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Title: The Life of Sir Isaac Newton

Author: David Brewster

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SIR ISAAC NEWTON.
HARPER’S FAMILY LIBRARY
Printed by R. Miller

Harper’s Stereotype Edition.

THE

LIFE
OF

SIR ISAAC NEWTON.

BY

DAVID BREWSTER, LL.D. F.R.S.

Ergo vivida vis animi pervicit, et extra
Processit longe flammantia mœnia mundi;
Atque omne immensum peragravit mente amimoque.
Lucret. lib. i. 1. 73.

The Birthplace of Newton.

NEW-YORK:
PRINTED AND PUBLISHED BY J. & J. HARPER;
NO. 82 CLIFF-STREET,

AND SOLD BY THE BOOKSELLERS GENERALLY THROUGHOUT
THE UNITED STATES.
1833.

TO

THE RIGHT HONOURABLE

LORD BRAYBROOKE.

The kindness with which your lordship intrusted to me some very
valuable materials for the composition of this volume has induced me to
embrace the present opportunity of publicly acknowledging it. But even if
this personal obligation had been less powerful, those literary attainments
and that enlightened benevolence which reflect upon rank its highest lustre
would have justified me in seeking for it the patronage of a name which
they have so justly honoured.
DAVID BREWSTER.
Allerly, June 1st, 1831.

PREFACE.
As this is the only Life of Sir Isaac Newton on any considerable scale
that has yet appeared, I have experienced great difficulty in preparing it for
the public. The materials collected by preceding biographers were
extremely scanty; the particulars of his early life, and even the historical
details of his discoveries, have been less perfectly preserved than those of
his illustrious predecessors; and it is not creditable to his disciples that they
have allowed a whole century to elapse without any suitable record of the
life and labours of a master who united every claim to their affection and
gratitude.
In drawing up this volume, I have obtained much assistance from the
account of Sir Isaac Newton in the Biographia Britannica; from the letters
to Oldenburg, and other papers in Bishop Horsley’s edition of his works;
from Turnor’s Collections for the History of the Town and Soke of
Grantham; from M. Biot’s excellent Life of Newton in the Biographie
Universelle; and from Lord King’s Life and Correspondence of Locke.
Although these works contain much important information respecting
the Life of Newton, yet I have been so fortunate as to obtain many new
materials of considerable value.
To the kindness of Lord Braybrooke I have been indebted for the
interesting correspondence of Newton, Mr. Pepys, and Mr. Millington,
which is now published for the first time, and which throws much light
upon an event in the life of our author that has recently acquired an
unexpected and a painful importance. These letters, when combined with
those which passed between Newton and Locke, and with a curious extract
from the manuscript diary of Mr. Abraham Pryme, kindly furnished to me
by his collateral descendant Professor Pryme of Cambridge, fill up a blank
in his history, and have enabled me to delineate in its true character that
temporary indisposition which, from the view that has been taken of it by

foreign philosophers, has been the occasion of such deep distress to the
friends of science and religion.
To Professor Whewell, of Cambridge, I owe very great obligations for
much valuable information. Professor Rigaud, of Oxford, to whose
kindness I have on many other occasions been indebted, supplied me with
several important facts, and with extracts from the diary of Hearne in the
Bodleian Library, and from the original correspondence between Newton
and Flamstead, which the president of Corpus Christi College had for this
purpose committed to his care; and Dr. J. C. Gregory, of Edinburgh, the
descendant of the illustrious inventor of the reflecting telescope, allowed
me to use his unpublished account of an autograph manuscript of Sir Isaac
Newton, which was found among the papers of David Gregory, Savilian
Professor of Astronomy at Oxford, and which throws some light on the
history of the Principia.
I have been indebted to many other friends for the communication of
books and facts, but especially to Sir William Hamilton, Bart., whose
liberality in promoting literary inquiry is not limited to the circle of his
friends.
D. B.
Allerly, June 1st, 1831.

CONTENTS.
Page

CHAPTER I.
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 Water-clock—His Self-moving
Cart—His Sun-dials—His Preparation for the
University 17

CHAPTER II.
Newton enters Trinity College, Cambridge—Origin
of his Propensity for Mathematics—He studies the
Geometry of Descartes unassisted—Purchases a
Prism—Revises Dr. Barrow’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 26

CHAPTER III.
Newton occupied in grinding Hyperbolical Lenses— 30
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

CHAPTER IV.
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 47

CHAPTER V.
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 reinvented 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 63

CHAPTER VI.
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 75

CHAPTER VII.
Newton’s Theory of the Colours of Natural Bodies
explained—Objections to it stated—New
Classification of Colours—Outline of a new
Theory proposed 82

CHAPTER VIII.
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 98

CHAPTER IX.
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” 106

CHAPTER X.

Astronomical Discoveries of Newton—Necessity of
combined Exertion to the completion of great
Discoveries—Sketch of the History or Astronomy
previous to the time of Newton—Copernicus,
1473–1543—Tycho Brahe, 1546–1601—Kepler,
1571–1631—Galileo, 1564–1642 110

CHAPTER XI.
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 Doctor 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 140

CHAPTER XII.
Doctrine of Infinite Quantities—Labours of Pappus 168
—Kepler—Cavaleri—Roberval—Fermat—Wallis
—Newton discovers the Binomial Theorem and
the Doctrine of Fluxions in 1606—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

CHAPTER XIII.
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 Manuscript—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 200

CHAPTER XIV.
No Mark of National Gratitude conferred upon 223
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

CHAPTER XV.
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 Secrecy—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 234

CHAPTER XVI.
Theological Studies of Sir Isaac—Their Importance
to Christianity—Motives to which they have been
ascribed—Opinions of Biot and La Place
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 Lexicon
Propheticum—His Four Letters to Dr. Bentley—
Origin of Newton’s Theological Studies—Analogy
between the Book of Nature and that of Revelation 242

CHAPTER XVII.

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 265

CHAPTER XVIII.
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 284

CHAPTER XIX.
Permanence of Newton’s Reputation—Character of 292
his Genius—His Method 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

Appendix, No. I.—Observations on the Family of Sir
Isaac Newton 307

Appendix, No. II.—Letter from Sir Isaac Newton to
Francis Aston, Esq., a young Friend who was on
the eve of setting out on his Travels 316

Appendix, No. III.—“A Remarkable and Curious
Conversation between Sir Isaac Newton and Mr.
Conduit.” 320

LIFE
OF
SIR ISAAC NEWTON.

CHAPTER I.
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
1
ascendency of his genius. The philosopher, 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
2
such an extremely diminutive size, 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
3
at Sewstern, 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
4
quitted Grantham. 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,
5
but often from life. 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
6
determined that he should proceed to Cambridge at the approaching term.

CHAPTER II.
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
7
with that attention which so excellent a writer deserved. 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.
8
Isaac Newton, 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.

CHAPTER III.
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,
9
or at least in 1667; and “in the year 1666 or before” 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
10
therewith the celebrated phenomena of colours.” 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
11
middle of the larger speculum, to transmit the light to an eye-glass; 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?

CHAPTER IV.
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
12
given to the world. “It was an esteem,” says he, “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,
13
a physician in Liege, 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
14
instead of guessing it, or had Newton been less confident than he was 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
15
of his tranquillity. “I intend,” says he, “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.”

CHAPTER V.
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
16
have been impressed upon his mind with all the force of an axiom. 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
17
public. 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
18
length of the coloured spaces and the divisions of a musical chord, 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.

CHAPTER VI.
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.

CHAPTER VII.
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
19
surfaces, 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
20
yet may perhaps variously refract 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
21
of Sir Isaac Newton’s Philosophy; 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
22
surface AE, 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
23
fibres; 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
24
transmitted, while part of the complementary light is reflected. 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
25
separating surfaces either white or coloured light may be reflected.
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,
26
which I have described in another place, 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,
27
and detaining it wholly within the body.
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
28
been added.

CHAPTER VIII.
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
29
posthumous work published in 1665, two years after his death.
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
30
in the subsequent history of optics.
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
31
aperture or from the focus of divergence; 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.

CHAPTER IX.
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
32
of a polarity in the rays of light has been suggested.
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
33
frequently reprinted both in England and on the Continent, and there
perhaps never was a work of profound science so widely circulated.

CHAPTER X.
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
34
to acquire the knowledge of the heavens; and kings 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
35
regular geometrical solids, 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
36
time saw the fourth satellite.
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.
37
Galileo, however, thought otherwise. A sense of degradation 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
38
1666 a work on Jupiter’s satellites. 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
39
of action.

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
40
expressly in Kepler.”

CHAPTER XI.
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
41
gravity, its force must decrease in the duplicate proportion, 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
42
cause 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
43
of it before the Royal Society in December, 1679. 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
44
body moved in a resisting medium.
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

45
himself informs us in his letter to Halley, 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
46
communicated to the Royal Society.
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
47
the law of gravity from the second law of Kepler.
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
48
direction, and at very remote distances from the centre of our system.
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
49
hypotheses of the Cartesians.’ 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
50
Gregory, at St. Andrew’s, 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
51
university, that the Principia rose to four times its original price. 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
52
mathematical. From a manuscript of Sir Isaac Newton’s, entitled “A
demonstration that the planets, by their gravity towards the sun, may move
53
in ellipses, 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
54
to the times in motions round an immoveable centre of attraction. Three
lemmas, containing properties of the ellipse, then prepare the reader for the
55
celebrated proposition, that when a body moves in an ellipse, 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.

CHAPTER XII.
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
56
near indeed that both Lagrange and Laplace 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
57
other.”
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
58
from his memory if he had not, a few weeks before, 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.
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John Colson, Professor of Mathematics in Cambridge.
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
60
time in 1779, in Dr. Horsley’s edition of his works. 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
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letter to the most distinguished mathematicians in Europe, 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
62
death of Oldenburg in the month of August, 1677, 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

63
idea of the generation of quantities.”] 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
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indivisibles of Cavaleri. 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
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the case; he called upon the society to silence his vain and unjust
66
clamours, 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
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after having seen mine.” 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
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28, 1714, 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
69
after his arrival, 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
70
Commercium Epistolicum, and the little piece 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
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privately circulated among the friends of the disputants.
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
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falsely ascribed to Newton. 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.

CHAPTER XIII.
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
73
design.
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
74
in 1688, though by a very narrow majority, 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
75
manuscripts and autograph letters. ‘On the 29th May, 1694, M. Colin, 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
76
on the 25th February, and the 4th on the 11th 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,
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second, and third fluxions. 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
78
fluxions. It appears, also, from the second book of the Optics, 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

79
letters, 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
80
of the mathematical question which had been submitted to his judgment.
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
81
with himself, and of discussion among his friends. 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
82
another book, and that I took you for a Hobbist. 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,
83
wish you extremely well, and am, without compliment, &c.”

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
84
Optics. The first paragraph expresses nearly the same ideas as some
sentences in the scholium beginning “Deus summus est ens æternum,
85
infinitum, absolute perfectum;” 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
86
concerned.
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.

CHAPTER XIV.
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
87
their species, but he was left in comparative poverty, 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
88
Cambridge. 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
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counsel.

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
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election by a very great majority. 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
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the 3d July, and was agreed to by the Lords on the 8th of the same month.

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In giving an account of this transaction, 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.

CHAPTER XV.
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
93
secret. 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
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about twenty-four quarto printed pages, 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,
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and was accompanied with observations by M. Freret, the object of which
96
was to refute the leading points of the system. 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,

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which was printed in the Philosophical Transactions for 1725. 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
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consists of six chapters: 1. On the Chronology of the Greeks; 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
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it to the other five chapters.
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
100
Philosophical Transactions for 1727, 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
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opinion with M. Daunou, “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
102
mentioned in history, and is not to be asserted without proving it.

CHAPTER XVI.
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.
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“From the nature of the subject,” 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
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beginning 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
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warranted by any thing which he has published; 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
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of the Royal Society while he was President.
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

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study of that work; 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.
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In the first 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.”
109
In the second 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
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highest heavens in parabolical lines.”
111
In the fourth letter 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
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profoundest parts of his own writings.
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.

CHAPTER XVII.
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.
Equal
Degrees
Parts
of Heat.
of Heat.
0 0 Freezing point of water.
1 12 Blood-heat.
2 24 Heat of melting wax.
Melting point of equal parts of tin and
3 48
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
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exceeding great velocity by the force of reflection.
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
114
his own handwriting. 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
115
obliged to adopt one.”
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;
116
it is about the cause of gravity,” which he goes on to explain; 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.
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In the registers of the Royal Society there exist several letters 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
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construction be such as I may hereafter describe.” 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
119
of pure yellow light of definite refrangibility.

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
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same phenomena above twenty years ago, and long before the
observations of Sir Isaac were communicated to the scientific world.

CHAPTER XVIII.
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
121
the Transactions.
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