91
In giving an account of this transaction,92 Mr.
Whiston states, that nobody understood Sir Isaac’s
paper, and that after sitting down he obstinately
kept silence, though he was much pressed to explain
himself more distinctly. At last, seeing that the
scheme was likely to be rejected, Whiston ventured
to say that Sir Isaac did not wish to explain more
through fear of compromising himself, but that he
really approved of the plan. Sir Isaac, he goes on
to say, repeated word for word what Whiston had
said. This is the part of Mr. Newton’s conduct
which M. Biot has described as puerile, and “tending
to confirm the fact of the aberration of his intellect
in 1693.” Before we can admit such a censure
we must be satisfied with the correctness of Whiston’s
statement. Newton’s paper is perfectly intelligible,
and we may easily understand how he might
have approved of Mr. Ditton’s plan as ingenious and
practicable under particular circumstances, though
he did not think it of that paramount importance
which would have authorized the House of Commons
to distinguish it by a parliamentary reward.
The conflict between public duty and a disposition
to promote the interests of Mr. Whiston and Mr.
Ditton was no doubt the cause of that embarrassment
of manner which the former of these mathematicians
has so unkindly brought before the public.
Respect in which Newton was held at the Court of George I.—The Princess
of Wales delighted with his Conversation—Leibnitz endeavours
to prejudice the Princess against Sir Isaac and Locke—Controversy
occasioned by his Conduct—The Princess obtains a Manuscript Abstract
of his System of Chronology—The Abbé Conti is, at her request,
allowed to take a Copy of it on the promise of Secresy—He prints it
surreptitiously in French, accompanied with a Refutation by M. Freret—Sir
Isaac’s Defence of his System—Father Souciet attacks it—and
is answered by Dr. Halley—Sir Isaac’s larger Work on Chronology
published after his Death—Opinions respecting it—Sir Isaac’s Paper
on the Form of the most ancient Year.
On the accession of George I. to the British throne
in 1714, Sir Isaac Newton became an object of interest
at court. His high situation under government,
his splendid reputation, his spotless character,
and, above all, his unaffected piety attracted
the attention of the Princess of Wales, afterward
queen-consort to George II. This lady, who possessed
a highly cultivated mind, derived the greatest
pleasure from conversing with Newton and corresponding
with Leibnitz. In all her difficulties, she
received from Sir Isaac that information and assistance
which she had elsewhere sought in vain, and
she was often heard to declare in public that she
thought herself fortunate in living at a time which
enabled her to enjoy the conversation of so great a
genius. But while Newton was thus esteemed by
the house of Hanover, Leibnitz, his great rival, endeavoured
to weaken and undermine his influence.
In his correspondence with the princess, he represented
the Newtonian philosophy, not only as physically
false, but as injurious to the interests of
religion. He asserted that natural religion was
rapidly declining in England, and he supported this
position by referring to the works of Locke, and to
the beautiful and pious sentiments contained in the
28th query at the end of the Optics. He represented
the principles of these great men as precisely the
same with those of the materialists, and thus endeavoured
to degrade the character of English philosophers.
These attacks of Leibnitz became subjects of conversation
at court, and when they reached the ear of
the king, his majesty expressed his expectation that
Sir Isaac Newton would draw up a reply. He accordingly
entered the lists on the mathematical part
of the controversy, and left the philosophical part
of it to Dr. Clarke, who was a full match for the
German philosopher. The correspondence which
thus took place was carefully perused by the princess,
and from the estimation in which Sir Isaac
continued to be held, we may infer that the views of
the English philosopher were not very remote from
her own.
When Sir Isaac was one day conversing with her
royal highness on some points of ancient history,
he was led to mention to her, and to explain, a new
system of chronology which he composed during his
residence at Cambridge, where he was in the habit,
as he himself expresses it, “of refreshing himself
with history and chronology when he was weary
with other studies.” The princess was so much
pleased with his ingenious system, that she subsequently,
in the year 1718, sent a message by the Abbé
Conti to Sir Isaac, requesting him to speak with her,
and she, on this occasion, requested a copy of the
interesting work which contained his system of chronology.
Sir Isaac informed her that it existed merely
in separate papers, which were not only in a state
of confusion, but which contained a very imperfect
view of the subject, and he promised, in a few days,
to draw up an abstract of it for her own private use,
and on the condition that it should not be communicated
to any other person. Some time after the
princess received the manuscript, she requested that
the Abbé Conti might be allowed to have a copy of
it. Sir Isaac granted this request, and the Abbé was
informed that he received a copy of the manuscript
with Sir Isaac’s leave, and at the princess’s request,
and that it was to be kept secret.93 The manuscript
which was thus rashly put into the hands of a
foreigner was entitled “A Short Chronicle from the
First Memory of Things in Europe to the Conquest
of Persia by Alexander the Great.” It consists of
about twenty-four quarto printed pages,94 with an
introduction of four pages, in which Sir Isaac states
that he “does not pretend to be exact to a year, that
there may be errors of five or ten years, and sometimes
twenty, but not much above.”
The Abbé Conti kept his promise of secrecy during
his residence in England, but he no sooner reached
Paris than he communicated it to M. Freret, a
learned antiquarian, who not only translated it, but
drew up observations upon it for the purpose of refuting
some of its principal results. Sir Isaac was
unacquainted with this transaction till he was informed
of it by the French bookseller, M. Cavalier,
who requested his leave to publish it, and charged
one of his friends in London to procure Sir Isaac’s
answer, which was as follows:—
“I remember that I wrote a Chronological index
for a particular friend, on condition that it should not
be communicated. As I have not seen the manuscript
which you have under my name, I know not
whether it be the same. That which I wrote was
not at all done with design to publish it. I intend
not to meddle with that which hath been given you
under my name, nor to give any consent to the publishing
of it.—I am your very humble servant,
“Isaac Newton.
“London, May 27th, 1725, O. S.”
Before this letter was written, viz. on the 21st
May, the bookseller had received the royal privilege
for printing the work; and when it was completed,
he sent a copy in a present to Sir Isaac, who received
it on the 11th November, 1725. It was entitled,
Abregé de Chronologie de M. Le Chevalier Newton,
fait par lui-meme, et traduit sur le manuscript Anglais,
and was accompanied with observations by M. Freret,95
the object of which was to refute the leading
points of the system.96 An advertisement was prefixed
to it, in which the bookseller defends himself
for printing it without the author’s leave, on the
ground that he had written three letters to obtain
permission, and had declared that he would take Sir
Isaac’s silence for consent. When Sir Isaac received
this work, he drew up a paper entitled, Remarks on
the Observations made on a Chronological Index of Sir
Isaac Newton, translated into French by the Observator,
and published at Paris, which was printed in the Philosophical
Transactions for 1725.97 In this paper Sir
Isaac gives a history of the transaction,—charges
the Abbé Conti with a breach of promise, and blames
the publisher for having asked his leave to print the
translation without sending him a copy for his perusal,
without acquainting him with the name of the
translator, and without announcing his intention of
printing along with it a refutation of the original.
The observations made by the translator against the
conclusions deduced by the author were founded on
an imperfect knowledge of Sir Isaac’s system; and
they are so specious, that Halley himself confesses
that he was at first prejudiced in favour of the observations,
taking the calculations for granted, and not
having seen Sir Isaac’s work.
To all the observations of M. Freret Sir Isaac returned
a triumphant answer. This presumptuous
antiquary had ventured to state at the end of his
observations, “that he believed he had stated enough
concerning the epochs of the Argonauts, and the
length of generations, to make people cautious about
the rest; for these are the two foundations of all this
new system of chronology.” He founds his arguments
against the epochs of the Argonauts, as fixed
by our author, on the supposition that Sir Isaac
places the vernal equinox at the time of the Argonautic
expedition in the middle of the sign of Aries,
whereas Sir Isaac places it in the middle of the constellation,—a
point corresponding with the middle of
the back of Aries, or 8° from the first star of Aries.
This position of the colure is assigned on the authority
of Eudoxus, as given by Hipparchus, who says
that the colure passed over the back of Aries. Setting
out with this mistake, M. Freret concludes that
the Argonautic expedition took place 532 years
earlier than Sir Isaac made it. His second objection
to the new system relates to the length of generations,
which he says is made only 18 or 20 years.
Sir Isaac, on the contrary, reckons a generation at
33 years, or 3 generations at 100; and it was the
lengths of the reigns of kings that he made 18 or 20
years. This deduction he founds on the reigns of
64 French kings. Now, the ancient Greeks and
Egyptians reckoned the length of a reign equal to
that of a generation; and it was by correcting this
mistake, and adopting a measure founded on fact,
that Sir Isaac placed the Argonautic expedition forty-four
years after the death of Solomon, and fixed some
of the other points of his system.
This answer of Sir Isaac’s to the objections of
Freret called into the field a fresh antagonist, Father
Souciet, who published five dissertations on the new
chronology. These dissertations were written in
a tone highly reprehensible; and the friends of Sir
Isaac, being apprehensive that the manner in which
his system was attacked would affect him more than
the arguments themselves, prevailed upon a friend to
draw up an abstract of Souciet’s objections, stripped
of the “extraordinary ornaments with which they
were clothed.” The perusal of these objections had
no other effect upon him than to convince him of
the ignorance of their author; and he was induced
to read the entire work, which produced no change
in his opinion.
In consequence of these discussions, Sir Isaac
was prevailed upon to prepare his larger work for
the press. He had nearly completed it at the time
of his death, and it was published in 1728, under the
title of The Chronology of Ancient Kingdoms amended,
to which is prefixed a short Chronicle, from the first
memory of Things in Europe to the Conquest of Persia
by Alexander the Great. It was dedicated to the
queen by Mr. Conduit, and consists of six chapters:
1. On the Chronology of the Greeks;98 2. Of the
Empire of Egypt; 3. Of the Assyrian Empire; 4.
Of the two contemporary Empires of the Babylonians
and Medes; 5. A Description of the Temple
of Solomon; 6. Of the Empire of the Persians.
The sixth chapter was not copied out with the other
five, which makes it doubtful whether or not it was
intended for publication; but as it was found among
his papers, and appeared to be a continuation of the
same work, it was thought right to add it to the
other five chapters.99
After the death of Newton, Dr. Halley, who had
not yet seen the larger work, felt himself called upon,
both as astronomer-royal and as the friend of the
author, to reply to the first and last dissertations of
Father Souciet, which were chiefly astronomical;
and in two papers printed in the Philosophical Transactions
for 1727,100 he has done this in a most convincing
and learned argument.
Among the supporters of the views of Newton,
we may enumerate Dr. Reid, Nauze, and some other
writers; and among its opponents, M. Freret, who
left behind him a posthumous work on the subject,
M. Fourmond, Mr. A. Bedford, Dr. Shuckford, Dr.
Middleton, Whiston, and the late M. Delambre. The
object of M. Fourmond is to show the uncertainty
of the astronomical argument, arising on the one
hand from the vague account of the ancient sphere
as given by Hipparchus; and, on the other, from the
extreme rudeness of ancient astronomical observations.
Delambre has taken a similar view of the
subject: he regards the observations of ancient
astronomers as too incorrect to form the basis of a
system of chronology; and he maintains, that if we
admit the accuracy of the details in the sphere of
Eudoxus, and suppose them all to belong to the
same epoch, all the stars which it contains ought at
that epoch to be found in the place where they are
marked, and we might thence verify the accuracy,
and ascertain the state of the observations. It follows,
however, from such an examination, that the
sphere would indicate almost as many different
epochs as it contains stars. Some of them even
had not, in the time of Eudoxus, arrived at the position
which had been for a long time attributed to
them, and will not even reach it for three hundred
years to come, and on this account he considers it
impossible to deduce any chronological conclusions
from such a rude mass of errors.
But however well-founded these observations may
be, we agree in opinion with M. Daunou,101 “that
they are not sufficient to establish a new system,
and we must regard the system of Newton as a
great fact in the history of chronological science,
and as confirming the observation of Varro, that the
stage of history does not commence till the first
Olympiad.”
Among the chronological writings of Sir Isaac
Newton we must enumerate his letter to a person
of distinction who had desired his opinion of the learned
Bishop Lloyd’s hypothesis concerning the form of the
most ancient year. This hypothesis was sent by the
Bishop of Worcester to Dr. Prideaux. Sir Isaac
remarks, that it is filled with many excellent observations
on the ancient year; but he does not “find
it proved that any ancient nations used a year of
twelve months and 360 days without correcting it
from time to time by the luminaries, to make the
months keep to the course of the moon, and the year
to the course of the sun, and returns of the seasons
and fruits of the earth.” After examining the years
of all the nations of antiquity, he concludes, “that no
other years are to be met with among the ancients
but such as were either luni-solar, or solar or lunar,
or the calendars of these years.” A practical year,
he adds, of 360 days is none of these. The beginning
of such a year would have run round the four
seasons in seventy years, and such a notable revolution
would have been mentioned in history, and is
not to be asserted without proving it.102
Theological Studies of Sir Isaac—Their Importance to Christianity—Motives
to which they have been ascribed—Opinions of Biot and Laplace
considered—His Theological Researches begun before his supposed
Mental Illness—The Date of these Works fixed—Letters to Locke—Account
of his Observations on Prophecy—His Historical Account
of two notable Corruptions of Scripture—His Lexicon Propheticum—His
Four Letters to Dr. Bentley—Origin of Newton’s Theological
Studies—Analogy between the Book of Nature and that of Revelation.
The history of the theological studies of Sir Isaac
Newton will ever be regarded as one of the most
interesting portions of his life. That he who among
all the individuals of his species possessed the highest
intellectual powers was not only a learned and
profound divine, but a firm believer in the great doctrines
of religion, is one of the proudest triumphs
of the Christian faith. Had he distinguished himself
only by an external respect for the offices and
duties of religion; and had he left merely in his last
words an acknowledgment of his faith, his piety
would have been regarded as a prudent submission
to popular feeling, and his last aspirations would
have been ascribed to the decay or to the extinction
of his transcendent powers. But he had been a
Christian from his youth, and though never intended
for the church, yet he interchanged the study of the
Scriptures with that of the laws of the material
universe; and from the examination of the works
of the Supreme Creator he found it to be no abrupt
transition to investigate the revelation of his will,
and to contemplate the immortal destinies of mankind.
But when the religious habits of Sir Isaac Newton
could not be ascribed to an ambition of popularity,
to the influence of weak health, or to the force of
professional impulse, it became necessary for the
apostles of infidelity to refer it to some extraordinary
cause. His supposed insanity was therefore
eagerly seized upon by some as affording a plausible
origin for his religious principles; while others,
without any view of supporting the cause of skepticism,
ascribed his theological researches to the
habits of the age in which he lived, and to a desire
of promoting political liberty, by turning against the
abetters of despotism those powerful weapons which
the Scriptures supplied. The anxiety evinced by
M. de Laplace to refer his religious writings to a
late period of his life seems to have been felt also
by M. Biot, who has gone so far as to fix the very
date of one of his most important works, and thus
to establish the suspicions of his colleague.
“From the nature of the subject,”103 says he, “and
from certain indications which Newton seems to
give at the beginning of his dissertation, we may
conjecture with probability that he composed it at
the time when the errors of Whiston, and a work
of Dr. Clarke on the same subject, drew upon them
the attacks of all the theologians of England, which
would place the date between the years 1712 and
1719. It would then be truly a prodigy to remark,
that a man of from seventy-two to seventy-five
years of age was able to compose, rapidly, as he
leads us to believe, so extensive a piece of sacred
criticism, of literary history, and even of bibliography,
where an erudition the most vast, the most
varied, and the most ready always supports an argument
well arranged and powerfully combined. * * *
At this epoch of the life of Newton the reading of
religious books had become one of his most habitual
occupations, and after he had performed the duties
of his office, they formed, along with the conversation
of his friends, his principal amusement. He
had then almost ceased to care for the sciences, and,
as we have already remarked, since the fatal epoch
of 1693, he gave to the world only three really new
scientific productions.”
Notwithstanding the prodigy which it involves, M.
Biot has adopted 1712–1719 as the date of this critical
dissertation;—it is regarded as the composition
of a man of seventy-two or seventy-five;—the reading
of religious works is stated to have become one of
his most habitual occupations, and such reading is
said to have been one of his principal amusements;
and all this is associated with “the fatal epoch of
1693,” as if his illness at that time had been the
cause of his abandoning science and betaking himself
to theology. Carrying on the same views, M.
Biot asks, in reference to Sir Isaac’s work on Prophecy,
“How a mind of the character and force of
Newton’s, so habituated to the severity of mathematical
considerations, so exercised in the observation
of real phenomena, and so well aware of the
conditions by which truth is to be discovered, could
put together such a number of conjectures without
noticing the extreme improbability of his interpretations
from the infinite number of arbitrary postulates
on which he has founded them?” We would apply
the same question to the reasoning by which M. Biot
fixes the date of the critical dissertation; and we
would ask how so eminent a philosopher could hazard
such frivolous conjectures upon a subject on
which he had not a single fact to guide his inquiries.
The obvious tendency, though not the design, of the
conclusion at which he arrives is injurious to the
memory of Newton, as well as to the interests of
religion; and these considerations might have
checked the temerity of speculation, even if it had
been founded on better data. The Newtonian interpretation
of the Prophecies, and especially that part
which M. Biot characterizes as unhappily stamped
with the spirit of prejudice, has been adopted by men
of the soundest and most unprejudiced minds; and
in addition to the moral and historical evidence by
which it is supported, it may yet be exhibited in all
the fulness of demonstration. But the speculation
of Biot respecting the date of Newton’s theological
works was never maintained by any other person
than himself, and is capable of being disproved by
the most incontrovertible evidence.
We have already seen, in the extract from Mr.
Pryme’s manuscript, that previous to 1692, when a
shade is supposed to have passed over his gifted
mind, Newton was well known by the appellation
of an “excellent divine,”—a character which could
not have been acquired without the devotion of many
years to theological researches; but, important as
this argument would have been, we are fortunately
not left to so general a defence. The correspondence
of Newton with Locke, recently published by
Lord King, places it beyond a doubt that he had begun
his researches respecting the Prophecies before
the year 1691,—before the forty-ninth year of his
age, and before the “fatal epoch of 1693.” The
following letter shows that he had previously discussed
this subject with his friend:—
Cambridge, Feb. 7, 1690–1.
“Sir,
“I am sorry your journey proved to so little purpose,
though it delivered you from the trouble of the
company the day after. You have obliged me by
mentioning me to my friends at London, and I must
thank both you and my Lady Masham for your
civilities at Oates, and for not thinking that I made
a long stay there. I hope we shall meet again in
due time, and then I should be glad to have your
judgment upon some of my mystical fancies. The
Son of Man, Dan. vii. I take to be the same with the
Word of God upon the White Horse in Heaven,
Apoc. xii., for both are to rule the nations with a rod
of iron; but whence are you certain that the Ancient
of Days is Christ? Does Christ anywhere sit upon
the throne? If Sir Francis Masham be at Oates,
present, I pray, my service to him, with his lady,
Mrs. Cudworth, and Mrs. Masham. Dr. Covel is
not in Cambridge.—I am your affectionate and
humble servant,
“Is. Newton.
“Know you the meaning of Dan. x. 21. There
is none that holdeth with me in these things but
Mich. the prince.”
Having thus determined the date of those investigations
which constitute his observations on the prophecies
of holy writ, particularly the prophecies of
Daniel and the Apocalypse, we shall proceed to fix
the latest date of his historical account of two notable
corruptions of the Scripture, in a letter to a friend.
This work seems to have been a very early production
of our author. It was written in the form
of a letter to Mr. Locke, and at that time Sir Isaac
seems to have been anxious for its publication.
Afraid, however, of being again led into a controversy,
and dreading the intolerance to which he
might be exposed, he requested Mr. Locke, who
was at that time meditating a voyage to Holland,
to get it translated into French, and published on
the Continent. Having abandoned his design of
visiting Holland, Locke transmitted the manuscript,
without Newton’s name, to his learned friend M. Le
Clerc, in Holland; and it appears, from a letter of
Le Clerc’s to Locke, that he must have received it
before the 11th April, 1691. M. Le Clerc delayed
for a long time to take any steps regarding its publication;
but in a letter dated January 20th, 1692, he
announced to Locke his intention of publishing the
tract in Latin. When this plan was communicated
to Sir Isaac, he became alarmed at the risk of detection,
and resolved to stop the publication of his
manuscript. This resolution was intimated to Mr.
Locke in the following letter:
Cambridge, Feb. 16th, 1691–2.
“Sir,
“Your former letters came not to my hand, but
this I have. I was of opinion my papers had lain
still, and am sorry to hear there is news about them.
Let me entreat you to stop their translation and impression
so soon as you can; for I design to suppress
them. If your friend hath been at any pains and
charge, I will repay it, and gratify him. I am very
glad my Lord Monmouth is till my friend, but intend
not to give his lordship and you any farther trouble.
My inclinations are to sit still. I am to beg his
lordship’s pardon for pressing into his company the
last time I saw him. I had not done it, but that Mr.
Paulin pressed me into the room. Miracles, of
good credit, continued in the church for about two
or three hundred years. Gregorius Thaumaturgus
had his name from thence, and was one of the latest
who was eminent for that gift; but of their number
and frequency I am not able to give you a just account.
The history of those ages is very imperfect.
Mr. Paulin told me you had writ for some of Mr.
Boyle’s red earth, and by that I knew you had the
receipt.—Your most affectionate and humble servant,
“Is. Newton.”
Hence we see that this celebrated treatise, which
Biot alleges to have been written between 1712 and
1719, was actually in the hands of Le Clerc in Holland
previous to the 11th April, 1691, and consequently
previous to the time of the supposed insanity
of its author. Mr. Locke lost no time in obeying the
request of his friend. Le Clerc instantly stopped the
publication of the letter, and, as he had never learned
the name of the author, he deposited the manuscript,
which was in the handwriting of Mr. Locke, in the
library of the Remonstrants, where it was afterward
found, and was published at London in 1754, under
the title of Two letters from Sir Isaac Newton to M.
Le Clerc,—a form which had never been given to it
by its author. The copy thus published was a very
imperfect one, wanting both the beginning104 and the
end, and erroneous in many places; but Dr. Horsley
has published a genuine edition, which has the form
of a single letter to a friend, and was copied from a
manuscript in Sir Isaac Newton’s handwriting, in the
possession of the Rev. Dr. Ekins, Dean of Carlisle.
Having thus determined as accurately as possible
the dates of the principal theological writings of Sir
Isaac, we shall now proceed to give some account
of their contents.
The Observations on the Prophecies of Daniel and
the Apocalypse of St. John were published in London
in 1733, in one volume 4to. The work is divided
into two parts, the first of which treats of the Prophecies
of Daniel, and the second of the Apocalypse
of St. John. It begins with an account of the different
books which compose the Old Testament; and
as the author considers Daniel to be the most distinct
in the order of time, and the easiest to be understood,
he makes him the key to all the prophetic
books in those matters which relate to the “last time.”
He next considers the figurative language of the
prophets, which he regards as taken “from the
analogy between the world natural and an empire
or kingdom considered as a world politic;” the heavens
and the things therein representing thrones and
dynasties; the earth, with the things therein, the
inferior people; and the lowest parts of the earth
the most miserable of the people. The sun is put
for the whole race of kings, the moon for the body
of the common people, and the stars for subordinate
princes and rulers. In the earth, the dry land and
the waters are put for the people of several nations.
Animals and vegetables are also put for the people
of several regions. When a beast or man is put for
a kingdom, his parts and qualities are put for the
analogous parts and qualities of the kingdom; and
when a man is taken in a mystical sense, his qualities
are often signified by his actions, and by the
circumstances and things about him. In applying
these principles he begins with the vision of the
image composed of four different metals. This
image he considers as representing a body of four
great nations which should reign in succession over
the earth, viz. the people of Babylonia, the Persians,
the Greeks, and the Romans; while the stone cut out
without hands is a new kingdom which should arise
after the four, conquer all those nations, become very
great, and endure to the end of time.
The vision of the four beasts is the prophecy of the
four empires repeated, with several new additions.
The lion with eagles’ wings was the kingdom of
Babylon and Media, which overthrew the Assyrian
power. The beast like a bear was the Persian empire,
and its three ribs were the kingdoms of Sardis,
Babylon, and Egypt. The third beast, like a leopard,
was the Greek empire, and its four heads and four
wings were the kingdoms of Cassander, Lysimachus,
Ptolemy, and Seleucus. The fourth beast, with its
great iron teeth, was the Roman empire, and its ten
horns were the ten kingdoms into which it was
broken in the reign of Theodosius the Great.
In the fifth chapter Sir Isaac treats of the kingdoms
represented by the feet of the image composed
of iron and clay which did not stick to one another,
and which were of different strength. These were
the Gothic tribes called Ostrogoths, Visigoths, Vandals,
Gepidæ, Lombards, Burgundians, Alans, &c.;
all of whom had the same manners and customs,
and spoke the same language, and who, about the
year 416 A. C. were all quietly settled in several
kingdoms within the empire, not only by conquest,
but by grants of emperor.
In the sixth chapter he treats of the ten kingdoms
represented by the ten horns of the fourth beast, into
which the western empire became divided about the
time when Rome was besieged and taken by the
Goths. These kingdoms were,
1. The kingdom of the Vandals and Alans in Spain and Africa.
2. The kingdom of Suevians in Spain.
3. The kingdom of the Visigoths.
4. The kingdom of the Alans in Gaul.
5. The kingdom of the Burgundians.
6. The kingdom of the Franks.
7. The kingdom of the Britains.
8. The kingdom of the Huns.
9. The kingdom of the Lombards.
10. The kingdom of Ravenna.
Some of these kingdoms at length fell, and new
ones sprung up; but whatever was their subsequent
number, they still retain the name of the ten kings
from their first number.
The eleventh horn of Daniel’s fourth beast is shown
in chapter vii. to be the Church of Rome in its triple
character of a seer, a prophet, and a king; and its
power to change times and laws is copiously illustrated
in chapter viii.
In the ninth chapter our author treats of the kingdom
represented in Daniel by the ram and he-goat,
the ram indicating the kingdom of the Medes and
Persians from the beginning of the four empires, and
the he-goat the kingdom of the Greeks to the end
of them.
The prophecy of the seventy weeks, which had
hitherto been restricted to the first coming of our
Saviour, is shown to be a prediction of all the main
periods relating to the coming of the Messiah, the
times of his birth and death, the time of his rejection
by the Jews, the duration of the Jewish war by which
he caused the city and sanctuary to be destroyed,
and the time of his second coming.
In the eleventh chapter Sir Isaac treats with great
sagacity and acuteness of the time of our Saviour’s
birth and passion,—a subject which had perplexed
all preceding commentators.
After explaining in the twelfth chapter the last
prophecy of Daniel, namely, that of the scripture of
truth, which he considers as a commentary on the
vision of the ram and he-goat, he proceeds in the
thirteenth chapter to the prophecy of the king who
did according to his will, and magnified himself above
every god, and honoured Mahuzzims, and regarded
not the desire of women. He shows that the Greek
empire, after the division of the Roman empire into
the Greek and Latin empires, became the king who
in matters of religion did according to his will, and
in legislation exalted and magnified himself above
every god.
In the second part of his work on the Apocalypse
of St. John, Sir Isaac treats, 1st, Of the time when
the prophecy was written, which he conceives to
have been during John’s exile in Patmos, and before
the epistle to the Hebrews and the epistles of Peter
were written, which in his opinion have a reference
to the Apocalypse; 2dly, Of the scene of the vision,
and the relation which the Apocalypse has to the
book of the law of Moses, and to the worship of God
in the temple; and, 3dly, Of the relation which the
Apocalypse has to the prophecies of Daniel, and of
the subject of the prophecy itself.
Sir Isaac regards the prophecies of the Old and
New Testaments, not as given to gratify men’s curiosities,
by enabling them to foreknow things, but that
after they were fulfilled, they might be interpreted
by the event, and afford convincing arguments that
the world is governed by Providence, he considers
that there is so much of this prophecy already fulfilled
as to afford to the diligent student sufficient
instances of God’s providence; and he adds, that
“among the interpreters of the last age, there is
scarce one of note who hath not made some discovery
worth knowing, and thence it seems one may gather
that God is about opening these mysteries. The
success of others,” he continues, “put me upon considering
it, and if I have done any thing which may
be useful to following writers, I have my design.”
Such is a brief abstract of this ingenious work,
which is characterized by great learning, and marked
with the sagacity of its distinguished author. The
same qualities of his mind are equally conspicuous
in his Historical Account of Two Notable Corruptions
of Scripture.
This celebrated treatise relates to two texts in the
Epistles of St. John and St. Paul. The first of these
is in 1 John v. 7. “For there are three that bear
record in heaven, the Father, the Son, and the Holy
Ghost, and these three are one.” This text he considers
as a gross corruption of Scripture, which had
its origin among the Latins, who interpreted the
Spirit, Water, and Blood to be the Father, Son, and
Holy Ghost, in order to prove them one. With the
same view Jerome inserted the Trinity in express
words in his version. The Latins marked his variations
in the margins of their books; and in the
twelfth and following centuries, when the disputations
of the schoolmen were at their height, the
variation began to creep into the text in transcribing.
After the invention of printing, it crept out of the
Latin into the printed Greek, contrary to the authority
of all the Greek manuscripts and ancient versions;
and from the Venetian press it went soon
after into Greece. After proving these positions
Sir Isaac gives the following paraphrase of this remarkable
passage, which is given in italics.
“Who is he that overcometh the world, but he that
believeth that Jesus is the Son of God, that Son spoken
of in the Psalms, where he saith, ‘thou art my Son;
this day have I begotten thee.’ This is he that, after
the Jews had long expected him, came, first in a mortal
body, by baptism of water, and then in an immortal
one, by shedding his blood upon the cross and
rising again from the dead; not by water only, but
by water and blood; being the Son of God, as well
by his resurrection from the dead (Acts xiii. 33), as
by his supernatural birth of the virgin (Luke i. 35).
And it is the Spirit also that, together with the water
and blood, beareth witness of the truth of his coming;
because the Spirit is truth; and so a fit and unexceptionable
witness. For there are three that bear record
of his coming; the Spirit, which he promised to send,
and which was since shed forth upon us in the form
of cloven tongues, and in various gifts; the baptism
of water, wherein God testified ‘this is my beloved
Son;’ and the shedding of his blood, accompanied with
his resurrection, whereby he became the most faithful
martyr, or witness, of this truth. And these three,
the spirit, the baptism, and passion of Christ, agree
in witnessing one and the same thing (namely, that
the Son of God is come); and, therefore, their evidence
is strong: for the law requires but two consenting
witnesses, and here we have three: and if
we receive the witness of men, the threefold witness of
God, which he bare of his Son, by declaring at his
baptism ‘this is my beloved Son,’ by raising him
from the dead, and by pouring out his Spirit on us,
is greater; and, therefore, ought to be more readily
received.”
While the Latin Church was corrupting the preceding
text, the Greek Church was doing the same
to St. Paul’s 1st Epistle to Timothy iii. 16. Great
is the mystery of godliness, God manifest in the flesh.
According to Sir Isaac, this reading was effected by
changing σ into ΘΣ, the abbreviation of Θεος, and after
proving this by a learned and ingenious examination
of ancient manuscripts, he concludes that the reading
should be Great is the mystery of Godliness who
(viz. our Saviour) was manifest in the flesh.
As this learned dissertation had the effect of depriving
the defenders of the doctrine of the Trinity
of the aid of two leading texts, Sir Isaac Newton has
been regarded as an Antitrinitarian; but such a conclusion
is not warranted by any thing which he has
published;105 and he distinctly warns us, that his object
was solely to “purge the truth of things spurious.”
We are disposed, on the contrary, to think
that he declares his belief in the doctrine of the
Trinity when he says, “In the eastern nations, and
for a long time in the western, the faith subsisted
without this text; and it is rather a danger to religion
than an advantage, to make it now lean upon a
bruised reed. There cannot be better service done
to the truth than to purge it of things spurious; and
therefore, knowing your prudence and calmness of
temper, I am confident I shall not offend you by telling
you my mind plainly; especially since it is no
article of faith, no point of discipline, nothing but a
criticism concerning a text of Scripture which I am
going to write about.” The word faith in the preceding
passage cannot mean faith in the Scriptures in
general, but faith in the particular doctrine of the
Trinity; for it is this article of faith only to which
the author refers when he deprecates its leaning on
a bruised reed. But, whatever be the meaning of
this passage, we know that Sir Isaac was greatly
offended at Mr. Whiston for having represented him
as an Arian; and so much did he resent the conduct
of his friend in ascribing to him heretical opinions,
that he would not permit him to be elected a Fellow
of the Royal Society while he was President.106
The only other religious works which were composed
by Sir Isaac Newton were his Lexicon Propheticum,
to which was added a Dissertation on the
sacred cubit of the Jews, and Four Letters addressed
to Dr. Bentley, containing some arguments in proof of
a Deity.
The Lexicon Propheticum was left incomplete, and
has not been published; but the Latin Dissertation
which was appended to it, in which he shows that
the cubit was about 26½ Roman unciæ, was published
in 1737 among the Miscellaneous Works of Mr. John
Greaves.
Upon the death of the Honourable Robert Boyle,
on the 30th of December, 1691, it was found, by a
codicil to his will, that he had left a revenue of 50l.
per annum to establish a lectureship, in which eight
discourses were to be preached annually in one of
the churches of the metropolis, in illustration of the
evidences of Christianity, and in opposition to the
principles of infidelity. Dr. Bentley, though a very
young man, was appointed to preach the first course
of sermons, and the manner in which he discharged
this important duty gave the highest satisfaction, not
only to the trustees of the lectureship, but to the
public in general. In the first six lectures Bentley
exposed the folly of atheism even in reference to the
present life, and derived powerful arguments for the
existence of a Deity from the faculties of the soul,
and the structure and functions of the human frame.
In order to complete his plan, he proposed to devote
his seventh and eighth lectures to the demonstration
of a Divine Providence from the physical constitution
of the universe, as established in the Principia.
In order to qualify himself for this task, he received
from Sir Isaac written directions respecting a list of
books necessary to be perused previous to the study
of that work;107 and having made himself master of
the system which it contained, he applied it with
irresistible force of argument to establish the existence
of an overruling mind. Previous to the publication
of these lectures, Bentley encountered a
difficulty which he was not able to solve, and he
prudently transmitted to Sir Isaac during 1692 a
series of queries on the subject. This difficulty occurred
in an argument urged by Lucretius, to prove
the eternity of the world from an hypothesis of deriving
the frame of it by mechanical principles from
matter endowed with an innate power of gravity, and
evenly scattered throughout the heavens. Sir Isaac
willingly entered upon the consideration of the subject,
and transmitted his sentiments to Dr. Bentley
in the four letters which have been noticed in a preceding
chapter.
In the first108 of these letters Sir Isaac mentions
that when he wrote his treatise about our system,
viz. the Third Book of the Principia, “he had an
eye upon such principles as might work, with considering
men, for the belief of a Deity, and he expresses
his happiness that it has been found useful
for that purpose. In answering the first query of
Dr. Bentley, the exact import of which we do not
know, he states, that, if matter were evenly diffused
through a finite space, and endowed with innate
gravity, it would fall down into the middle of the
space, and form one great spherical mass; but if it
were diffused through an infinite space, some of it
would collect into one mass, and some into another,
so as to form an infinite number of great masses.
In this manner the sun and stars might be formed if
the matter were of a lucid nature. But he thinks it
inexplicable by natural causes, and to be ascribed to
the counsel and contrivance of a voluntary Agent,
that the matter should divide itself into two sorts,
part of it composing a shining body like the sun, and
part an opaque body like the planets. Had a natural
and blind cause, without contrivance and design,
placed the earth in the centre of the moon’s orbit,
and Jupiter in the centre of his system of satellites,
and the sun in the centre of the planetary system,
the sun would have been a body like Jupiter and the
earth, that is, without light and heat, and consequently
he knows no reason why there is only one
body qualified to give light and heat to all the rest,
but because the Author of the system thought it convenient,
and because one was sufficient to warm
and enlighten all the rest.
To the second query of Dr. Bentley, he replies
that the motions which the planets now have could
not spring from any natural cause alone, but were
impressed by an intelligent Agent. “To make such
a system with all its motions required a cause which
understood and compared together the quantities of
matter in the several bodies of the sun and planets,
and the gravitating powers resulting from thence;
the several distances of the primary planets from
the sun, and of the secondary ones from Saturn, Jupiter,
and the earth, and the velocities with which
those planets could revolve about those quantities
of matter in the central bodies; and to compare and
adjust all these things together in so great a variety
of bodies, argues that cause to be not blind and fortuitous,
but very well skilled in mechanics and geometry.”
In the second109 letter, he admits that the spherical
mass formed by the aggregation of particles would
affect the figure of the space in which the matter
was diffused, provided the matter descends directly
downwards to that body, and the body has no diurnal
rotation; but he states, that by earthquakes loosening
the parts of this solid, the protuberance might
sink a little by their weight, and the mass by degrees
approach a spherical figure. He then proceeds to
correct an error of Dr. Bentley’s in supposing that
all infinites are equal. He admits that gravity might
put the planets in motion, but he maintains that,
without the Divine power, it could never give them
such a circulating motion as they have about the
sun, because a proper quantity of a transverse motion
is necessary for this purpose; and he concludes
that he is compelled to ascribe the frame of this
system to an intelligent Agent.
The third letter contains opinions confirming or
correcting several positions which Dr. Bentley had
laid down, and he concludes it with a curious examination
of the opinion of Plato, that the motion of
the planets is such as if they had been all created
by God in some region very remote from our system,
and let fall from thence towards the sun, their
falling motion being turned aside into a transverse
one whenever they arrived at their several orbits.
Sir Isaac shows that there is no common place such
as that conjectured by Plato, provided the gravitating
power of the sun remains constant; but that
Plato’s affirmation is true if we suppose the gravitating
power of the sun to be doubled at that moment
of time when they all arrive at their several
orbits. “If we suppose,” says he, “the gravity of
all the planets towards the sun to be of such a quantity
as it really is, and that the motions of the
planets are turned upwards, every planet will ascend
to twice its height from the sun. Saturn will ascend
till he be twice as high from the sun as he is
at present, and no higher; Jupiter will ascend as
high again as at present, that is, a little above the
orb of Saturn; Mercury will ascend to twice his
present height, that is, to the orb of Venus; and so
of the rest; and then, by falling down again from
the places to which they ascended, they will arise
again at their several orbs with the same velocities
they had at first, and with which they now revolve.
“But if so soon as their motions by which they
revolve are turned upwards, the gravitating power
of the sun, by which their ascent is perpetually retarded,
be diminished by one-half, they will now
ascend perpetually, and all of them, at all equal distances
from the sun, will be equally swift. Mercury,
when he arrives at the orb of Venus, will be
as swift as Venus; and he and Venus, when they
arrive at the orb of the earth, will be as swift as the
earth; and so of the rest. If they begin all of them
to ascend at once, and ascend in the same line, they
will constantly, in ascending, become nearer and
nearer together, and their motions will constantly
approach to an equality, and become at length
slower than any motion assignable. Suppose, therefore,
that they ascended till they were almost contiguous,
and their motions inconsiderably little, and
that all their motions were at the same moment of
time turned back again, or, which comes almost to
the same thing, that they were only deprived of their
motions, and let fall at that time, they would all at
once arrive at their several orbs, each with the velocity
it had at first; and if their motions were then
turned sideways, and at the same time the gravitating
power of the sun doubled, that it might be
strong enough to retain them in their orbs, they
would revolve in them as before their ascent. But
if the gravitating power of the sun was not doubled,
they would go away from their orbs into the highest
heavens in parabolical lines.”110
In the fourth letter111 he states, that the hypothesis
that matter is at first evenly diffused through the
universe is in his opinion inconsistent with the
hypothesis of innate gravity without a supernatural
power to reconcile them, and therefore it infers a
Deity. “For if there be innate gravity, it is impossible
now for the matter of the earth and all the
planets and stars to fly up from them, and become
evenly spread throughout all the heavens without a
supernatural power; and certainly that which can
never be hereafter without a supernatural power,
could never be heretofore without the same power.”
These letters, of which we have endeavoured to
give a brief summary, will well repay the most
attentive perusal by the philosopher as well as the
divine. They are written with much perspicuity of
language and great power of thought, and they
contain results which incontestably prove that their
author was fully master of his noblest faculties,
and comprehended the profoundest parts of his own
writings.112
The logical acuteness, the varied erudition, and
the absolute freedom from all prejudice which shine
throughout the theological writings of Newton,
might have protected them from the charge of having
been written in his old age, and at a time when
a failure of mind was supposed to have unfitted him
for his mathematical investigations. But it is fortunate
for his reputation, as well as for the interests
of Christianity, that we have been able to prove the
incorrectness of such insinuations, and to exhibit
the most irrefragable evidence that all the theological
writings of Newton were composed in the vigour
of his life, and before the crisis of that bodily disorder
which is supposed to have affected his reason.
The able letters to Dr. Bentley were even written
in the middle of that period when want of sleep and
appetite had disturbed the serenity of his mind, and
enable us to prove that this disturbance, whatever
was its amount, never affected the higher functions
of his understanding.
When a philosopher of distinguished eminence,
and we believe not inimical to the Christian faith,
has found it necessary to make a laboured apology
for a man like Newton writing on theological subjects,
and has been led to render that apology more
complete by referring this class of his labours to a
mind debilitated by age and weakened by its previous
aberrations, it may be expected from an English
biographer, and one who acknowledges the
importance of revealed truth, and the paramount
interest of such subjects above all secular studies,
to suggest the true origin of Newton’s theological
inquiries.
When a mind of great and acknowledged power
first directs its energies to the study of the material
universe, no indications of order attract his notice,
and no proofs of design call forth his admiration.
In the starry firmament he sees no bodies of stupendous
magnitude, and no distances of immeasurable
span. The two great luminaries appear vastly inferior
in magnitude to many objects around him, and
the greatest distances in the heavens seem even inferior
to those which his own eye can embrace on
the surface of the earth. The planets, when observed
with care, are seen to have a motion among
the fixed stars, and to vary in their magnitude and
distances, but these changes appear to follow no
law. Sometimes they move to the east, sometimes
to the west, sometimes towards the north, and
sometimes towards the south, and at other times
they are absolutely stationary. No system, in short,
appears, and no general law seems to direct their
motions. By the observations and inquiries of
astronomers, however, during successive ages, a
regular system has been recognised in this chaos of
moving bodies, and the magnitudes, distances, and
revolutions of every planet which composes it has
been determined with the most extraordinary accuracy.
Minds fitted and prepared for this species of
inquiry are capable of understanding the great
variety of evidence by which the truth of the planetary
system is established; but thousands of individuals
who are even distinguished in other branches
of knowledge are incapable of such researches, and
view with a skeptical eye the great and irrefragable
truths of astronomy.
That the sun is stationary in the centre of our
system,—that the earth moves round the sun, and
round its own axis,—that the earth is 8000 miles in
diameter, and the sun one hundred and ten times as
large,—that the earth’s orbit is 190 millions of miles
in breadth,—and that if this immense space were
filled with light, it would appear only like a luminous
point at the nearest fixed star,—are positions absolutely
unintelligible and incredible to all who have
not carefully studied the subject. To millions of
our species, then, the great book of nature is absolutely
sealed, though it is in the power of all to
unfold its pages, and to peruse those glowing passages
which proclaim the power and wisdom of its
mighty Author.
The book of revelation exhibits to us the same
peculiarities as that of nature. To the ordinary
eye it presents no immediate indications of its
Divine origin. Events apparently insignificant—supernatural
interferences seemingly unnecessary—doctrines
almost contradictory—and prophecies
nearly unintelligible occupy its pages. The history
of the fall of man—of the introduction of moral
and physical evil—the prediction of a Messiah—the
actual advent of our Saviour—his instructions—his
miracles—his death—his resurrection—and the subsequent
propagation of his religion by the unlettered
fishermen of Galilee, are each a stumbling block to
the wisdom of this world. The youthful and vigorous
mind, when first summoned to peruse the Scriptures,
turns from them with disappointment. It
recognises in them no profound science—no secular
wisdom—no Divine eloquence—no disclosures of
nature’s secrets—no direct impress of an Almighty
hand. But, though the system of revealed truth
which this book contains is, like that of the universe,
concealed from common observation, yet the labours
of centuries have established its Divine origin, and
developed in all its order and beauty the great plan
of human restoration. In the chaos of its incidents
we discover the whole history of our species,
whether it is delineated in events that are past or
shadowed forth in those which are to come,—from
the creation of man and the origin of evil, to the
extinction of his earthly dynasty and the commencement
of his immortal career.
The antiquity and authenticity of the books which
compose the sacred canon,—the fulfilment of its
prophecies,—the miraculous works of its founder,—his
death and resurrection, have been demonstrated
to all who are capable of appreciating the force of
historical evidence; and in the poetical and prose
compositions of the inspired authors we discover a
system of doctrine and a code of morality traced in
characters as distinct and legible as the most unerring
truths in the material world. False systems of
religion have indeed been deduced from the sacred
record,—as false systems of the universe have
sprung from the study of the book of nature,—but
the very prevalence of a false system proves the
existence of one that is true; and though the two
classes of facts necessarily depend on different
kinds of evidence, yet we scruple not to say that
the Copernican system is not more demonstrably
true than the system of theological truth contained
in the Bible. If men of high powers, then, are still
found, who are insensible to the evidence which
sustains the system of the universe, need we wonder
that there are others whose minds are shut
against the effulgent evidence which intrenches the
strongholds of our faith.
If such, then, is the character of the Christian
faith, we need not be surprised that it was embraced
and expounded by such a genius as Sir Isaac Newton.
Cherishing its doctrines, and leaning on its
promises, he felt it his duty, as it was his pleasure,
to apply to it that intellectual strength which had
successfully surmounted the difficulties of the material
universe. The fame which that success procured
him he could not but feel to be the breath of
popular applause, which administered only to his
personal feelings; but the investigation of the sacred
mysteries, while it prepared his own mind for its
final destiny, was calculated to promote the spiritual
interests of thousands. This noble impulse he did
not hesitate to obey, and by thus uniting philosophy
with religion, he dissolved the league which genius
had formed with skepticism, and added to the cloud
of witnesses the brightest name of ancient or of
modern times.
The minor Discoveries and Inventions of Newton—His Researches on
Heat—On Fire and Flame—On Elective Attraction—On the Structure
of Bodies—His supposed Attachment to Alchymy—His Hypothesis
respecting Ether as the Cause of Light and Gravity—On the Excitation
of Electricity in Glass—His Reflecting Sextant invented
before 1700—His Reflecting Microscope—His Prismatic Reflector as a
Substitute for the small Speculum of Reflecting Telescopes—His
Method of varying the Magnifying Power of Newtonian Telescopes—His
Experiments on Impressions on the Retina.
In the preceding chapters we have given an account
of the principal labours of Sir Isaac Newton;
but there still remain to be noticed several of his
minor discoveries and inventions, which could not
properly be introduced under any general head.
The most important of these, perhaps, are his
chymical researches, which he seems to have pursued
with more or less diligence from the time
when he first witnessed the practical operations of
chymistry during his residence at the apothecary’s
at Grantham. His first chymical experiments were
probably made on the alloys of metals, for the purpose
of obtaining a good metallic composition for
the specula of reflecting telescopes. In his paper
on thin plates he treats of the combinations of solids
and fluids; but he enters more largely on these and
other subjects in the queries published at the end
of his Optics.
One of his most important chymical papers is
his Tabula quantitatum et graduum caloris, which
was published in the Philosophical Transactions.
This short paper contains a comparative scale of
temperature from that of melting ice to that of a
small kitchen coal-fire. The following are the
principal points of the scale, the intermediate
degrees of heat having been determined with great
care.
Degrees
of Heat. | Equal Parts
of Heat. |
|---|
| 0 |
0 |
Freezing point of water. |
| 1 |
12 |
Blood-heat. |
| 2 |
24 |
Heat of melting wax. |
| 3 |
48 |
Melting point of equal parts of tin and bismuth. |
| 4 |
96 |
Melting point of lead. |
| 5 |
192 |
Heat of a small coal-fire. |
The first column of this table contains the degrees
of heat in arithmetical progression, and the second
in geometrical progression,—the second degree being
twice as great as the first, and so on. It is obvious
from this table, that the heat at which equal parts
of tin and bismuth melt is four times greater than
that of blood-heat, the heat of melting lead eight
times greater, and the heat of a small coal-fire sixteen
times greater.
This table was constructed by the help of a thermometer,
and of red-hot iron. By the former he
measured all heats as far as that of melting tin;
and by the latter he measured all the higher heats.
For the heat which heated iron loses in a given time
is as the total heat of the iron; and therefore, if the
times of cooling are taken equal, the heats will be
in a geometrical progression, and may therefore be
easily found by a table of logarithms.
He found by a thermometer constructed with linseed
oil, that if the oil, when the thermometer was
placed in melting snow, occupied a space of 1000
parts, the same oil, rarefied with one degree of heat,
or that of the human body, occupied a space of
10256; in the heat of water beginning to boil, a
space of 10705; in the heat of water boiling violently,
10725; in the heat of melted tin beginning to
cool, and putting on the consistency of an amalgam,
11516, and when the tin had become solid, 11496.
Hence the oil was rarefied in the ratio of 40 to 39
by the heat of the human body; of 15 to 14 by the
heat of boiling water; of 15 to 13 in the heat of
melting tin beginning to solidify; and of 23 to 20 in
the same tin when solid. The rarefaction of air
was, with the same heat, ten times greater than that
of oil, and the rarefaction of oil fifteen times greater
than that of spirit of wine. By making the heats
of oil proportional to its rarefaction, and by calling
the heat of the human body 12 parts, we obtain the
heat of water beginning to boil, 33; of water boiling
violently, 34; of melted tin beginning to solidify,
72; and of the same become solid, 70.
Sir Isaac then heated a sufficiently thick piece
of iron till it was red-hot; and having fixed it in a
cold place, where the wind blew uniformly, he put
upon it small pieces of different metals and other
fusible bodies, and noted the times of cooling, till
all the particles, having lost their fluidity, grew cold,
and the heat of the iron was equal to that of the
human body. Then, by assuming that the excesses
of the heats of the iron and of the solidified particles
of metal above the heat of the atmosphere,
were in geometrical progression when the times
were in arithmetical progression, all the heats were
obtained. The iron was placed in a current of air,
in order that the air heated by the iron might always
be carried away by the wind, and that cold air
might replace it with a uniform motion; for thus
equal parts of the air were heated in equal times,
and received a heat proportional to that of the iron.
But the heats thus found had the same ratio to one
another with the heats found by the thermometer;
and hence he was right in assuming that the rarefactions
of the oil were proportional to its heats.
Another short chymical paper by Sir Isaac Newton
has been published by Dr. Horsley. It is entitled
De Natura Acidorum, but is principally occupied
with a number of brief opinions on chymical subjects.
This paper was written later than 1687, as it
bears a reference to the Principia; and the most important
facts which it contains seem to have been
more distinctly reproduced in the queries at the end
of the Optics.
The most important of these queries relate to fire,
flame, and electric attractions, and as they were revised
in the year 1716 and 1717, they may be regarded
as containing the most matured opinions of their
author. Fire he regards as a body heated so hot as
to emit light copiously, and flame as a vapour, fume,
or exhalation heated so hot as to shine. In his long
query on elective attractions, he considers the small
particles of bodies as acting upon one another at
distances so minute as to escape observation. When
salt of tartar deliquesces, he supposes that this arises
from an attraction between the saline particles and
the aqueous particles held in solution in the atmosphere,
and to the same attraction he ascribes it that
the water will not distil from the salt of tartar without
great heat. For the same reason sulphuric acid
attracts water powerfully, and parts with it with
great difficulty. When this attractive force becomes
very powerful, as in the union between sulphuric
acid and water, so as to make the particles “coalesce
with violence,” and rush towards one another with
an accelerated motion, heat is produced by the mixture
of the two fluids. In like manner, he explains
the production of flame from the mixture of cold
fluids,—the action of fulminating powders,—the combination
of iron filings with sulphur,—and all the
other chymical phenomena of precipitation, combination,
solution, and crystallization, and the mechanical
phenomena of cohesion and capillary attraction.
He ascribes hot springs, volcanoes, fire-damps,
mineral coruscations, earthquakes, hot suffocating
exhalations, hurricanes, lightning, thunder, fiery
meteors, subterraneous explosions, land-slips, ebullitions
of the sea, and waterspouts, to sulphureous
steams abounding in the bowels of the earth, and
fermenting with minerals, or escaping into the atmosphere,
where they ferment with acid vapours fitted
to promote fermentation.
In explaining the structure of solid bodies, he is
of opinion, “that the smallest particles of matter
may cohere by the strongest attractions, and compose
bigger particles of weaker virtue; and many
of these may cohere and compose bigger particles
whose virtue is still weaker; and so on for divers
successions, until the progression end in the biggest
particles, on which the operations in chymistry and
the colours of natural bodies depend, and which, by
adhering, compose bodies of a sensible magnitude.
If the body is compact, and bends or yields inward
to pression, without any sliding of its parts, it is hard
and elastic, returning to its figure with a force rising
from the mutual attraction of its parts. If the parts
slide upon one another, the body is malleable or soft.
If they slip easily, and are of a fit size to be agitated
by heat, and the heat is big enough to keep them in
agitation, the body is fluid; and if it be apt to stick
to things, it is humid; and the drops of every fluid
affect a round figure, by the mutual attraction of their
parts, as the globe of the earth and sea affects a
round figure, by the mutual attraction of its parts, by
gravity.”
Sir Isaac then supposes, that, as the attractive
force of bodies can reach but to a small distance from
them, “a repulsive virtue ought to succeed;” and he
considers such a virtue as following from the reflection
of the rays of light, the rays being repelled without
the immediate contact of the reflecting body, and
also from the emission of light, the ray, as soon as
it is shaken off from a shining body by the vibrating
motion of the parts of the body, getting beyond the
reach of attraction, and being driven away with exceeding
great velocity by the force of reflection.113
Many of the chymical views which Sir Isaac thus
published in the form of queries were in his own
lifetime illustrated and confirmed by Dr. Stephen
Hales, in his book on Vegetable Statics,—a work of
great originality, which contains the germ of some
of the finest discoveries in modern chymistry.
Although there is no reason to suppose that Sir
Isaac Newton was a believer in the doctrines of
alchymy, yet we are informed by the Reverend Mr.
Law that he had been a diligent student of Jacob
Behmen’s writings, and that there were found among
his papers copious abstracts from them in his own
handwriting.114 He states also that Sir Isaac, together
with one Dr. Newton, his relation, had, in the earlier
part of his life, set up furnaces, and were for several
months at work in quest of the philosopher’s tincture.
These statements may receive some confirmation
from the fact, that there exist among the
Portsmouth papers many sheets, in Sir Isaac’s own
writing, of Flammel’s Explication of Hieroglyphic
Figures, and in another hand, many sheets of William
Yworth’s Processus Mysterii Magni Philosophicus,
and also from the manner in which Sir Isaac
requests Mr. Aston to inquire after one Borry in
Holland, who always went clothed in green, and who
was said to possess valuable secrets; but Mr. Law
has weakened the force of his own testimony, when
he asserts that Newton borrowed the doctrine of
attraction from Behmen’s first three propositions of
eternal nature.
On the 7th December, 1675, Sir Isaac Newton communicated
to the Royal Society a paper entitled
An hypothesis explaining properties of light, in which
he, for the first time, introduces his opinions respecting
ether, and employs them to explain the nature
of light, and the cause of gravity. “He was induced,”
he says, “to do this, because he had observed
the heads of some great virtuosos to run much upon
hypotheses, and he therefore gave one which he was
inclined to consider as the most probable, if he were
obliged to adopt one.”115
This hypothesis seems to have been afterward a
subject of discussion between him and Mr. Boyle, to
whom he promised to communicate his opinion more
fully in writing. He accordingly addressed to him a
long letter, dated February 28th, 1678–9, in which
he explains his views respecting ether, and employs
them to account for the refraction of light,—the cohesion
of two polished pieces of metal in an exhausted
receiver,—the adhesion of quicksilver to glass tubes,—the
cohesion of the parts of all bodies,—the cause
of filtration,—the phenomena of capillary attraction,—the
action of menstrua on bodies,—the transmutation
of gross compact substances into aerial ones,—and
the cause of gravity. From the language used
in this paper, we should be led to suppose that Sir
Isaac had entirely forgotten that he had formerly
treated the general subject of ether, and applied it
to the explanation of gravity. “I shall set down,”
says he, “one conjecture more which came into my
mind now as I was writing this letter; it is about the
cause of gravity,” which he goes on to explain;116 and
he concludes by saying, that “he has so little fancy
to things of this nature, that, had not your encouragement
moved me to it, I should never, I think, thus far
have set pen to paper about them.”
These opinions, however, about the existence of
ether, Newton seems to have subsequently renounced;
for in the manuscript in the possession
of Dr. J. C. Gregory, which we have already mentioned,
and which was written previous to 1702, he
states, that ether is neither obvious to our senses,
nor supported by any arguments, but is a gratuitous
assumption, which, if we are to trust to reason and
to our senses, must be banished from the nature of
things; and he goes on to establish, by various arguments,
the validity of this opinion. This renunciation
of his former hypothesis probably arose from
his having examined more carefully some of the
phenomena which he endeavoured to explain by it.
Those of capillary attraction, for example, he had
ascribed to the ether “standing rarer in the very sensible
cavities of the capillary tubes than without
them,” whereas he afterward discovered their true
cause, and ascribed them to the reciprocal attraction
of the tube and the fluid. But, however this may
be, there can be no doubt that he resumed his early
opinions before the publication of his Optics, which
may be considered as containing his views upon this
subject.
The queries which contain these opinions are the
18th–24th, all of which appeared for the first time in
the second English edition of the Optics. If a body
is either heated or loses its heat when placed in
vacuo, he ascribes the conveyance of the heat in
both cases “to the vibration of a much subtiler medium
than air;” and he considers this medium as the
same with that by which light is refracted and reflected,
and by whose vibrations light communicates
heat to bodies, and is put into fits of easy reflection
and transmission.
This ethereal medium, according to our author, is
exceedingly more rare and more elastic than air.
It pervades all bodies, and is expanded through all
the heavens. It is much rarer within the dense
bodies of the sun, stars, planets, and comets, than
in the celestial spaces between them, and also more
rare within glass, water, &c. than in the free and
open spaces void of air and other grosser bodies.
In passing out of glass, water, &c. and other dense
bodies into empty space, it grows denser and denser
by degrees, and this gradual condensation extends
to some distance from the bodies. Owing to its
great elasticity, and, consequently, its efforts to
spread in all directions, it presses against itself, and,
consequently, against the solid particles of bodies,
so as to make them continually approach to one
another, the body being impelled from the denser
parts of the medium towards the rarer with all that
power which we call gravity.
In employing this medium to explain the nature
of light, Newton does not suppose, with Descartes,
Hooke, Huygens, and others, that light is nothing
more than the impression of those undulations on
the retina. He regards light as a peculiar substance,
composed of heterogeneous particles thrown off with
great velocity, and in all directions, from luminous
bodies; and he supposes that these particles while
passing through the ether, excite in it vibrations or
pulses which accelerate or retard the particles of
light, and thus throw them into their alternate fits
of easy reflection and transmission.
Hence, if a ray of light falls upon a transparent
body, in which the ether consists of strata of variable
density, the particles of light acted upon by the
vibrations which they create will be urged with an
accelerated velocity in entering the body, while their
velocity will be retarded in quitting it. In this manner
he conceives the phenomena of refraction to be
produced, and he shows how in such a case the
refraction would be regulated by the law of the
sines.
In order that the ethereal medium may produce
the fits of easy reflection and transmission, he conceives
that its vibrations must be swifter than light.
He computes its elasticity to be 490,000,000,000
times greater than that of air, in proportion to its
density, and about 600,000,000 times more rare than
water, from which he infers that the resistance
which it would oppose to the motions of the planets
would not be sensible in 10,000 years. He considers
that the functions of vision and hearing may be performed
chiefly by the vibrations of this medium,
executed in the bottom of the eye, or in the auditory
nerve by the rays of light, and propagated through
the solid, pellucid, and uniform capillamenta of the
optic or auditory nerves into the place of sensation;
and he is of opinion that animal motion may be
performed by the vibrations of the same medium,
excited in the brain by the power of the will, and
propagated from thence by the solid, pellucid, and
uniform capillamenta of the nerves into the muscles
for contracting and dilating them.
In the registers of the Royal Society there exist
several letters117 on the excitation of electricity in
glass, which were occasioned by an experiment of
this kind having been mentioned in Sir Isaac’s
hypothesis of light. The society had ordered the
experiment to be tried at their meeting of the 16th
December, 1675; but, in order to secure its success,
Mr. Oldenburg wrote to Sir Isaac for a more particular
account of it. Sir Isaac being thus “put
upon recollecting himself a little farther about it,”
remembers that he made the experiment with a
glass fixed at the distance of the 1/3d of an inch from
one end of a brass hoop, and only the 1/8th of an inch
from the other. Small pieces of thin paper were
then laid upon the table; when the glass was laid
above them and rubbed, the pieces of paper leaped
from the one part of the glass to the other, and
twirled about in the air. Notwithstanding this explicit
account of the experiment, it entirely failed
at the Royal Society, and the secretary was desired
to request the loan of Sir Isaac’s apparatus,
and to inquire whether or not he had secured the
papers from being moved by the air, which might
have somewhere stole in. In a letter, dated 21st
December, Sir Isaac recommended to the society to
rub the glass “with stuff whose threads may rake
its surface, and, if that will not do, to rub it with
the fingers’ ends to and fro, and knock them as
often upon the glass.” These directions enabled
the society to succeed with the experiment on the
13th January, 1676, when they used a scrubbing
brush of short hog’s bristles, and the heft of a knife
made with whalebone.
Among the minor inventions of Sir Isaac Newton,
we must enumerate his reflecting instrument for
observing the moon’s distance from the fixed stars
at sea. The description of this instrument was communicated
to Dr. Halley in the year 1700; but, either
from having mislaid the manuscript, or from attaching
no value to the invention, he never communicated
it to the Royal Society, and it remained among
his papers till after his death in 1742, when it was
published in the Philosophical Transactions. The
following is Sir Isaac’s own description of it as
communicated to Dr. Halley.
“In the annexed figure PQRS denotes a plate of
brass, accurately divided in the limb DQ, into ½ degrees,
½ minutes, and 1/12 minutes, by a diagonal
scale; and the ½ degrees, and ½ minutes, and 1/12
minutes, counted for degrees, minutes, and 1/6 minutes.
AB is a telescope three or four feet long, fixed on
the edge of that brass plate. G is a speculum fixed
on the brass plate perpendicularly as near as
may be to the object-glass of the telescope, so as
to be inclined forty-five degrees to the axis of
the telescope, and intercept half the light which
would otherwise come through the telescope to the
eye. CD is a moveable index turning about the
centre C, and, with its fiducial edge, showing the
degrees, minutes, and 1/6 minutes on the limb of the
brass plate PQ; the centre C must be over against
the middle of the speculum G. H is another speculum,
parallel to the former, when the fiducial edge
of index falls on 0° 0′ 0″; so that the same star may
then appear through the telescope in one and the
same place, both by the direct rays and by the reflexed
ones; but if the index be turned, the star shall
appear in two places, whose distance is showed on
the brass limb by the index.
Fig. 12.
“By this instrument the distance of the moon
from any fixed star is thus observed: view the star
through the perspicil by the direct light, and the
moon by the reflexed (or on the contrary); and
turn the index till the star touch the limb of the
moon, and the index shall show on the brass limb
of the instrument the distance of the star from the
moon’s limb; and though the instrument shake by
the motion of the ship at sea, yet the moon and star
will move together as if they did really touch one
another in the heavens; so that an observation may
be made as exactly at sea as at land.
“And by the same instrument may be observed
exactly the altitudes of the moon and stars, by
bringing them to the horizon; and thereby the latitude
and times of observation may be determined
more exactly than by the ways now in use.
“In the time of the observation, if the instrument
move angularly about the axis of the telescope, the
star will move in a tangent of the moon’s limb, or
of the horizon; but the observation may notwithstanding
be made exactly, by noting when the line
described by the star is a tangent to the moon’s
limb, or to the horizon.
“To make the instrument useful, the telescope
ought to take in a large angle; and to make the
observation true, let the star touch the moon’s limb,
not on the outside, but on the inside.”
This ingenious contrivance is obviously the very
same invention as that which Mr. Hadley produced
in 1731, and which, under the name of Hadley’s
Quadrant, has been of so great service in navigation.
The merit of its first invention must therefore be
transferred to Sir Isaac Newton.
In the year 1672, Sir Isaac communicated to
Mr. Oldenburg his design for a microscope, which
he considered to be as capable of improvement as
the telescope, and perhaps more so, because it
requires only one speculum. This microscope is
shown in the annexed diagram, where AB is the
object-metal, CD the eye-glass, F their common
focus, and O the other focus of the metal in which
the object is placed. This ingenious idea has been
greatly improved in modern times by Professor
Amici, who makes AB a portion of an ellipsoid,
whose foci are O and F, and who places a small
plain speculum between O and AB, in order to reflect
the object, which is placed on one side AP, for
the purpose of being illuminated.
Fig. 13.
In another letter to Mr. Oldenburg, dated July
11th in the same year, he suggests another improvement
in microscopes, which is to “illuminate the
object in a darkened room with the light of any
convenient colour not too much compounded: for
by that means the microscope will, with distinctness,
bear a deeper charge and larger aperture,
especially if its construction be such as I may hereafter
describe.”118 This happy idea I have some
years ago succeeded in realizing, by illuminating
microscopic objects with the light of a monochromatic
lamp, which discharges a copious flame of
pure yellow light of definite refrangibility.119
Fig. 14.
Fig. 15.
In order to remedy the evils arising from the
weak reflecting power of speculum metal, and from
its tarnishing by exposure to the air, Sir Isaac proposed
to substitute for the small oval speculum a
triangular prism of glass or crystal ABC. Its side
AB ba he supposes to perform the office of that metal,
by reflecting towards the eye-glass the light which
comes from the concave speculum DF, fig. 13,
whose light he supposes to enter into this prism at
its side CB bc, and lest any colours should be produced
by the refraction of these planes, it is requisite
that the angles of the
prism at Aa and Bb be
precisely equal. This
may be done most conveniently,
by making them
half right angles, and consequently
the third angle
at Cc a right one. The
plane AB ba will reflect
all the light incident upon
it; but in order to exclude
unnecessary light,
it will be proper to cover
it all over with some black substance excepting two
circular spaces of the planes Ac and Bc, through
which the useful light may pass. The length of the
prism should be such that its sides Ac and Bc may
be square, and so much of the angles B and b as are
superfluous ought to be ground off, to give passage
for as much light as is possible from the object to
the speculum.
Fig. 16.
One great advantage of this prism, which cannot
be obtained from the oval metal, is, that without
using two glasses the object may be erected, and
the magnifying power of the telescope varied at
pleasure, by merely varying the distances of the
speculum, the prism, and the eye-glass. This will
be understood from fig. 16, where AI represents
the great concave speculum, EF the eye-glass, and
BCD the prism of glass, whose sides BC and CD
are not flat, but spherically convex. The rays which
come from G, the focus of the great speculum AI,
will, by the refraction of the first side BC, be reduced
to parallelism, and after reflection from the
base CD, will be made by the refraction of the next
side BD to converge to the focus H of the eye-glass
EF. If we now bring the prism BCD nearer the
image at G, the point H will recede from BD, and
the image formed there will be greater than that at
G, and if we remove the prism BCD from G, the
point H will approach to BD, and the image at H
will be less than that at G. The prism BCD performs
the same part as a convex lens, G and H
being its conjugate foci, and the relative size of the
images formed at these points being proportional to
their distance from the lens. This construction
would be a good one for varying optically the angular
distance of a pair of wires placed in the focus of
the eye-glass EF; and by bisecting the lenticular
prism BCD, and giving the halves a slight inclination,
we should be able to separate and to close the
two images or disks which would thus be produced,
and thus form a double image micrometer.
Among the minor and detached labours of Sir
Isaac, we must not omit his curious experiments on
the action of light upon the retina. Locke seems
to have wished his opinion respecting a fact stated
in Boyle’s Book on Colours, and in a letter from
Cambridge, dated June 30th, 1691, he communicated
to his friend the following very remarkable observations
made by himself.
“The observation you mention in Mr. Boyle’s
book of colours I once made upon myself with the
hazard of my eyes. The manner was this; I looked
a very little while upon the sun in the looking-glass
with my right eye, and then turned my eyes into a
dark corner of my chamber, and winked, to observe
the impression made, and the circles of colours
which encompassed it, and how they decayed by
degrees, and at last vanished. This I repeated a
second and a third time. At the third time, when
the phantasm of light and colours about it were
almost vanished, intending my fancy upon them to
see their last appearance, I found, to my amazement,
that they began to return, and by little and
little to become as lively and vivid as when I had
newly looked upon the sun. But when I ceased to
intend my fancy upon them, they vanished again.
After this, I found, that as often as I went into the
dark, and intended my mind upon them, as when
a man looks earnestly to see any thing which is
difficult to be seen, I could make the phantasm return
without looking any more upon the sun; and
the oftener I made it return, the more easily I could
make it return again. And at length, by repeating
this without looking any more upon the sun, I made
such an impression on my eye, that, if I looked upon
the clouds, or a book, or any bright object, I saw
upon it a round bright spot of light like the sun,
and, which is still stranger, though I looked upon
the sun with my right eye only, and not with my
left, yet my fancy began to make an impression
upon my left eye, as well as upon my right. For if
I shut my right eye, or looked upon a book or the
clouds with my left eye, I could see the spectrum
of the sun almost as plain as with my right eye, if I
did but intend my fancy a little while upon it; for
at first, if I shut my right eye, and looked with my
left, the spectrum of the sun did not appear till I intended
my fancy upon it; but by repeating, this appeared
every time more easily. And now, in a few
hours’ time, I had brought my eyes to such a pass,
that I could look upon no bright object with either
eye but I saw the sun before me, so that I durst
neither write nor read; but to recover the use of my
eyes, shut myself up in my chamber made dark, for
three days together, and used all means to divert
my imagination from the sun. For if I thought
upon him, I presently saw his picture, though I was
in the dark. But by keeping in the dark, and employing
my mind about other things, I began in
three or four days to have some use of my eyes
again; and, by forbearing to look upon bright objects,
recovered them pretty well, though not so
well but that, for some months after, the spectrum
of the sun began to return as often as I began to
meditate upon the phenomena, even though I lay in
bed at midnight with my curtains drawn. But now
I have been very well for many years, though I am
apt to think, if I durst venture my eyes, I could still
make the phantasm return by the power of my
fancy. This story I tell you, to let you understand,
that in the observation related by Mr. Boyle, the
man’s fancy probably concurred with the impression
made by the sun’s light to produce that phantasm
of the sun which he constantly saw in bright objects.
And so your question about the cause of this phantasm
involves another about the power of fancy,
which I must confess is too hard a knot for me to
untie. To place this effect in a constant motion is
hard, because the sun ought then to appear perpetually.
It seems rather to consist in a disposition
of the sensorium to move the imagination strongly,
and to be easily moved, both by the imagination
and by the light, as often as bright objects are looked
upon.”
These observations possess in many respects a high
degree of interest. The fact of the transmission
of the impression from the retina of the one eye to
that of the other is particularly important; and it
deserves to be remarked, as a singular coincidence,
that I had occasion to observe and to describe the
same phenomena above twenty years ago,120 and long
before the observations of Sir Isaac were communicated
to the scientific world.
His Acquaintance with Dr. Pemberton, who edits the Third Edition of
the Principia—His first Attack of ill Health—His Recovery—He is
taken ill in consequence of attending the Royal Society—His Death
on the 20th March, 1727—His Body lies in state—His Funeral—He
is buried in Westminster Abbey—His Monument described—His Epitaph—A
Medal struck in honour of him—Roubiliac’s full-length
Statue of him erected in Cambridge—Division of his Property—His
Successors.
About the year 1722, Sir Isaac was desirous of
publishing a third edition of his Principia, and the
premature death of Mr. Cotes having deprived him
of his valuable aid, he had the good fortune to become
acquainted with Dr. Henry Pemberton, a young
and accomplished physician, who had cultivated
mathematical learning with considerable success.
M. Poleni, an eminent professor in the University
of Padua, having endeavoured, on the authority of
a new experiment, to overturn the common opinion
respecting the force of bodies in motion, and to establish
that of Leibnitz in its place, Dr. Pemberton
transmitted to Dr. Mead a demonstration of its
inaccuracy. Dr. Mead communicated this paper to
Sir Isaac, who not only highly approved of it, but
added a demonstration of his own, drawn from
another consideration of the subject; and this was
printed without his name, as a postscript to Pemberton’s
paper, when it appeared in the Transactions.121
In a short time after the commencement of their
acquaintance, Sir Isaac engaged Dr. Pemberton to
superintend the new edition of the Principia. In
discharging this duty, Dr. Pemberton had occasion
to make many remarks on this work, which Sir Isaac
always received with the utmost goodness, and the
new edition appeared with numerous alterations in
1726. On the occasions upon which he had personal
intercourse with Sir Isaac, and which were
necessarily numerous, he endeavoured to learn his
opinions on various mathematical subjects, and to
obtain some historical information respecting his
inventions and discoveries. Sir Isaac entered freely
into all these topics and during the conversations
which took place, and while they were reading
together Dr. Pemberton’s popular account of Sir
Isaac’s discoveries, he obtained the most perfect
evidence that, though his memory was much decayed,
yet he was fully able to understand his own
writings.
During the last twenty years of his life, which he
spent in London, the charge of his domestic concerns
devolved upon his beautiful and accomplished
niece, Mrs. Catharine Barton, the wife of Colonel
Barton, for whom, as we have already seen, the
Earl of Halifax had conceived the warmest affection.
This lady, who had been educated at her
uncle’s expense, married Mr. Conduit, and continued
to reside with her husband in Sir Isaac’s house till
the time of his death.
In the year 1722, when he had reached the
eightieth year of his age, he was seized with an
incontinence of urine, which was ascribed to stone
in the bladder, and was considered incurable. By
means of a strict regimen, however, and other precautions,
he was enabled to alleviate his complaint,
and to procure long intervals of ease. At this time
he gave up the use of his carriage, and always went
out in a chair. He declined all invitations to dinner,
and at his own house he had only small parties. In
his diet he was extremely temperate. Though he
took a little butcher meat, yet the principal articles
of his food were broth, vegetables, and fruit, of
which he always ate very heartily. In spite of all
his precautions, however, he experienced a return
of his old complaint, and in August, 1724, he passed
a stone the size of a pea, which came away in two
pieces, the one at the distance of two days from the
other. After some months of tolerable good health,
he was seized in January, 1725, with a violent cough
and inflammation of the lungs; and in consequence
of this attack, he was prevailed upon, with some
difficulty, to take up his residence at Kensington,
where his health experienced a decided improvement.
In February, 1725, he was attacked in both
his feet with a fit of the gout, of which he had received
a slight warning a few years before, and the
effect of this new complaint was to produce a great
and beneficial change in his general health. On
Sunday the 7th March, when his head was clearer
and his memory stronger than Mr. Conduit had
known it to be for some time, he entered into a long
conversation on various subjects in astronomy. He
explained to Mr. Conduit how comets might be
formed out of the light of vapours discharged from
the sun and the fixed stars as the centres of systems.
He conceived that these luminaries were
replenished by the same comets being again returned
to them; and upon this principle he explained the
extraordinary lights which were seen among the
fixed stars by Hipparchus, Tycho Brahe, and Kepler’s
disciples, and which he supposed to arise from the
additional fuel which they received.122
Notwithstanding the improvement which his health
had experienced, his indisposition was still sufficiently
severe to unfit him for the discharge of his
duties at the mint; and as his old deputy was confined
with the dropsy, he was desirous in 1725 of
resigning his office to Mr. Conduit. Difficulties
probably were experienced in making this arrangement,
but his nephew discharged for him all the
duties of his office; and during the last year of his
life he hardly ever went to the mint.
But though every kind of motion was calculated
to aggravate his complaint, and though he had derived
from absolute rest and from the air at Kensington
the highest benefit, yet great difficulty was
experienced in preventing him from occasionally
going to town. Feeling himself able for the journey,
he went to London on Tuesday the 28th of
February, 1727, to preside at a meeting of the Royal
Society. On the following day Mr. Conduit considered
him better than he had been for many years,
and Sir Isaac was himself so sensible of this improvement
in his health, that he assured his nephew
that on the Sunday preceding, he had slept from
eleven o’clock at night till eight o’clock next morning
without waking. He had undergone, however,
great fatigue in attending the meeting of the Royal
Society, and in paying and receiving visits, and the
consequence of this was a violent return of his
former complaint. He returned to Kensington on
Saturday the 4th March, and was attended by Dr.
Mead and Dr. Cheselden, who pronounced his disease
to be stone, and held out no hopes of his
recovery. From the time of his last journey to
London he had experienced violent fits of pain with
very short intermissions; and though the drops of
sweat ran down his face during these severe paroxysms,
yet he never uttered a cry or a complaint, or
displayed the least marks of peevishness or impatience;
but during the short intervals of relief which
occurred, he smiled and conversed with his usual
gayety and cheerfulness. On Wednesday the 15th
of March he seemed a little better; and slight,
though groundless hopes were entertained of his
recovery. On the morning of Saturday the 18th
he read the newspapers, and carried on a pretty long
conversation with Dr. Mead, when all his senses and
faculties were strong and vigorous; but at six o’clock
of the same evening he became insensible, and he
continued in that state during the whole of Sunday,
and till Monday the 20th, when he expired between
one and two o’clock in the morning, in the eighty-fifth
year of his age.
His body was removed from Kensington to London,
and on Tuesday the 28th March it lay in state
in the Jerusalem Chamber, and was thence conveyed
to Westminster Abbey, where it was buried near the
entrance into the choir on the left-hand. The pall
was supported by the Lord High Chancellor, the
Dukes of Roxburghe and Montrose, and the Earls
of Pembroke, Sussex, and Macclesfield, who were
Fellows of the Royal Society. The Hon. Sir Michael
Newton, Knight of the Bath, was chief
mourner, and was followed by some other relations,
and several distinguished characters who were intimately
acquainted with the deceased. The funeral
service was performed by the Bishop of Rochester,
attended by the prebend and choir.
Sensible of the high honour which they derived
from their connexion with so distinguished a philosopher,
the relations of Sir Isaac Newton who
inherited his personal estate,123 agreed to devote 500l.
to the erection of a monument to his memory, and
the dean and chapter of Westminster appropriated
for it a place in the most conspicuous part of the
Abbey, which had often been refused to the greatest
of our nobility. This monument was erected in
1731. On the front of a sarcophagus resting on a
pedestal are sculptured in basso-relievo youths bearing
in their hands the emblems of Sir Isaac’s principal
discoveries. One carries a prism, another a
reflecting telescope, a third is weighing the sun and
planets with a steelyard, a fourth is employed about
a furnace, and two others are loaded with money
newly coined. On the sarcophagus is placed the
figure of Sir Isaac in a cumbent posture, with his
elbow resting on several of his works. Two youths
stand before him with a scroll, on which is drawn a
remarkable diagram relative to the solar system, and
above that is a converging series. Behind the sarcophagus
is a pyramid, from the middle of which
rises a globe in mezzo-relievo, upon which several
of the constellations are drawn, in order to show
the path of the comet of 1681, whose period Sir
Isaac had determined, and also the position of the
solstitial colure mentioned by Hipparchus, and by
means of which Sir Isaac had, in his Chronology,
fixed the time of the Argonautic expedition. A figure
of Astronomy as Queen of the Sciences sits weeping
on the Globe with a sceptre in her hand, and a
star surmounts the summit of the pyramid. The
following epitaph is inscribed on the monument.
Hic situs est
Isaacus Newton, Eques Auratus,
Qui Animi Vi prope divina,
Planetarum Motus, Figuras,
Cometarum Semitas, Oceanique Æstus,
Sua Mathesi facem preferente,
Primus demonstravit.
Radiorum Lucis dissimilitudines,
Colorumque inde nascentium Proprietates,
Quas nemo antea vel suspicatus erat, pervestigavit,
Naturæ, Antiquitates, S. Scripturæ,
Sedulus, sagax, fidus Interpres,
Dei Opt. Max. Majestatem Philosophia asseruit,
Evangelii simplicitatem moribus expressit.
Sibi gratulentur Mortales, tale tantumque extitisse,
Humani Generis Decus.
Natus xxv. Decemb. MDCXLII. Obiit. xx. Mar.
MDCCXXVII.
Of which the following is a literal translation:
Here lies
Isaac Newton, Knight,
Who, by a Vigour of Mind almost supernatural,
First demonstrated
The Motions and Figures of the Planets,
The Paths of the Comets, and the Tides of the Ocean.
He diligently investigated
The different Refrangibilities of the Rays of Light,
And the Properties of the Colours to which they give rise.
An assiduous, sagacious, and faithful Interpreter
Of Nature, Antiquity, and the Holy Scriptures,
He asserted in his Philosophy the Majesty of God,
And exhibited in his conduct the Simplicity of the Gospel.
Let Mortals rejoice
That there has existed such and so great
An Ornament of Human Nature.
Born 25th Dec. 1642, Died 20th March, 1727.
In the beginning of 1731, a medal was struck at
the Tower in honour of Sir Isaac Newton. It had
on one side the head of the philosopher, with the
motto, Felix cognoscere causas, and on the reverse a
figure representing the mathematics.
On the 4th February, 1755, a magnificent full-length
statue of Sir Isaac Newton in white marble
was erected in the antechapel of Trinity College.
He is represented standing on a pedestal in a loose
gown, holding a prism, and looking upwards with an
expression of the deepest thought. On the pedestal
is the inscription,
Qui genus humanum ingenio superavit.
Who surpassed all men in genius.
This statue, executed by Roubiliac, was erected
at the expense of Dr. Robert Smith, the author of
the Compleat System of Optics, and professor of astronomy
and experimental philosophy at Cambridge.—It
has been thus described by a modern poet:
Hark where the organ, full and clear,
With loud hosannas charms the ear;
Behold, a prism within his hands,
Absorbed in thought great Newton stands
Such was his brow, and looks serene,
His serious gait and musing mien,
When taught on eagle wings to fly,
He traced the wonders of the sky;
The chambers of the sun explored,
Where tints of thousand hues were stored.
Dr. Smith likewise bequeathed the sum of 500l.
for executing a painting on glass for the window at
the south end of Trinity College, Cambridge. The
subject represents the presentation of Sir Isaac
Newton to his majesty George III., who is seated
under a canopy with a laurel chaplet in his hand, and
attended by the British Minerva, apparently advising
him to reward merit in the person of the great philosopher.
Below the throne, the Lord Chancellor
Bacon is proposing to register the reward about to
be conferred upon Sir Isaac. The original drawing
of this absurd picture was executed by Cypriani,
and cost one hundred guineas.
The personal estate of Sir Isaac Newton, which
was worth about 32,000l., was divided among his
four nephews and four nieces of the half-blood, the
grandchildren of his mother by the Reverend Mr.
Smith. The family estates of Woolsthorpe and
Sustern he bequeathed to John Newton, the heir-at-law,
whose great-grandfather was Sir Isaac’s uncle.
This gentleman does not seem to have sufficiently
valued the bequest, for he sold them in 1732, to Edmund
Turnor of Stoke Rocheford.124 A short time
before his death, Sir Isaac gave away an estate in
Berkshire to the sons and daughter of a brother of
Mrs. Conduit, who, in consequence of their father
dying before Sir Isaac, had no share in the personal
estate; and he also gave an estate of the same value,
which he bought at Kensington, to Catharine, the
only daughter of Mr. Conduit, who afterward married
Mr. Wallop, the eldest son of Lord Lymington.
This lady was afterward Viscountess Lymington,
and the estate of Kensington descended to the late
Earl of Portsmouth, by whom it was sold. Sir Isaac
was succeeded as master and warden in the mint by
his nephew, John Conduit, Esq., who wrote a treatise
on the gold and silver coin, and who died in
1737, leaving behind him his wife and daughter, the
former of whom died in 1739, in the 59th year of
her age.
Permanence of Newton’s Reputation—Character of his Genius—His
Methods of Investigation similar to that used by Galileo—Error in
ascribing his Discoveries to the Use of the Methods recommended by
Lord Bacon—The Pretensions of the Baconian Philosophy examined—Sir
Isaac Newton’s social Character—His great Modesty—The
Simplicity of his Character—His religious and moral Character—His
Hospitality and Mode of Life—His Generosity and Charity—His
Absence—His personal Appearance—Statues and Pictures of
him—Memorials and Recollections of him.
Such were the last days of Sir Isaac Newton, and
such the last laurels which were shed over his grave.
A century of discoveries has since his day been
added to science; but brilliant as these discoveries
are, they have not obliterated the minutest of his
labours, and have served only to brighten the halo
which encircles his name. The achievements of
genius, like the source from which they spring, are
indestructible. Acts of legislation and deeds of war
may confer a high celebrity, but the reputation which
they bring is only local and transient; and while
they are hailed by the nation which they benefit,
they are reprobated by the people whom they ruin
or enslave. The labours of science, on the contrary,
bear along with them no counterpart of evil. They
are the liberal bequests of great minds to every
individual of their race, and wherever they are welcomed
and honoured they become the solace of
private life, and the ornament and bulwark of the
commonwealth.
The importance of Sir Isaac Newton’s discoveries
has been sufficiently exhibited in the preceding
chapters: the peculiar character of his genius, and
the method which he pursued in his inquiries, can
be gathered only from the study of his works, and
from the history of his individual labours. Were
we to judge of the qualities of his mind from the
early age at which he made his principal discoveries,
and from the rapidity of their succession, we should
be led to ascribe to him that quickness of penetration,
and that exuberance of invention, which is
more characteristic of poetical than of philosophical
genius. But we must recollect that Newton was
placed in the most favourable circumstances for the
development of his powers. The flower of his
youth and the vigour of his manhood were entirely
devoted to science. No injudicious guardian controlled
his ruling passion, and no ungenial studies or
professional toils interrupted the continuity of his
pursuits. His discoveries were, therefore, the fruit
of persevering and unbroken study; and he himself
declared, that whatever service he had done to the
public was not owing to any extraordinary sagacity,
but solely to industry and patient thought.
Initiated early into the abstractions of geometry,
he was deeply imbued with her cautious spirit; and
if his acquisitions were not made with the rapidity
of intuition, they were at least firmly secured; and
the grasp which he took of his subject was proportional
to the mental labour which it had exhausted.
Overlooking what was trivial, and separating what
was extraneous, he bore down with instinctive
sagacity on the prominences of his subject, and
having thus grappled with its difficulties, he never
failed to intrench himself in its strongholds.
To the highest powers of invention Newton
added, what so seldom accompanies them, the talent
of simplifying and communicating his profoundest
speculations.125 In the economy of her distributions,
nature is seldom thus lavish of her intellectual gifts.
The inspired genius which creates is rarely conferred
along with the matured judgment which
combines, and yet without the exertion of both the
fabric of human wisdom could never have been
reared. Though a ray from heaven kindled the
vestal fire, yet an humble priesthood was required to
keep alive the flame.
The method of investigating truth by observation
and experiment, so successfully pursued in the Principia,
has been ascribed by some modern writers of
great celebrity to Lord Bacon; and Sir Isaac Newton
is represented as having owed all his discoveries
to the application of the principles of that distinguished
writer. One of the greatest admirers of
Lord Bacon has gone so far as to characterize him
as a man who has had no rival in the times which
are past, and as likely to have none in those which
are to come. In a eulogy so overstrained as this,
we feel that the language of panegyric has passed
into that of idolatry; and we are desirous of weighing
the force of arguments which tend to depose
Newton from the high-priesthood of nature, and to
unsettle the proud destinies of Copernicus, Galileo,
and Kepler.
That Bacon was a man of powerful genius, and
endowed with varied and profound talent,—the most
skilful logician,—the most nervous and eloquent
writer of the age which he adorned, are points which
have been established by universal suffrage. The
study of ancient systems had early impressed him
with the conviction that experiment and observation
were the only sure guides in physical inquiries;
and, ignorant though he was of the methods, the
principles, and the details of the mathematical
sciences, his ambition prompted him to aim at the
construction of an artificial system by which the
laws of nature might be investigated, and which
might direct the inquiries of philosophers in every
future age. The necessity of experimental research,
and of advancing gradually from the study of facts
to the determination of their cause, though the
groundwork of Bacon’s method, is a doctrine which
was not only inculcated but successfully followed
by preceding philosophers. In a letter from Tycho
Brahe to Kepler, this industrious astronomer urges
his pupil “to lay a solid foundation for his views
by actual observation, and then by ascending from
these to strive to reach the causes of things;” and
it was no doubt under the influence of this advice
that Kepler submitted his wildest fancies to the test
of observation, and was conducted to his most
splendid discoveries. The reasonings of Copernicus,
who preceded Bacon by more than a century,
were all founded upon the most legitimate induction.
Dr. Gilbert had exhibited in his treatise on the
magnet126 the most perfect specimen of physical research.
Leonardo da Vinci had described in the
clearest manner the proper method of philosophical
investigation;127 and the whole scientific career of
Galileo was one continued example of the most
sagacious application of observation and experiment
to the discovery of general laws. The names of
Paracelsus, Van Helmont, and Cardan have been
ranged in opposition to this constellation of great
names, and while it is admitted that even they had
thrown off the yoke of the schools, and had succeeded
in experimental research, their credulity and
their pretensions have been adduced as a proof that
to the “bulk of philosophers” the method of induction
was unknown. The fault of this argument consists
in the conclusion being infinitely more general
than the fact. The errors of these men were not
founded on their ignorance, but on their presumption.
They wanted the patience of philosophy and
not her methods. An excess of vanity, a waywardness
of fancy, and an insatiable appetite for that
species of passing fame which is derived from eccentricity
of opinion, moulded the reasonings and disfigured
the writings of these ingenious men; and it
can scarcely admit of a doubt, that, had they lived
in the present age, their philosophical character
would have received the same impress from the
peculiarity of their tempers and dispositions. This
is an experiment, however, which cannot now be
made; but the history of modern science supplies
the defect, and the experience of every man furnishes
a proof that in the present age there are
many philosophers of elevated talents and inventive
genius who are as impatient of experimental research
as Paracelsus, as fanciful as Cardan, and as
presumptuous as Van Helmont.
Having thus shown that the distinguished philosophers
who flourished before Bacon were perfect
masters both of the principles and practice of inductive
research, it becomes interesting to inquire
whether or not the philosophers who succeeded
him acknowledged any obligation to his system, or
derived the slightest advantage from his precepts.
If Bacon constructed a method to which modern
science owes its existence, we shall find its cultivators
grateful for the gift, and offering the richest
incense at the shrine of a benefactor whose generous
labours conducted them to immortality. No
such testimonies, however, are to be found. Nearly
two hundred years have gone by, teeming with
the richest fruits of human genius, and no grateful
disciple has appeared to vindicate the rights of the
alleged legislator of science. Even Newton, who
was born and educated after the publication of the
Novum Organon, never mentions the name of Bacon
or his system, and the amiable and indefatigable
Boyle treated him with the same disrespectful
silence. When we are told, therefore, that Newton
owed all his discoveries to the method of Bacon,
nothing more can be meant than that he proceeded
in that path of observation and experiment which
had been so warmly recommended in the Novum
Organon; but it ought to have been added, that the
same method was practised by his predecessors,—that
Newton possessed no secret that was not used
by Galileo and Copernicus,—and that he would
have enriched science with the same splendid discoveries
if the name and the writings of Bacon had
never been heard of.
From this view of the subject we shall now proceed
to examine the Baconian process itself, and
consider if it possesses any merit as an artificial
method of discovery, or if it is at all capable of being
employed, for this purpose, even in the humblest
walks of scientific inquiry.
The process of Lord Bacon was, we believe, never
tried by any philosopher but himself. As the subject
of its application, he selected that of heat. With
his usual erudition, he collected all the facts which
science could supply,—he arranged them in tables,—he
cross-questioned them with all the subtlety of a
pleader,—he combined them with all the sagacity
of a judge,—and he conjured with them by all the
magic of his exclusive processes. But, after all this
display of physical logic, nature thus interrogated
was still silent. The oracle which he had himself
established refused to give its responses, and the
ministering priest was driven with discomfiture from
his own shrine. This example, in short, of the application
of his system, will remain to future ages
as a memorable instance of the absurdity of attempting
to fetter discovery by any artificial rules.
Nothing even in mathematical science can be
more certain than that a collection of scientific facts
are of themselves incapable of leading to discovery,
or to the determination of general laws, unless they
contain the predominating fact or relation in which
the discovery mainly resides. A vertical column of
arch-stones possesses more strength than the same
materials arranged in an arch without the key-stone.
However nicely they are adjusted, and however nobly
the arch may spring, it never can possess either
equilibrium or stability. In this comparison all the
facts are supposed to be necessary to the final result;
but, in the inductive method, it is impossible
to ascertain the relative importance of any facts, or
even to determine if the facts have any value at all,
till the master-fact which constitutes the discovery
has crowned the zealous efforts of the aspiring philosopher.
The mind then returns to the dark and
barren waste over which it has been hovering; and
by the guidance of this single torch it embraces,
under the comprehensive grasp of general principles,
the multifarious and insulated phenomena which
had formerly neither value nor connexion. Hence
it must be obvious to the most superficial thinker,
that discovery consists either in the detection of
some concealed relation—some deep-seated affinity
which baffles ordinary research, or in the discovery
of some simple fact which is connected by slender
ramifications with the subject to be investigated;
but which, when once detected, carries us back by
its divergence to all the phenomena which it embraces
and explains.
In order to give additional support to these views,
it would be interesting to ascertain the general character
of the process by which a mind of acknowledged
power actually proceeds in the path of successful
inquiry. The history of science does not
furnish us with much information on this head, and
if it is to be found at all, it must be gleaned from
the biographies of eminent men. Whatever this
process may be in its details, if it has any, there
cannot be the slightest doubt that in its generalities
at least it is the very reverse of the method of induction.
The impatience of genius spurns the restraints
of mechanical rules, and never will submit
to the plodding drudgery of inductive discipline.
The discovery of a new fact unfits even a patient
mind for deliberate inquiry. Conscious of having
added to science what had escaped the sagacity of
former ages, the ambitious spirit invests its new
acquisition with an importance which does not belong
to it. He imagines a thousand consequences
to flow from his discovery: he forms innumerable
theories to explain it, and he exhausts his fancy in
trying all its possible relations to recognised difficulties
and unexplained facts. The reins, however,
thus freely given to his imagination, are speedily
drawn up. His wildest conceptions are all subjected
to the rigid test of experiment, and he has thus been
hurried by the excursions of his own fancy into new
and fertile paths, far removed from ordinary observation.
Here the peculiar character of his own genius
displays itself by the invention of methods of
trying his own speculations, and he is thus often led
to new discoveries far more important and general
than that by which he began his inquiry. For a
confirmation of these views, we may refer to the
History of Kepler’s Discoveries; and if we do not
recognise them to the same extent in the labours of
Newton, it is because he kept back his discoveries
till they were nearly perfected, and therefore withheld
the successive steps of his inquiries.
The social character of Sir Isaac Newton was
such as might have been expected from his intellectual
attainments. He was modest, candid, and
affable, and without any of the eccentricities of genius,
suiting himself to every company, and speaking
of himself and others in such a manner that he was
never even suspected of vanity. “But this,” says
Dr. Pemberton, “I immediately discovered in him,
which at once both surprised and charmed me.
Neither his extreme great age nor his universal reputation
had rendered him stiff in opinion, or in any
degree elated. Of this I had occasion to have
almost daily experience. The remarks I continually
sent him by letters on the Principia were received
with the utmost goodness. These were so far from
being any ways displeasing to him, that on the contrary
it occasioned him to speak many kind things
of me to my friends, and to honour me with a public
testimony of his good opinion.”
The modesty of Sir Isaac Newton in reference to
his great discoveries was not founded on any indifference
to the fame which they conferred, or upon
any erroneous judgment of their importance to
science. The whole of his life proves, that he knew
his place as a philosopher, and was determined to
assert and vindicate his rights. His modesty arose
from the depth and extent of his knowledge, which
showed him what a small portion of nature he had
been able to examine, and how much remained to
be explored in the same field in which he had himself
laboured. In the magnitude of the comparison
he recognised his own littleness; and a short time
before his death he uttered this memorable sentiment:—“I
do not know what I may appear to the
world; but to myself I seem to have been only like
a boy playing on the seashore, and diverting myself
in now and then finding a smoother pebble or a prettier
shell than ordinary, while the great ocean of
truth lay all undiscovered before me.” What a lesson
to the vanity and presumption of philosophers,—to
those especially who have never even found the
smoother pebble or the prettier shell! What a preparation
for the latest inquiries, and the last views
of the decaying spirit,—for those inspired doctrines
which alone can throw a light over the dark ocean
of undiscovered truth!
The native simplicity of Sir Isaac Newton’s mind
is finely portrayed in the affecting letter in which
he acknowledges to Locke that he had thought and
spoken of him uncharitably; and the humility and
candour in which he asks forgiveness could have
emanated only from a mind as noble as it was pure.
In the religious and moral character of our author
there is much to admire and to imitate. While he
exhibited in his life and writings an ardent regard
for the general interests of religion, he was at the
same time a firm believer in revelation. He was
too deeply versed in the Scriptures, and too much
imbued with their spirit, to judge harshly of other
men who took different views of them from himself.
He cherished the great principles of religious toleration,
and never scrupled to express his abhorrence
of persecution, even in its mildest form. Immorality
and impiety he never permitted to pass unreproved;
and when Dr. Halley128 ventured to say any
thing disrespectful to religion, he invariably checked
him, and said, “I have studied these things,—you
have not.”129
After Sir Isaac Newton took up his residence in
London, he lived in a very handsome style, and kept
his carriage, with an establishment of three male
and three female servants. In his own house he
was hospitable and kind, and on proper occasions
he gave splendid entertainments, though without
ostentation or vanity. His own diet was frugal, and
his dress was always simple; but on one occasion,
when he opposed the Honourable Mr. Annesley in
1705, as a candidate for the university, he is said to
have put on a suit of laced clothes.
His generosity and charity had no bounds, and he
used to remark, that they who gave away nothing
till they died never gave at all. Though his wealth
had become considerable by a prudent economy, yet
he had always a contempt for money, and he spent
a considerable part of his income in relieving the
poor, in assisting his relations, and in encouraging
ingenuity and learning. The sums which he gave
to his relations at different times were enormous;130
and in 1724 he wrote a letter to the Lord Provost
of Edinburgh, offering to contribute 20l. per annum
to a provision for Mr. Maclaurin, provided he accepted
the situation of assistant to Mr. James Gregory,
who was professor of mathematics in the university.
The habits of deep meditation which Sir Isaac
Newton had acquired, though they did not show
themselves in his intercourse with society, exercised
their full influence over his mind when in the
midst of his own family. Absorbed in thought he
would often sit down on his bedside after he rose,
and remain there for hours without dressing himself,
occupied with some interesting investigation which
had fixed his attention. Owing to the same absence
of mind, he neglected to take the requisite quantity
of nourishment, and it was therefore often necessary
to remind him of his meals.131
Sir Isaac Newton is supposed to have had little
knowledge of the world, and to have been very ignorant
of the habits of society. This opinion has,
we think, been rashly deduced from a letter which
he wrote in the twenty-seventh year of his age to
his young friend, Francis Aston, Esq., who was about
to set out on his travels. This letter is a highly
interesting production; and while it shows much
knowledge of the human heart, it throws a strong
light upon the character and opinions of its author.
In his personal appearance, Sir Isaac Newton was
not above the middle size, and in the latter part of
his life was inclined to be corpulent. According to
Mr. Conduit “he had a very lively and piercing eye,
a comely and gracious aspect, with a fine head of
hair as white as silver, without any baldness, and
when his peruke was off was a venerable sight.”
Bishop Atterbury asserts,132 on the other hand, that
the lively and piercing eye did not belong to Sir
Isaac during the last twenty years of his life. “Indeed,”
says he, “in the whole air of his face and
make there was nothing of that penetrating sagacity
which appears in his compositions. He had something
rather languid in his look and manner which
did not raise any great expectation in those who did
not know him.” This opinion of Bishop Atterbury
is confirmed by an observation of Mr. Thomas
Hearne,133 who says “that Sir Isaac was a man of no
very promising aspect. He was a short, well-set
man. He was full of thought, and spoke very little in
company, so that his conversation was not agreeable.
When he rode in his coach, one arm would be out
of his coach on one side and the other on the other.”
Sir Isaac never wore spectacles, and never “lost
more than one tooth to the day of his death.”
Besides the statue of Sir Isaac Newton executed
by Roubiliac, there is a bust of him by the same
artist in the library of Trinity College, Cambridge.
Several good paintings of him are extant. Two
of these are in the hall of the Royal Society of
London, and have, we believe, been often engraved.
Another, by Vanderbank, is in the apartments of
the Master’s lodge in Trinity College, and has been
engraved by Vertue. Another, by Valentine Ritts,
is in the landing-place near the entrance to Trinity
College library; but the best, from which our engraving
is copied, was painted by Sir Godfrey Kneller,
and is in the possession of Lord Egremont at
Petworth. In the university library there is preserved
a cast taken from his face after death.
Every memorial of so great a man as Sir Isaac
Newton has been preserved and cherished with peculiar
veneration. His house at Woolsthorpe, of which
we have given an engraving, has been religiously
protected by Mr. Turnor of Stoke Rocheford, the
proprietor. Dr. Stukeley, who visited it in Sir
Isaac’s lifetime, on the 13th October, 1721, gives the
following description of it in his letter to Dr. Mead,
written in 1727: “’Tis built of stone as is the way
of the country hereabouts, and a reasonable good
one. They led me up stairs and showed me Sir
Isaac’s study, where I suppose he studied when in
the country in his younger days, or perhaps when
he visited his mother from the university. I observed
the shelves were of his own making, being
pieces of deal boxes which probably he sent his
books and clothes down in on those occasions.
There were some years ago two or three hundred
books in it of his father-in-law, Mr. Smith, which
Sir Isaac gave to Dr. Newton of our town.”134
When the house was repaired in 1798, a tablet of
white marble was put up by Mr. Turnor in the room
where Sir Isaac was born, with the following inscription:
“Sir Isaac Newton, son of John Newton, Lord
of the manor of Woolsthorpe, was born in this room
on the 25th December, 1642.”
Nature and Nature’s laws lay hid in night,
God said, “Let Newton be,” and all was light.
The following lines have been written upon the
house:
Here Newton dawned, here lofty wisdom woke,
And to a wondering world divinely spoke.
If Tully glowed, when Phædrus’ steps he trode,
Or fancy formed Philosophy a god;
If sages still for Homer’s birth contend
The Sons of Science at this dome must bend.
All hail the shrine! All hail the natal day,
Cam boasts his noon,—This Cot his morning ray.
The house is now occupied by a person of the
name of John Wollerton. It still contains the two
dials made by Newton, but the styles of both are
wanting. The celebrated apple-tree, the fall of one
of the apples of which is said to have turned the
attention of Newton to the subject of gravity, was
destroyed by wind about four years ago; but Mr.
Turnor has preserved it in the form of a chair.135
The chambers which Sir Isaac inhabited at Cambridge
are known by tradition. They are the apartments
next to the great gate of Trinity College, and
it is believed that they then communicated by a
staircase with the observatory in the Great Tower,—an
observatory which was furnished by the contributions
of Newton, Cotes, and others. His telescope,
represented in fig. 3, page 41, is preserved in the
library of the Royal Society of London, and his globe,
his universal ring-dial, quadrant, compass, and a reflecting
telescope said to have belonged to him, in
the library of Trinity College. There is also in the
same collection a long and curled lock of his silver
white hair. The door of his bookcase is in the Museum
of the Royal Society of Edinburgh.
The manuscripts, letters, and other papers of Newton
have been preserved in different collections. His
correspondence with Cotes relative to the second
edition of the Principia, and amounting to between
sixty and a hundred letters, a considerable portion
of the manuscript of that work, and two or three
letters to Dr. Keill on the Leibnitzian controversy,
are preserved in the library of Trinity College, Cambridge.
Newton’s letters to Flamstead, about thirty-four
in number, are deposited in the library of Corpus
Christi College, Oxford.136 Several letters of Newton,
and, we believe, the original specimen which he
drew up of the Principia, exist among the papers of
Mr. William Jones (the father of Sir William Jones),
which are preserved at Shirburn Castle, in the library
of Lord Macclesfield. But the great mass of Newton’s
papers came into the possession of the Portsmouth
family through his niece, Lady Lymington,
and have been safely preserved by that noble family.
There is reason to believe that they contain nothing
which could be peculiarly interesting to science; but
as the correspondence of Newton with contemporary
philosophers must throw considerable light on
his personal history, we trust that it will ere long be
given to the public.
