Full text of "Memoirs of the life writings, and discoveries of Sir Isaac Newton"

. Presented to the
LIBRARY of the

UNIVERSITY OF TORONTO

^. J. R. McLeod

J'lX. CLC

/h/i^.

MEMOIRS ^.x-e^'t.

THE LIFE, WRITINGS, AND DISCOVERIES

SIR ISAAC NEWTON.

BY SIR DAVID BREWSTER, K.H.

A.M., LL.D., D.C.L., F.R.S., and M.R.T.A.,

One of the Eight A ssociates of the Imperial Institute of France— Officer of the Legion of Honour-
Chevalier of the Prussian Order of Merit of Frederick the Great — Honorary or CorrespomlinK
Member of the Academies of St. Petersburg, Vienna, Berlin, Turin, Copenhagen,
.Stockholm, Munich, Gottingen, Brussels, Haerlem, Erlangen , Canton de
Vaud, Jlodena, Florence, Venice, Washington, New York, Boston,
Quebec, Cape Town, etc. etc. ; and Principal and Vice-
Chancellor of the University of Edinburgh.

^ctijnb (gbiiion.

VOL. I.

EDINBURGH:
EDMONSTON AND DOUGLAS.

M D C C C L X.

£rgo vivida vis animi pervicit. et extra

Processit longe flammantia moenia mundi ;

Atqae omne imraensum paragravit menw animoque.

LncRETios.Lib.

TO HIS ROYAL HIGHNESS

PRINCE ALBERT, K.G.

CHANCELLOR OF THE UNIVERSITY OF CAMBRIDGE.

Sir,
In dedicating this Work to your Royal Highness, I seek for
it the protection of a name indissolubly associated with the
Sciences and the Arts. An account of the Life, Writings, and
Discoveries of Sir Isaac Newton might have been appropriately
inscribed to the Chancellor <3f the University of Cambridge, the
birthplace of Newton's genius, and the scene of his intellectual
achievements ; but that illustrious name is more honourably
placed beside that of a Prince who has given such an impulse
to the Arts and Sciences of England, and whose views, were
they seconded by Statesmen willing to extend Education and
advance Science, would raise our country to a higher rank than
it now holds among the nations of Europe, in the arts of Peace
and of War. It is from the trenches of Science alone that war
can be successfully waged ; and it is in its patronage and liberal
endowment that nations will find their best and cheapest de-
fence.

VI DEDICATION.

That your Royal Highness may be enabled to realize those
noble and patriotic views respecting the national encouragement
of Science, and the consolidation of our Scientific Institutions,
vi^hich you have so much at heart, and that you may long live
to enjoy the reputation which you have so justly earned, is tlie
ardent wish of,

Sir,

Your Royal Highness's

Humble and obedient Ser^'aut,

DAVID BREWSTER.

St. Leonard's College,

St. Andrews, May 12, 1855.

PREFACE.

In consequence of the wide circulation of the Life of Sir
Isaac Newton, which I drew up for the " Family Library " in
1831, I was induced to undertake a larger work, in order to give
a more detailed account of his Life, Writings, and Discoveries.
For this purpose I applied in 1837 to the Honourable Newton
FeUowes, one of the trustees of the Earl of Portsmouth, for per-
mission to inspect the Manuscripts and Correspondence of Sir
Isaac, which, through his grandniece, Miss Conduitt, afterwards
Lady Lymington, had come into the possession of that noble
family. Mr. FeUowes kindly granted my request, and his amiable
and accomplished son, Mr. Henry Arthur FeUowes, who, had
he Uved, would now have been Earl of Portsmouth, met me in
June 1837, at Hurtsbourne Park, to assist me in examining
and making extracts from the large mass of papers which Sir
Isaac had left behind him.

In this examination our attention was particularly directed
to such letters and papers as were calculated to throw light
upon his early and academical life, and, with the assistance of
Mr. FeUowes, who copied for me several important documents,
I was enabled to collect many valuable materials unknown to
preceding biographers.

After the death of Sir Isaac, his nephew, Mr. Conduitt, drew

Vlll PREFACE.

up a memorial, containing a sketch of his life, for the use of
Fontenelle, the Secretary to the Academy of Sciences in Paris,
whose duty it was to write his Eloge, as one of the eight Asso-
ciates of the Academy. This memorial was published by Ed-
mond Turnor, Esq., in his " Collections for the History of the
Town and Soke of Grantham," and was supposed to contain all
the information that Mr. Conduitt could collect from persons
then alive, and from other sources, respecting Sir Isaac's life.
This, however, was a mistake. After the publication of Fon-
tenelle's Eloge, Mr. Conduitt resolved to draw up a Life of his
illustrious relative, and, with this view, he wrote the follow-
ing letter, requesting the assistance of Sir Isaac's personal
friends :' —

" Gth February 172|.

" Sir, — I have taken the liberty to trouble you with some
short hints of that part of our honoured friend, Sir I. Newton's
life, which I must beg the favour of you to undertake, there
being nobody, without dispute, so well qualified to do it as
yourself. I send you, at the same time, FonteneUe's Eloge,
wherein you will find a very imperfect attempt of the same
kind ; but I fear he had neither abilities nor inclination to do
justice to that great man, who had eclipsed the glory of their
hero, Descartes. As Sir I. Newton was a national man, I think
every one ought to contribute to a work intended to do him
justice, particularly those who had so great a share in his
esteem as you had ; and as I pretend to nothing more than to
compile it, I shall acquaint the public in the Preface, to whom
they are indebted for each particular part of it.

1 This letter is docqueted by Conduitt, " Letter sent by me concerning Sir I. N.'s
Inventions."

PREFACE. IX

" I am persuaded that the hints I have sent you are very-
imperfect, and that your own genius will suggest to you many
others much more proper and significant, and I beg of you to
put down everything that occurs to your thoughts, and you
think fit to be inserted in such a work.

" I conjure you not to put off what I take the liberty to
recommend to you. As on one hand the complying with my
request will be a mark of your gratitude to your old friend, and
an eternal obligation on me, so your delaying it will be the
most mortifying disappointment to,

" Sir,

" Your most humble Servant,

" John Conduitt."^

Although Mr. Conduitt had at this time resolved to compile
a Life of Sir Isaac, and had obtained much information from
Dr. Stukely, Mr. Wickins, and Dr. Humphrey Newton of
Grantham, yet he seems to have so far relinquished his design,
that in June 1729, nearly eighteen months after the date of
his letter, he intimates to a friend^ that " he has some thoughts
of writing the Life of Sir Isaac Newton himself." That he
made the attempt, appears from an indigested mass of manu-
script which he has left behind him, and which does not lead

1 1 hare not succeeded in ascertaining to whom this letter was addressed. It was
probably a circular sent to more than one person. I have found a letter from John
Craig, and a paper by De Moivre, which have the appearance of being answers to it,
but the dates of both are earlier than that of Conduitt's letter. In a letter dated April
16, 1729, Conduitt made a similar application to Professor Machin.

2 In a letter on the subject of a large " monumental picture to Newton's memory,"
for Conduitt himself. This letter is docqueted, " sent to Westgarth," who seems to have
been )khen in Italy.

X PREFACE.

US to regret that he abandoned his design. The materials,
however, which he obtained from Mrs. Conduitt, and from the
friends of Newton then alive, are of great value ; and, in so
far as Mr. H. A. Fellowes and I could make an abstract of
these and other manuscripts during a week's visit at Hurts-
bourne Park, I have availed myself of them in composing the
first volume of this work, which was printed before the papers
themselves came into my hands.

Before I began the second volume, which contains the history
of the Fluxionary controversy, and the Life of Newton subse-
quent to the publication of the first edition of the Principia^
I had the good fortune to obtain from the Earl of Portsmouth,
through the kindness of Lord Brougham, the collection of
manuscripts and correspondence which the late Mr. H. A.
Fellowes had examined and arranged as peculiarly fitted to
throw light on the Life and Discoveries of Sir Isaac. In these
manuscripts I found much new information respecting the
history of the Frincipia, which, though it might have been
more appropriately placed in the first volume, I have introduced
into those chapters of the second which relate to the period
when the other editions of the Principia were published.

In the different controversies in which Newton's discoveries
involved him, his moral character had never been the subject
of suspicion. In Hooke, he found a jealous but an honest
rival, who, though he claimed discoveries which substantially
belonged to Newton, never cast a reproach upon his name ;
and amid all the bitterness of the Fluxionary controversy,
Leibnitz and Bernoulli, and their anonymous auxiliaries, never
hesitated to acknowledge the purity of Newton's motives, and
the scrupulous correctness of his conduct. It was reserved for

PREFACE. XI

two English astronomers, the one a contemporary and the other
a disciple, to misrepresent and calumniate their illustrious
countryman.

In 1835, the scientific world was startled by the publication
of Baily's Life of Flamsteed, a huge volume, deeply affecting
the character of Newton, and, strange to say, printed and cir-
culated throughout the world, at the expense of the Board of
Admiralty. The friends of the great philosopher were thus
summoned to a painful controversy, which, had it been raised
in his lifetime, would have been summarily extinguished ; but
a century and a quarter had elapsed before the slumbering
calumnies revived, and it was hardly to be expected that the
means of defence would have enjoyed the same vitality. Under
these circumstances Mr. Fellowes and I anxiously searched, but
in vain, for the letters of Flamsteed to Newton, and other
relative documents which were necessary for his defence. In
this difficulty, some of the admirers of Newton, among whom
I must mention my friend Mr. Kobert Brown, the distinguished
President of the Linnean Society, sent me some important
facts ; but valuable as they were, they were not sufficient to
refute the calumnies of the Astronomer-Royal, From this
embarrassment, however, I have been relieved by the receipt
of all Flamsteed' s letters and other important papers which
Newton had careftdly preserved, and which Mr, Fellowes had
discovered and set aside for my use. With these documents
I trust I have been able, though at a greater length than I
could have wished, to defend the illustrious subject of this
work against a system of calumny and misrepresentation un-
exampled in the history of science.

When I published my Life of Neiuton in 1831, I had not

XU PREFACE.

seen his correspoudeuce with Mr. Cotes and other mathema-
ticians in the Library of Trinity College. Mr. Halliwell,
however, who had made copious extracts from these manu-
scripts, kindly put them into my hands ; but the subsequent
publication of the correspondence by Mr. Edleston, has enabled
me to make a more advantageous use of these valuable materials.

Dr. Monk, Bishop of Gloucester and Bristol, had "often
expressed in private a wish and request that some one of the
many accomplished Newtonians who are resident in that society
would favour the world by publishing the whole collection,"^
and I have no doubt that it was from this public expression of
it, in his able and interesting Life of Dr. Bentley^ that the
Masters and Seniors of Trinity College resolved to publish the
coiTespondence.

This valuable work, edited by Mr. Edleston, Fellow of
Trinity, is a most important contribution to the History of
Mathematical and Physical Science. The admirable synopsis
which it contains of Newton's Life ; — the learned and able
annotations illustrative of his history ; and the explanatory
notes on the letters themselves, throw much light on the sub-
jects to which they refer, and have been of essential service to
me in the composition of this work. But in addition to the
obligations which I owe to Mr. Edleston, in common with
every friend of science, I have to acknowledge others of a more
personal kind. During the printing of the second volume,
which he has had the kindness to peruse, I have received from
him much new and important information, and availed myself
of his judicious criticisms and useful suggestions.

To Professor De Morgan, to whom the public owes a brief

1 LifeofBentley,T^.UQ.

PREFACE. Xm

but interesting biographical sketch of Newton, and who has
carefully investigated various points in the Fluxionary con-
troversy, I have been indebted for much information, and for
his kind revision of the sketch I had given of the early history
of the Infinitesimal Calculus. On a few questions in the life
of Newton, and the history of his discoveries, my opinion
differs somewhat from his ; but I have been able to confirm,
from the documents in my possession, many of his views on
important points which he was the first to investigate and to
publish.

From my late amiable and distinguished friend Professor
Rigaud of Oxford, too early cut off in his scientific career, I
obtained valuable aid whenever I encountered difficulties or
required information. His "Historical Essay on the Principia,"
which he generously offered to withhold from the public, till
I had finished the present work, is a most important contribu-
tion to the history of Newton's discoveries, and I am glad to
be able to complete the correspondence between Newton and
Halley, which Mr. Rigaud was the first to publish in its
genuine state.

The Rev. Jeffrey Ekins, Rector of Sampford, whose family,
from their connexion with Newton, have been long in possession
of several of his theological manuscripts and letters, has obli-
gingly sent me copies of many of them, and has otherwise
favoured me with much useful information.

To Lord Brougham, Sir John Lubbock, Mr. Cutts Barton,
and other friends, I have to return my best thanks for the
assistance they have given me.

In concluding this Preface, I can hardly avoid referring to
Sir Isaac Newton's religious opinions. In the chapter which

XIV PREFACE.

relates to them I have touched lightly, and unwillingly, on a
subject so tender ; and in publishing the most interesting of
the manuscripts in which these opinions are recorded, I have
done little more than submit them to the judgment of the
reader. Though adverse to my own, and I believe to the
opinions of those to whom his memory is dearest, I did not
feel myself justified, had I been so disposed, to conceal from
the public that which they have long suspected, and must have
sooner or later known. What the gifted mind of !N^ewton
believed to be truth, T dare not pronounce to be error. By
the great Teacher alone can truth be taught, and it is only at
His tribunal that a decision will be given on those questions,
often of words, which have kept at variance the wisest and tlie
best of men.

St. Leonard's College,

St. Andrews, May 12, 1855.

CONTENTS OF VOLUME L

CHAPTER I.

PAGB

Great Discoveries previous to the Birth of Sir Isaac Newton — Pre-eminence
of his Reputation— The Interest attached to the Study of his Life and
Writings — His Birth and Parentage— An only and Posthumous Child —
Notice of his Descent — Inherits the small Property of Woolsthorpe — His
Mother marries again— Is sent to a Day-school— His Education at Grant-
ham School — His idle Habits there — His Love of Mechanical Pursuits —
His Windmill, Water-clock, Self-moving Carriage, and Kites— His At-
tachment to Miss Storey — His Love of Drawing and Poetry — His Unfit-
ness to be a Farmer — His Dials, Water-wheels, and Anemometer— Leaves
Grantham School — His Commonplace Book and College Expenses, . 1-16

CHAPTER 11.

Newton enters Trinity College, Cambridge — Origin of his Love of Mathematics
—Studies Descartes' Geometry, and the Writings of Schooten and Wallis
— Is driven from Cambridge by the Plague — Observes Limar Halos in
1664 — Takes his Degree of B.A. in 1665— Discovers Fluxions in the same
Year — His first Speculations on Gravity — Purchases a Prism to study
Colours — Revises Barrow's Optical Lectures, but does not correct his
erroneous Opinions about Colours — Is elected a Minor Fellow of Trinity
in 1667, and a Major Fellow in 1668— Takes his Degree of M. A.— His Note-
Book, with his Expenses from 1666 to 1669 — Makes a small Reflecting
Telescope — His Letter of Advice to Francis Aston, when going upon his
Travels — His Chemical Studies— His Taste for Alchemy — His Paper on
Fluxions sent to Barrow and Collins in 1669, .... 17-32

CHAPTER III.

Newton succeeds Barrow in the Lucasian Chair — Hyperbolic Lenses proposed
by Descartes and Others — Opinions of Descartes and Isaac Vossius on
Colours — Newton discovers the Composition of White Light, and the dif-

CONTENTS.

iXJ^Z:^^*

ferent Refrangibility of the Rays that compose it — Having discovered the
Cause of the Imperfection of Refracting Telescopes, he attempts the Con-
struction of Reflecting ones — Constructs a second Reflecting Telescope in
1668, which is examined by the Royal Society, and shown to the King-
Discussions respecting the Gregorian, Newtonian, and Cassegrainian Tele-
scope — James Gregory the Inventor of the Reflecting Telescope — At-
tempts to construct one — Newton makes a Speculum of silvered glass —
Glass Specula by Short in 1730, and Airy in 1822 — Hadley constructs two
fine Reflecting Telescopes — Telescopes by Bradley, Molyneux, and Hawks-
bee— Short's Reflecting Telescopes with Metallic Specula — Magnificent
Telescope of Sir William Herschel with a fovir-feet Speculum — Munifi-
cence of George iii. — Astronomical Discoveries of Sir Wm. Herschel — Tele-
scopes of Sir J. Herschel and Mr. Ramage — Gigantic Telescope of the
Earl of Rosse with a six-feet Speculum— Progress of Telescopic Discovery
— Proposal to send a fine Telescope to a Southern Climate,

CHAPTEK IV.

Newton writes Notes on Kinkhuysen's Algebra — and on Harmonic and Infi-
nite Series — Delivers Optical Lectures at Cambridge — Is elected a Fellow
of the Royal Society — Communicates to them his Discoveries on the dif-
ferent Refrangibility and Nature of Light — Popular account of them —
They involve him in various Controversies — His Dispute with Pardies —
With Linus — With Gascoigne and Lucas — The Influence of these Disputes
on his Mind — His Controversy with Dr. Hooke and Monsieur Huygens.
arising from their Attachment to the Undulatory Theory of Light-
Harassed with these Discussions he resolves to publish nothing more on
Optics — Intimates to Oldenburg his Resolution to withdraw from the Royal
Society from his Inability to make the Weekly Payments — The Council
agree to dispense with these Payments — He is allowed by a Royal Grant
to hold his Fellowship along with the Lucasian Chair without taking
Orders— Hardship of his Situation in being obliged to plead Poverty to
the Royal Society — Draws up a Scheme for extending the Royal Society,
by paying certain of its Members — The Scheme was found among his
Papers — Soundness of his Views relative to the Endowment of Science
by the Nation — Arguments in support of them, .... 61-95

CHAPTEK V.

Mistake of Newton in supposing the Length of the Spectra to be the same in all
Bodies — And in despairing of the Improvement of Refracting Telescopes
— In his Controversy with Lucas he was on the eve of discovering the dif-
ferent Dispersive Powers of Bodies — Mr. Chester More Hall makes this Dis-
covery, and constructs Achromatic Telescopes, but does not publish his
Discovery — Mr. DoUond rediscovers the Principle of the Achromatic Tele-

CONTENTS. XVll

PAGE

scope, and takes out a Patent— Principle of the Achromatic Telescojie
explained— Dr. Blair's Aplanatic Telescopes— Great Improvements on the
Achromatic Telescope by the Flint-Glass of Guinant, Fraunhofer, and
Bontemps — Mistake of Newton in forming his Spectrum from the Sun's
Disc — Dark Lines in the Spectrum — Newton's Analysis of the Spectrum
incorrect — New Analysis of the Spectrum by Absorption, &c., defended
against the Objections of Helmholtz, Bernard, and others— Change in the
Refrangibility of Light maintained by Professor Stokes— Objections to
his Theory, 96-111

CHAPTER VI.

Newton on the Cause of the Moon's Libration— Is occupied with the subject
of Planting Cider Trees— Sends to Oldenburg his Discourse on Light and
Colours, containing his Hypothesis concerning Light — Views of Descartes
and Hooke, who adopt the Hypothesis of an Ether, the vibrations of
which produce Light— Rejected by Newton, who proposes a Modification
of it, but solely as an illustration of his Views, and not as a Truth — Light
is neither Ether, nor its vibrating Motion — Corpuscles from the Sun act
upon the Ether — Hooke claims Newton's Hypothesis as contained in his
Micrographia — Discussions on the subject— Ilooke's Letter to Newton pro-
posing a Private Discussion as more suitable— Newton's Reply to this
Letter, acknowledging the value of Hooke's Discoveries — Oldenburg the
cause of the Differences between Hooke and Newton — Newton's Letter to
Boyle on the subject of Ether — His conjecture on the Cause of Gravity —
Newton supposed to have abandoned the Emission Theory — Dr. Young's
supposition incorrect — Newton's mature judgment in favour of the Emission
Theory, 112-132

CHAPTER VII.

Newton's Hypothesis of Refraction and Reflexion— Of Transparency and
Opacity — Hypothesis of Colours — The Spectrum supposed to be divided
like a Musical String — Incorrectness of this Speculation — Hooke's Observa-
tions on the Colours of Thin Plates explained by the vibrations produced .
in the Ether by the Luminous Corpuscles — Hooke claims this Theory as
contained in his Micrographia — Newton's Researches on the Colours of
Thin Plates — Previous Observations of Boyle — Hooke's elaborate Experi-
ments on these Colours— His Explanation of them— Dr. Young's Observa-
tions upon it — Newton acknowledges his obligations to Hooke — Newton's
Analysis of the Colours seen between two Object-G lasses— Corrections of
it by MM. Provostayes and Desaius — Newton's Theory of Fits of easy Re-
flexion and Transmission — Singular Phenomenon in the Fracture of a
Quartz Crystal — Newton's Observations on the Colours of Thick Plates —
Recent Experiments on the same subject, . . , .

VOL. I. ' h

XVIU CONTENTS.

CHAPTER VIII.

PAGB

Influence of Colour in the Material World— Newton's Theory of the Colours of
Natural Bodies — Coloured Bodies reflect only Light of their own Colour,
absorbing all the other parts of White Light— The Colours of Natural
Bodies are those of Thin Plates— The transparent parts reflecting one
Colour and transmitting another — Arrangement of the Colours exhibited
in Natural Bodies into Seven Classes — Coloured Juices and Solutions, Oxi-
dated Films, Metals, &c. &c. — Newton's Theory applicable only to one
class of Colours— Objections to it stated— Mr. Jamin's Researches on the
Colours of Metals — Cause of Colours must be in the Constitution of Bodies
—Examples of the EflFect of Heat upon Rubies and Nitrous Gas— Effect of
Sudden Cooling — On Phosphorus— Effect of Jlechanical Action on Iodide of
Mercury — Indication of a New Theory— And of the Cause of the Absorption
of Definite Rays— Illustration of these Views in a remarkable Tourmaline, 154-168

CHAPTER IX.

Newton's Discoveries on the Inflexion of Light — Previous Researches of Hooke
— Newton's Animadversions on them ofi'ensive to Hooke — Newton's Theory
of Inflexion aa described by Grimaldi, having made no experiments of his
own — Discoveries of Grimaldi, which anticipate those of Hooke — Hooke
suggests the Doctrine of Interference — Newton's Experiments on Inflexion
— His "Views upon the subject unsettled — Modern Researches— Dr. Young
discovers the Law of Interference — Discoveries of Fresnel and Arago —
Fraunhofer's Experiments — Diff'raction by Grooved Surfaces — Diffraction
by Transparent Lines— Phenomena of Negative Diffraction — Experiments
and Discoveries of Lord Brougham — Explanation of Diffraction by the Un-
dulatory Theory, . 169-183

CHAPTER X.

Miscellaneous Optical Researches of Newton — His Experiments on the Abso-
lute Refractive Powers of Bodies— More Recent Experiments — His Con-
jecture respecting the Inflammability of the Diamond, confirmed by more
Direct Experiments — His Erroneous Law of Double Refraction — His Ob-
servations on the Polarity of Doubly Refracted Images — Discoveries on
Double Refraction in the present Century — His Experiments on the Eye
* of a Sheep— Results of them— His Three Letters on Briggs's New Theory
of Vision — His Theory of the Semi-Decussation of the Optic Nerves —
Partly anticipated by Rohault— Opinions of later writers on Vision, of
Reid, Brown, WoUaston, Twining, and Alison, discussed — The true Laws
of Sensation and Vision — Newton's Observations on the Impression of
Strong Light upon the Retina— More recent Observations— His Reflecting
Sextant — His Reflecting Microscope — His Reflecting Prism for Reflecting
Telescopes— His Method of varying the Magnifying Power of Newtonian
Telescopes — Newton's Treatise on Optics— His Lectiones Opticas, . . 184-218

CONTENTS. XIX

CHAPTER XI.

Astronomical Discoveries of Newton— Combined exertion necessary for the
completion of Great Discoveries — Sketch of the History of Astronomy
previous to the time of Newton— Discoveries of Nicolas Copernicus, born
1473, died 1553— He places the Sun in the Centre of the System— His
Work on the Revolutions of the Heavenly Bodies, printed at the expense
of Cardinal Schonberg, and dedicated to Pope Paul in.— Tycho Brahe,

. bom 1546, died 1601— His Observatory of Uraniburg— Is visited by
James vi. — Is persecuted by the Danish Minister — Retires to Germany
—His Discoveries and Instruments — The Tychonic System — John Kep-
ler, born 1571, died 1631— His Speculation on the Six Regular Solids-
Discovers the Ellipticity of Mars' Orbit— His Laws of the Planetary Mo-
tions — His Ideas of Gravitation— His Religious Character — Galileo, born
1564, died 1642— The first to apply a Telescope to the Heavens— Dis-
covers the Four Satellites and Belts of Jupiter — His Researches in Me-
chanics — Is summoned before the Inquisition for Heresy — Retracts his
Opinions, bub persists in teaching the Doctrine of the Earth's Motion— Is
again summoned before the Inquisition — His Sentence to Imprisonment
for Life — Becomes Blind — His Scientific Character — Labours of Bouillaud,
and of Borelli— Suggestions of Dr. Hooke on Gravity— His Circular Pen-
dulum — His Experiments with it — His Views respecting the Cause of the
Planetary Motions, ........ 219-251

CHAPTER XII.

The first Idea of Gravity occurs to Newton in 1665— His first Speculations
upon it— He abandons the Subject from having employed an erroneous
measure of the Earth's Radius— He resumes the Subject in consequence
of a discussion with Dr. Hooke, but lays it aside, being occupied with his
Optical Experiments— By adopting Picard's Measure of the Earth, he
discovers the Law of Gravity, and the Cause of the Planetary Motions—
Dr. Halley goes to Cambridge, and urges him to publish his Treatise on
Motion— The Germ of the Principia, which was composed in 1685 and
1686 — Correspondence with Flamsteed— Manuscript of Principia sent to
the Royal Society— Halley undertakes to publish it at his own expense-
Dispute with Hooke, who claims the discovery of the Law of Gravity —
The Principia published in 1687— The new edition of it by Cotes begun
in 1709, and published in 1713— Character and Contents of the Work-
General Account of the Discoveries it contains— They meet with opposi-
tion from the followers of Descartes — Their reception in foreign countries
— Progress of the Newtonian Philosophy iu England and Scotland, . 252-

XX CONTENTS.

CHAPTER XIII.

PACE

The Newtonian Philosophy stationary for half a century, owing to the im-
perfect state of Mechanics, Optics, and Analysis— Developed and extended
by the French Mathematicians — Influence of the Academy of Sciences-
Improvements in the Infinitesimal Calculus — Christian Mayer on the
Arithmetic of Sines — D'Alembert's Calculus of Partial Differences — La-
grange's Calculus of Variations— The Problem of Three Bodies — Importance
of the Lunar Theory — Lunar Tables of Clairaut, D'Alembert, and Euler
— The Superior Tables of Tobias Mayer gain the Prize offered by the English
Board of Longitude — Euler receives part of the English Reward, and also
a Reward from the French Board — Laplace discovers the cause of the
Moon's Acceleration, and completes the Lunar Theory — Lagrange's Solution
of the Problem of Three Bodies as applied to the Planets— Inequalities of
Jupiter and Saturn explained by Laplace — Stability of the Solar System
the Proof of Design — Maclaurin, Laplace, and others, on the Figure of the
Earth— Researches of Laplace on the Tides, and the Stable Equilibrium of -
the Ocean— Theoretical Discovery of Neptune by Adams and Leverrier
—New Satellites of Saturn and Neptune — Extension of Saturn's Ring and
its Partial Fluidity— Twenty-seven Asteroids discovered— Leverrier's theory
of them — Comets with Elliptic Orbits within our System — Law of Gravity
applied to Double Stars— Spiral Nebulae— Motion of the Solar System in
Space, 30(

CHAPTER XIV.

History of the Infinitesimal Calculus— Archimedes— Pappus— Napier— Edward
Wright — Kepler's Treatise on Stereometry— Cavalieri's Geometria Indi-
visibilium— Roberval — Toricelli— Ferraat— Wallis's Arithmetica Infinito-
rum—Hudde— Gregory— Slusius— Newton's Discovery of Fluxions in
1655— General Account of the Method, and of its Applications— His
Analysis per Equationes. &c. — His Discoveries communicated to English
and Foreign Mathematicians— The Method of Fluxions and Quadratures
—Account of his other Mathematical Writings— He solves the Problems
proposed by Bernoulli and Leibnitz — Leibnitz visits London, and corre-
sponds with the English Mathematicians, and with Newton through Olden-
burg — He discovers the Differential Calculus, and communicates it to
Newton — Notice of Oldenburg— Celebrated Scholium respecting Fluxions
in the Principia— Account of the changes upon it— Leibnitz's Manuscripts
in Hanover, ......... 334-363

CONTENTS.

APPENDIX TO VOLUME I.

No. I.— Letter from Mr. Newton to Francis Aston, Esq., a young Friend who

was on the eve of setting out upon his Travels, . . .

II.— An Hypothesis explaining the Properties of Light discoursed of in my

several Papers, .....

III. — Drawing and Measures of the Eye of a Sheep, .

IV.— Letter from Newton to Dr. Wm. Briggs,

v.— Second Letter of Newton to Dr. Briggs, .

VI. — Newton's Fifteenth Query,

VII. — Description of the Optic Nerves and their Juncture in the Brain, by

Sir Isaac Newton, . • .

VIII.— Correspondence between Halley and Newton, .

IX. — Halley's Verses prefixed to the Principia,

X.— Brief Notice of Professor Cotes,

XI. — Newton's Directions to Dr. Bentley for Studying the Principia, and

John Craige's list of Authors to be read before Studying the Principia,

XII.— Draught Copies of the Scholium to Lemma ii. Book il.,

XIII.— Letters from, Wallis to Newton, ......

PAGE

365

368
388
390
394
395

396
399
417

418

420
426
428

LIST OF ENGRAVINGS AND WOODCUTS.

VOL. I.

PORTRAIT OF SIR ISAAC NEWTON,

THE HOUSE AT WOOLSTHORPE, THE BIRTHPLACE OF NEWTON,

SIR ISAAC Newton's reflecting telescope, .

FRONT VIEW OF LORD ROSSe's TELESCOPE,
BACK VIEW OF DO. DO.,

56
57

VOL. II.

ROUBILLIAC's STATUE OF NEWTON IN TRINITY COLLEGE,
THE ROOMS OF SIR ISAAC NEWTON IN TRINITY COLLEGE,
THE HOUSE OF SIR ISAAC NEWTON IN MARTIN STREET,
ENGRAVING FROM A CAST OF SIR ISAAC NEWTOn's FACE, TAKEN

AFTER DEATH, . . . . .

ENGRAVING OF A BOX BELONGING TO SIR GEORGE HAMILTON

SEYMOUR, G.C.B., WHICH WAS PRESENTED BY SIR ISAAC

NEWTON TO THE EARL OF ABERCORN,

46
193

338
342

MEMOIRS

LIFE AND WRITINGS OF SIR ISAAC NEWTON.

CHAPTER I.

Great discoveries previous to the birth of Sir Isaac Newton — Pre-eminence of his repu-
tation — The interest attached to the study of his life and writings — His birth and
parentage — An only and posthumous child — Notice of his descent — Inherits the small
property of Woolsthorpe — His mother marries again— Is sent to a day-school— His
education at Grantham School — His idle habits there — His love of mechanical pur-
suits — His windmill, water-clock, self-moving carriage, and kites — His attachment to
Miss Storey — His love of drawing and poetry — His unfitness to be a farmer — His
dials, water-wheels, and anemometer — Leaves Grantham School — His commonplace
book and college expenses.

The seventeenth century haa always been regarded as the
most interesting and eventful period in the history of positive
knowledge. The discoveries and speculations of a preceding
age had prepared the way for some grand generalization of the
phenomena of the material world ; and sages of lofty intellect
heralded the advent of that Master-mind by which it was to be
accomplished. The establishment by Copernicus of the true
Solar System, and of its independence of the sidereal universe,
led to the investigation of those general laws with which Kepler
laid the foundations of Physical Astronomy ; while, in com-
bination with these, the observations of Tycho, the telescopic
discoveries of Galileo, and the speculations of Hooke and Borelli,
contributed in no slight degree to the establishment of the theory
of universal gravitation, by which Sir Isaac Newton has im-

VOL. I. A

'I LIFE OP SIR ISAAC NEWTON. CHAP. I.

mortalized his name, and perpetuated the intellectual glory of
his country.

A generalization of such vast extent, enabling us to determine
the position and aspects of the planets during thousands of years
that are past, and for thousands of years to come, could not
but be regarded as an achievement of the highest order : and
the name of Newton, therefore, has, by universal consent, been
placed at the head of those great men who have been the
benefactors and ornaments of their species. Imposing as are
the attributes with which Time has invested the sages of anti-
quity — its poets and its philosophers ; and dazzling as are the
glories of its heroes and its lawgivers, their reputation pales in
the presence of his ; and the vanity of no presumptuous school,
and the partiality of no rival nation, has ventured to question
the ascendency of his genius. The philosopher, indeed, to whom
posterity will probably assign the place next to Newton, has
characterized his great work, — The Principles of Natural
Philoscyphy, as pre-eminent above every other production of
human genius,^ and has thus divested of extravagance the
encomium of contemporary friendship.

Nee fas est propius mortali attingere Divos.

HALtET.

So near the gods — man cannot nearer go.

But while the history of such discoveries must, to the in-
tellectual world, be a subject of exciting interest, the biography
of him who made them, — the details of his life, his studies and
his opinions, cannot fail to arrest the attention and influence
the judgment of every cultivated mind. Though the path of
such a man may have lain in the secluded vale of humble life,
unmarked by those dramatic incidents which throw a lustre
even round perishable names, yet the inquiring spirit will linger
over the history of a mind so richly endowed, will study its
intellectual and moral phases, and will seek the shelter of its

1 The Marquis La Place. — See his Exposition du Systeme du Monde, Livre cinquieme,
chap. Ti. p. 33(5.

1642-61. LIFE OF SIR ISAAC NEWTON. 6

authority on those solemn questions which Reason has aban-
doned to Faith and Hope.

If we look for instruction from the opinions of ordinary men,
and watch their conduct as an exemplar for our own, how in-
teresting must it be to follow the most exalted genius through
the labyrinth 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 wields
his powers of invention and discovery ; — how he comports
himself in the arena of intellectual strife ; and in what senti-
ments, and with what aspirations, he leaves the world which
he has adorned.

In each and all of these phases, the writings and the life of
Sir Isaac Newton abound with the richest counsel. Here the
philosopher will learn the art of patient observation by which
alone he can acquire an immortal name ; the moralist will trace
the lineaments of a character exhibiting 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 reverence
the mysteries of his faith.

Isaac Newton was born in the Manor-house of Woolsthorpe,
a hamlet in the parish of Colsterworth, in the county of Lincoln,
close to the village of Colsterworth, and about six miles south
of Grantham, between one and two o'clock in the morning of
the 25th December, old style, 1642, in the same year in which
Galileo died. His father, Isaac Newton, who was proprietor
and farmer of the manor of Woolsthorpe, died in the thirty-
seventh year of his age, a little more than a year after the
death of his father Robert Newton, and only a few months
after his marriage to Hannah Ayscough, daughter of James
Ayscough of Market Overton, in Rutlandshire. Mrs. Newton
had thus been left in a state of pregnancy, and appears to have

LIFE OF SIR ISAAC NEWTON.

CHAP. I.

given a premature birth to her only and posthumous child.
The infant thus ushered into the world was of such a diminutive
size, that, as his mother afterwards expressed it to Newton
himself, he might have been put into a quart-mug, and so
feeble apparently was his constitution, that two women who
were sent to Lady Pakenham's at North Witham, to obtain for
him some tonic medicine, did not expect to find him alive
on their return. Providence, however, disappointed their
fears, 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.

Manor-house, Woolstliorpe ; the Birthplace of Sir Isaac Newton, showing the
Solar Dials which he made when a boy.

The small Manor of Woolsthorpe is said to have been more
than a hundred years in the possession of the family, who,

1642-61. LIFE OF SIR ISAAC NEWTON. 5

according to one account, were descended from Sir John Newton
of Westby, in Lincolnshire, and, according to another, from a
Scotch family in East Lothian. The Manor-house is situated
in a pleasant little hollow on the west side of the valley of the
river Witham, which rises near it, and one spring of which is
in the Manor. From the house there is an agreeable prospect
of the village of Colsterworth to the east, and, according to
Dr. Stukely, the air is so good, combining the sharpness of the
midland part of the kingdom with the more genial temperature
of the low parts of Lincolnshire, that the country round Wools-
thorpe was called the Montpellier of England. The Manor-
house consists of two storeys, and is built of stone. Sir Isaac's
study before he went to college, and when he visited his
mother from the University, was in the upper flat. The book-
shelves are described by Dr. Stukely as having been made by
Sir Isaac himself with pieces of deal-boxes, and as having
contained 200 or 300 books belonging to his father-in-law,
Dr. Smith, which Sir Isaac presented to Dr. Newton of
Grantham.

The Manor of Woolsthorpe, Sir Isaac's paternal estate, pur-
chased by his grandfather in 1623, from Eobert Underwood,
was worth only £30 per annum, but his mother possessed a
small estate at Sewstern, on the borders of Leicestershire, and
about three miles south-east of Woolsthorpe, which was worth
about £50 per annum ; and it is probable that the cultivation
of the little farm, on which she resided, added to the limited
rental upon which she had to support herself and educate
her son.

Under the guardianship of his uncle, James Ayscough, and
the tender care of his mother, young Newton remained at
Woolsthorpe acquiring gradually that strength of constitution
which was essential to the development of his intellectual
powers. Before, however, he had reached his fourth year, he
was deprived of his mother's care, in consequence of her mar-
riage, on the 27th January 1645, to the Rev. Barnabas Smith,

6 LIFE OF SIR ISAAC NEWTON. CHAP. I.

rector of North Witham ;^ and her duties devolved upon her
mother, the wife of James Ayscough, and a daughter of Mr.
Blythe of Stroxton, who. for this purpose, took up her residence
at Woolsthorpe. At the usual age Isaac was sent to two little
day-schools at Skillington and Stoke, two hamlets about a mile
to the north of Woolsthorpe, and about the same distance from
each other, acquiring the education in reading, writing, and
arithmetic, which such seminaries afforded.

When he reached the age of twelve he was sent to the pub-
lic school at Grantham, then taught by Mr. Stokes, who had
the character of being a good teacher, and was boarded at the
house of Mr. Clark, an apothecary in the town, whose grandson,
Mr. Clark, exercised the same profession there in 1727, the
year of Newton's death. The house in which our young phi-
losopher lodged, was next to the George Inn, " northward in
the High Street, which was rebuilt about 1711." According
to the confessions which Sir Isaac himself made to Mr. Conduit,
he was extremely inattentive to his studies, and stood very low
in the school. When he was the last in the lowermost form
but one, the boy next above him, as they were going to school,
gave him a kick on the stomach, which occasioned a great
degree of pain. As soon as the scholars were dismissed, New-

1 The issue of this marriage was a son and two daughters — Benjamin, Mary, and
Hannah Smith, from whom were descended the four nephews and nieces who inherited
Sir Isaac's personal estate.

The following account, from Conduit's MSS., of Mrs. Newton's marriage to Mr. Smith,
was given to Mr. Conduit "by Mrs. Hutton, whose maiden name was Ayscough :—

" Mr. Smith, a neighbouring clei^man, who had a Tery good estate, had lived a
bachelor till he was pretty old, and one of his parishioners advising him to marry, he
said he did not know where to meet with a good wife. The man answered. The widow
Newton is an extraordinary good woman. But, saith Mr. Smith, how do I know she
will have me, and I don't care to ask and be denied ; but if you will go and ask her, I
will pay you for your day's work. He went accordingly. Her answer was, she would
be advised by her brother Ayscough. Upon which Mr. Smith sent the same person to
Mr. Ayscough on the same errand, who, upon consulting with his sister, treated with
Mr. Smith, who gave her son Isaac a parcel of land, being one of the terms insisted upon
by the widow if she married him." This parcel of land was given by Mrs. Smith, and
was probably her property of Sewstern. — See the Annual Register 1776, Characters,
p. 25.

1642-61. LIFE OF SIR ISAAC NEWTON. 7

ton challenged the boy to fight, and for this purpose they went
into the churchyard. The schoolmaster's son came up to them
during the fight, and, " clapping one on the back and winking
to the other," encouraged them both to continue the encounter.
Though Sir Isaac was not so robust as his antagonist, yet he
had much more spirit and resolution, and therefore succeeded
in the combat, beating his opponent till he declared he would
fight no more. The schoolmaster's son, who seems to have
been an amateur in the art, told Sir Isaac that he must treat
the other as a coward by rubbing his nose against the wall.
The victor accordingly took the advice, and dragging his victim
by the ears, thrust his face against the wall of the church.
The success which thus attended his first struggle for superiority
induced him to repeat it in a better cause. Although vanquished
in the churchyard, his antagonist still stood above him in the
school, a victory more honourable than that which Newton had
achieved ; and though the schoolmaster and his son would have
given a different decision on the relative merits of the youthful
combatants, yet Newton took the right view of his own position,
and resolved to possess the moral as well as the physical supe-
riority. He accordingly exerted himself in the preparation of
his lessons, and, after many a severe struggle in which he and
his adversary were alternately successful, he not only gained
the individual victory, but rose to the highest place in the
school. «

It is very probable that Newton's idleness arose from the
occupation of his mind with subjects in which he felt a deeper
interest. He had not been long at school before he exhibited
a taste for mechanical inventions. With the aid of little saws,
hammers, hatchets, and tools of all sorts, he was constantly
occupied during his play-hours in the construction of models of
known machines, and amusing contrivances. The most import-
ant pieces of mechanism which he thus constructed, were a
wind-mill, a water-clock, and a carriage to be moved by the
person who sat in it. When a wind-mill was in the course of

8 LIFE OF SIR ISAAC NEWTON. CHAP. I.

being erected near Grantham, on the way to Gunnerby, Sir
Isaac frequently watched the operations of the workmen, and
acquired such a thorough knowledge of its mechanism, that he
completed a working model of it, which Dr. Stukely says was
" as clean and curious a piece of workmanship as the original."
This model was frequently placed upon the top of the house in
which he lived at Grantham, and was put in motion by the
action of the wind upon its sails. In calm weather, however,
another mechanical agent was required, and for this purpose a
mouse was put in requisition, which went by the name of the
miller. It does not distinctly appear how the mouse was com-
pelled to perform a function so foreign to its ordinary habits,
but it was supposed to act upon something like a tread-wheel
when attempting to reach some corn placed above it ; or, ac-
cording to another supposition, it was placed within a wheel,
and by pulling a string tied to its tail, it went forward " by
way of resistance," as Dr. Stukely observes, and thus turned
the mill.

The water-clock constructed by Sir Isaac was a more use-
ful piece of mechanism than his wind-mill. It was made out
of a box which he begged from Mrs. Clark's brother, and,
according to Dr. Stukely, to whom it was described by those
who had seen it, " it resembled pretty much our common clocks
and clock-cases," but was less in size, being about four feet in
height, and of a proportional breadth. There was a dial-plate
at top with figures of the hours. The index was turned by a
piece of wood, which " either fell or rose by water dropping."
The clock stood in Sir Isaac's bedroom, and it was his daily
practice to supply it every morning with the proper quantity of
water. It was frequently resorted to by the inmates of Mr.
Clark's house to ascertain the hour of the day, and it remained
there long after Sir Isaac went to Cambridge. Dr. Stukely
informs us, that having had occasion to talk of clepsydrae, or
water-clocks, Newton remarked that their chief inconvenience
arose from the furring up of the small hole through which the

1642-61. LIFE OF SIK ISAAC NEWTON. \)

water passed, by the impurities which it contained, — a cause of
inequality in its measure of time, the reverse of what takes
place in clocks made with sand, which enlarges the hole
through which it descends.

The mechanical carriage which Sir Isaac is said to have in-
vented, was a four-wheeled vehicle, and was moved with a
handle or winch wrought by the person who sat in it. We
can find no distinct information respecting its construction or
use, but it must have resembled a Merlin's chair, which is
fitted only to move on the smooth surface of a floor, and not
to overcome the inequalities of a common road.^

Although Sir Isaac was at this time a " sober, silent, and
thinking lad," who never took part in the games and amuse-
ments of his school-fellows, but employed all his leisure hours
in " knocking and hammering in his lodging-room," yet he was
anxious to please them by " inventing diversions for them above
the vulgar kind." In this way he often succeeded in alluring
them from trifling amusements, and teaching them, as Dr.
Stukely says, " to play philosophically ;"• or, as Dr. Paris has
better expressed it, in the title of his charming little work, to
make " philosophy in sport science in earnest." With this
view he introduced the flying of paper kites, and he is said to
have investigated their best forms and proportions, as well as
the number and position of the points to which the string

1 It is a curious fact that Leibnitz, the rival of Newton, had laboured at similar inven-
tions. In a letter written to Sir Isaac from Hanover, about a month after Leibnitz's death,
on the 14th November 1716, the AbbS Conti informs him that Leibnitz had laboured
all his life to invent machines, which had never succeeded, and that he was particularly
desirous of constructing a wind-mill for mines, and a carriage to be moved without
horses. Fontenelle, in his Eloge on Leibnitz, mentions these two inventions in different
terms. He had bestowed, says he, much time and labour upon bis wind-mill for drain-
ing the water from the deepest mines, but was thwarted in its execution by certain
workmen who had opposite interests. In the matter of carriages, his object was merely
to render them lighter and more commodious ; but a doctor, who believed that Leibnitz
had prevented him from getting a pension from the King of Hanover, stated in some
printed work, that he had contemplated the invention of a carriage which would perform
the journey from Hanover to Amsterdam in twenty-four hours. — Mdm. Acad. Par.
1718. Hist. p. 116.

10 LIFE OF SIR ISAAC NEWTON. CHAP. I.

should be attached. He constructed also lanterns of " crimpled
paper," in which he placed a candle to light him to school in
the dark winter mornings ; and in dark nights he tied them to
the tails of his kites, in order to terrify the country people, who
took them for comets.

Hitherto the attention of Sir Isaac had not been directed to
any of the celestial phenomena, and when he did study the
apparent daily motion of the sun, he was probably led to it
by the imperfect measure of time which he obtained from his
water-clocks. In the yard of the house where he lived, he was
frequently observed to watch the motion of the sun. He drove
wooden pegs into the walls and roofs of the buildings, as gnomons
to mark by their shadows the hours and half-hours of the day.
It does not appear that he knew how to adjust these lines to
the latitude of Grantham ; but he is said to have succeeded,
after some years' observation, in making them so exact, that
anybody could tell what o'clock it was by Isaac's Bwil^ as it
was called. It was probably at the same time that he carved
two dials on the walls of his own house at Woolsthorpe ; but,
though we have seen them there, we were not able to determine
whether they were executed by a tentative process like those in
Mr. Clark's yard, or were more accurately projected, from a
knowledge of the doctrine of the sphere.^

But saws and hammers were not the only tools which our
young philosopher employed. He was expert also with his
pencil and his pen, drawing with the one and inditing verses
with the other. It is not improbable that he received some in-

1 One of these dials was taken down in 1844, along with the stone on which it was cut,
by Mr. Tumor of Stoke Rochford, and presented by his uncle, the Rev. Charles Tumor,
to the Museum of the Royal Society. The dial was traced on a large stone in the south
wall, at the angle of the building, and about six feet from the ground. The name New-
ton, with the exception of the first two letters, which have been obliterated, may be seen
under the dial in rude and capital letters. The other dial is smaller than this, but not
in good preservation. The gnomons of these dials have unfortunately disappeared. In
the woodcut representing the manor-house of Woolsthorpe, the birthplace of Sir Isaac,
are shown the places on the wall where the dials were traced.— See VhiL Trans. 1845,
pp. 141. 142.

1642-61. LIFE OF SIR ISAAC NEWTON. 1 1

struction in drawing from his writing-master, called " Old
Barley," who lived in the place occupied, in Dr. Stukely's time,
by " the Millstone Alehouse in Castle Street." But whether
he was instructed or self-taught, he seems to have made some
progress in the art. His room was furnished with pictures
drawn by himself, some of them being copied from prints, and
some from life. The frames of these pictures were made by
himself, and " coloured over in a workmanlike manner."
Among these portraits Dr. Stukely enumerates " several of the
King's heads, Dr. Donne, Mr. Stokes, his teacher at Grantham,
and King Charles i." In addition to these portraits, there
were well-designed drawings of " birds, beasts, men, ships, and
mathematical diagrams, executed with charcoal on the wall,
which remained till the house was pulled down in 1711."

Although Sir Isaac told Mr. Conduit that he " excelled par-
ticularly in making verses," yet it is strange that no authentic
specimen of his poetry has been preserved. Beneath his por-
trait of Charles i. the follow verses were written : —

A secret art my soul requires to try,
If prayers can giye me what the wars deny.
Three crowns distinguished here, in order do
Present their ohjects 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.

Mrs. Vincent, who repeated these lines to Dr. Stukely from
memory, fancied that they were written by Sir Isaac ; but
even if he had thus early tasted of the Pierian spring, he must
have lost his relish for its sparkling waters, as he often expressed
in his later years a dislike for poetry ; — "not unlike Plato," as
Conduit observes when mentioning this fact, "who, though he had
addicted himself to poetry in his younger days, would not, in his
serious years, allow even Homer a place in his commonwealth."

12 LIFE OF STE ISAAC NEWTON. CHAP. I.

During the seven years which Sir Isaac spent at Grantham,
there were some female inmates in Mr. Clark's house, in whose
society he took much pleasure, and spent much of his leisure
time. One of these, Miss Storey, sister to Dr. Storey, a physi-
cian at Buckminster, near Colsterworth, and the daughter of
Mr. Clark's second wife, was two or three years younger than
Newton, and seems to have added to great personal attractiohe Town and Soke of Grantham, &c. By Edmund
TtiRNOR, F.R.S., F.S.A. Lond. 1806, pp. 159, 160. Conduit's MSS. were written sub-
sequently to the Memoirs above referred to.

2 Demoivre says that the book on Astrology was bought at Stourbridge, the seat of
the Cambridge fair, close to the town.

8 Newton's copy of Descartes' Geometry I have seen among the family papers. It is
marked in many places with his own hand, Error, Error, non est Geom.

20 LIFE OF SIR ISAAC NEWTON. CHAP. II.

without having received any assistance.^ The neglect which
he had shown of the elementary truths of geometry he after-
wards regarded as a mistake in his mathematical studies ; and
on a future occasion he expressed to Dr. Pemberton his regret
that " he had applied himself to the works of Descartes,
and other algebraic writers, before he had considered the
Elements of Euclid with that attention which so excellent a
writer deserved." ^

The study of Descartes' Geometry seems to have inspired
Newton with a love of the subject, and to have introduced him
to the higher mathematics. In a small commonplace book,
bearing on the 7th page the date of Jan. 1663-4, there are
several articles on angular sections, and the squaring of curves
and " crooked lines that may be squared," several calculations
about musical notes ; — geometrical propositions from Francis
Vieta and Schooten ; — annotations out of Wallis's Arithmetic of
Infinites, together with observations on Refraction, — on the
grinding of " spherical optic glasses," — on the errors of lenses,
and the method of rectifying them, and on the extraction of all
kinds of roots, particularly those " in affected powers." ^

This commonplace book is particularly interesting from its
containing the following important entry by Newton himself,
after the lapse of thirty-five years, and when he had completed
all liis discoveries.

'^ July 4, 1699. — By consulting an account of my expenses
at Cambridge,* in the years 1663 and 1664, I find that in the
year 1664, a little before Christmas, I, being then Senior

1 This statement is diflferent from that of Conduit in his Memoirs, but I give it on his
own authority, as founded on later inquiries.

2 Pemberton's Vkw of Sir Isaac Newton's Philosophy. Pref.

3 In this commonplace book we find the date November 1665, so that its contents
were written in 1664 and 1665.

* In the commonplace book which contains the " annotations out of Schooten and
Wallis," no expenses are entered, so that there must be another note-book which I have
not found, in which the purchase of Schooten's Miscellanies and Descartes' Geometry is
recorded. It is not likely that the second note-book of 1659, mentioned by Conduit,
cantained expenses incurred in 1663 and 1664.

1661-69. LIFE OF SIR ISAAC NEWTON. 21

Sopliister, bought Schooteii's Miscellanies and Cartes' Geometry
(liaving read this Geometry and Oughtred's Clavis^ clean over
half a year before), and borrowed Wallis's works, and by con-
sequence made these annotations out of Schooten and Wallis,
in winter between the years 1664 and 1665. At such time
I found the method of Infinite Series; and in summer 1665,
being forced from Cambridge by the plague, ^ I computed the
area of the Hyperbola at Boothby,^ in Lincolnshire, to two and
fifty figures by the same method.

Is. Newton."

In consequence of the devotion of his mind to these abstract
studies, and his long-continued observations upon a comet in
1664,* which made him sit up late at night. Sir Isaac's health
was impaired to such a degree, as Mr. Conduit informs us, that
from this illness " he learnt to go to bed betimes." In the
beginning of the same year, on the 19th February, Sir Isaac's
attention was directed to the subject of circles round the moon,
by two coronas of three and five-and-a-half degrees each, accom-
panied by the halo of 22° 35', of which he subsequently gave
the theory in his Treatise on Optics.^ In this year there were
forty-four vacancies in the scholarships of Trinity College, and
Newton was elected to one of them on the 28th of April. On
this occasion he was examined in Euclid by Dr. Barrow, who

1 Conduit remarks that in reading this work he did not entirely understand it, espe-
cially what " relates to Quadratic and Cubic Equations." — MSS. A translation of the
Clavis was published and recommended by Halley in 1694.

2 The plague commenced in Westminster about the end of 1664. It raged during the
hotter months of 1665, and had so far abated before the end of the year, that the inha-
bitants returned to their homes in December. The date of Newton's quitting Cambridge,
viz., 1665, as written under his own hand in his commonplace book, coincides with these
facts, and is on this account probably the correct one ; but Pemberton makes the date
1666, which is adopted by Professor Rigaud, and seems to be given by Newton himself
in the Phil. Trans, vol. vl p. 3080. Rigaud's Hist. Essay on the first publication of
Sir Isaac Newton's Principia, p. 1, note.

8 A village in Lincolnshire, near Sleaford, where Newton was probably on a visit.
< This comet passed its perihelion on the 4th December at midnight.
5 Book II. Part IV. Obs. 13.

22 LIFE OF SIR ISAAC NEWTON. CHAP. II.

formed an indifFerent opinion of his knowledge, and hence he
was led not only to read Euclid with care, but to fomi a more
favourable estimate of the ancient geometer when he came to
the interesting propositions on the equality of parallelograms on
the same base and between the same parallels.^ In the month
of January 1665, Newton took the degree of Bachelor of
Arts, along with twenty-five other members of Trinity College,
but we are not able to ascertain the academical rank which he
held among the graduates, as the grace for that year does not
contain the order of seniority of the Bachelors of Arts. The
Proctors at this time were John Slader of Trinity, and Benjamin
Pulleyn of Trinity, Newton's tutor, and the persons appointed
in conjunction with them to examine the Questionists, were
John Eachard of Catherine Hall, the satirical author of the
Grounds, d-c, of tJie Contempt of tlie Clergy^ and Tliomas
Gipps of Trinity. 2

In the same year Newton committed to writing his first
discovery of Fluxions. This paper, written by his own hand,
and dated May 20, 1665, represents in pricked letters the
fluxions applied to their fluents, and in another leaf of the
same waste book the method of fluxions is described without
pricked letters, and bears the date of May 16, 1666. In the
same book, with the date of November 13, 1665, there is
another paper on Fluxions, with their application to the draw-
ing of tangents, and " the finding the radius of curvity of any
curve." ^ In the month of October 1666, Newton drew up
another small tract, in which the method of Fluxions is again
put down without pricked letters, and applied to Equations
involving roots or surds."*

' Conduit's MSS.

2 Edleston's Corresjyondence, &c. &c , App. xxi. xIt.

3 Rigaud's Hist. Essap.&c, App. No. 11. p. 20. From the Macclesfield MSS. Eaphson
Historia Fluxionum, Cap. I. p. 1, Cap. xiii. p. 92, and English Edition, pp. 115, lid.

* These papers in the Macclesfield Collection are quoted by Newton himself in his
Observations on Leibnitz's celebrated Letter to the Abbg Conti, dated 9th April 1716.
See Raphson's Hi$t. of Fluxions, pp. 10'3 and 110.

1661-69. LIFE OF SIR ISAAC NEWTON. 23

It was doubtless in the same remarkable year 1666, or
perhaps in the autumn of 1665, that Newton's mind was first
directed to the subject of Gravity. He appears to have left
Cambridge some time before the 8th of August 1665, when
the College was " dismissed " on account of the Plague, and it
was therefore in the autumn of that year, and not in that of
1666, that the apple is said to have fallen from the tree at
Woolsthorpe, and suggested to Newton the idea of gravity.
When sitting alone in the garden, and speculating on the
power of gravity, it occurred to him that as the same power by
which the apple fell to the ground, was not sensibly diminished
at the greatest distance from the centre of the earth to which
we can reach, neither at the summits of the loftiest spires, nor
on the tops of the highest mountains, it might extend to the
moon and retain her in her orbit, in the same manner as it
bends into a curve a stone or a cannon ball, when projected in
a straight line from the surface of the earth. If the moon was
thus kept in her orbit by gravitation to the earth, or, in other
words, its attraction, it was equally probable, he thought, that
the planets were kept in their orbits by gravitating towards the
sun. Kepler had discovered the great law of the planetary
motions, that the squares of their periodic times were as the
cubes of their distances from the sun, and hence Newton drew
the important conclusion that the force of gravity or attraction,
by which the planets were retained in their orbits, varied
inversely as the square of their distances from the sun. Know-
ing the force of gravity at the earth's surface, he was, therefore,
led to compare it with the force exhibited in the actual motion
of the moon, in a circular orbit ; but having assumed that the
distance of the moon from the earth was equal to sixty of the
earth's semidiameters, he found that the force by which the
moon was drawn from its rectilineal path in a second of time
was only 13-9 feet, whereas at the surface of the earth it was
16-1 in a second. This great discrepancy between his theory
and what he then considered to be the fact, induced him to

24 LIFE OF SIR ISAAC NEWTON. CHAP. II.

abandon the subject, and pursue other studies with which he
had been previously occupied.^

It does not appear from any of the documents which I have
seen, at what time Newton made his first optical discoveries.
On the authority of one of his memorandum books, containing
an account of his expenses, it is stated by Conduit that he
purchased a prism, in order to make some experiments on Des-
cartes' Theory of Colours, and that he not only detected the
oTTOTS of the French philosopher, but established his own \dews
of the subject ; but this is contradicted by Newton himself,
who distinctly informs us that it was in the beginning of the
year 1666, that he procured a glass prism "to try therewith
the phenomena of colours." ^ There is no evidence, however,
that he used it for this purpose, and there is every reason to^'
believe that he was not acquainted with the true composition
of light when Dr. Barrow completed his Optical Lectures,
published in 1669.^ In the preface of this work. Dr. Barrow
acknowledges his obligation to his colleague Mr. Isaac Newton,
as a man of a fine disposition and great genius, for having
revised the MSS., and corrected several oversights, and made
some additions of his own.* Now, in the twelfth Lecture there

1 Neither Pemberton nor Whiston, who received from Newton himself the history of
his first ideas of Gravity, records the story of the falling apple. It was mentioned,
however, to Voltaire by Catherine Barton, Newton's niece, and to Mr. Green by JIartin
Folkes, the President of the Royal Society. We saw the apple-tree in 1814, and brought
away a portion of one of its roots. The tree was so much decayed that it was taken
down in 1820, and the wood of it carefully preserved by Mr. Tumor of Stoke Rocheford.
See Voltaire's Philosophic de Neicton, 3me part. Chap. III. Green's Philosophy of Ex-
patmve and Contractive Forces, p. 972, and Rigaud's Hist. Essay, p. 2.

2 Phil. Trans, vol. vi. p. S07o.

3 " Verum quod tenellae matres factitant, a me depulsum partum amicorum baud
recusantium nutriciae curae commisi, prout ipsis visum esset, educandum aut exponen-
dum, quorum unus (ipsos enim honestum duco nominatim agnoscere) D. Isaacvs
.Seu'tonus, collega noster (peregregiae vir indolis ac insignis peritiae) exemplar revisit,
aliqua corrigenda monens, sed et de suo nonuUa penu suggerens quae nosiris alicubi
cum laude inexa cernes." The other friend was John Collins, whom he calls the Mer-
sennus of our nation. Epist. ad Lectorcm. The imprimatur of this volume is dated
March 1668-9.

* The addition by Newton is a singularly elegant and expeditious method at the end

1661-69. LIFE OF SIR ISAAC NEWTON. 25

are some observations on the nature and origin of colours, which
are so erroneous and unphilosophical, that Newton could not
have permitted his friend to publish them had he been then in
the possession of their true theoiy. According to Barrow, who
introduces the subject of colours as an unusual digression, White
is that which discharges a copious light, scattered equally in every
direction. Black is that which emits light not at all, or very
sparingly. Bed is that which emits light more condensed than
usual, but interrupted by shady interstices. Blue is that which
discharges a rarefied light, or one excited by a weaker force, as
in bodies which consist of white and black particles arranged
alternately, such, for example, as the clear ether in which there
float fewer particles that reflect light, while the rest take away
light, the sea in which the white salt is mixed with the hlack
water, and the blue shadows seen at the same time by candle
and day light, which are produced by the whiteness of the
paper mixed with the faint light or blackness of the twilight.
Yellow consists of much white and a little red interspersed,
and Purple of much blue and some red. Green seems to have
puzzled Dr. Barrow. He says that it is somehow allied to
Blue; but he adds, let wiser men find out the difference, I
dare not conjecture. These opinions are so unsound, that they
could not fail to have attracted the attention of Newton, who
had certainly begun to study the subject of colours ; and if he
had discovered at this time that white was a mixture of all the
colours, and hlack a privation of them all, he could not have
permitted the absurd speculations of his friend and master to
pass uncorrected.^

While "Newton was thus occujjied with the subjects of
Fluxions and Gravity, he " applied himself also to the grinding
of optic glasses of other figures than spherical." Descartes, in

of Lect. xiv., of determining geometrically in every case the image formed by lenses,
and describing the lens which {irojects the image on a given point.

1 Barrow introduces the subject of colours by the following remarkable sentence :
"Quoniam colorum ineidit mentio, quid si de illis (etsi prcetcr morem et ordinein)
puvcula divinavero f'—Lect. xii. ad flnem.

2Q LIFE OF SIR ISAAC NEWTON. CHAP. II.

his Dioptrics, publisliecl in 1629, and more recently James
Gregory, in his Optica Fromota, published in 1663, had shown
that parallel and diverging rays could only be reflected or
refracted to a point or focus by mirrors or lenses, whose sur-
faces were paraboloidal, ellipsoidal, or hyperboloidal, or of some
other form not spherical. Descartes had even invented and
described machines by which lenses of these shapes could be
ground and polished, and it was the universal opinion that the
perfection of refracting telescopes and microscopes depended on
the degree of accuracy with which lenses of these forms could
be executed.

While engaged in this work Newton made his first experi-
ments with the prism, and he was soon induced to abandon
what he calls his "glass-works," in consequence of having
found " that the perfection of telescopes was limited not so
much for want of glasses truly figured according to the pre-
scriptions of optick authors (which all men have hitherto ima-
gined), as because light itself is a heterogeneous mixture of
diff"erently refrangible rays, so that were a glass so exactly
figured as to collect any one sort of rays into one point, it
could not collect those also into the same point, which having
the same incidence upon the same medium, are apt to suffer a
different refraction." He was therefore led to " take reflec-
tion 5 into consideration," but in consequence of the interruption
produced by the Plague, " it was more than two years before
he proceeded."

After his return to Cambridge, 1 on the disappearance of the

1 The only information which we have relative to the times of Newton's leaving and
returning to Cambridge, in consequence of the Plague, is contained in the following note
by Mr. Edleston : —

"The College was 'dismissed' June 22d, on the reappearance of the Plague. The
Fellows and Scholars were allowed their commons during their absence. Newton re-
ceived on this account 38. 4d. weekly, for 13 weeks, ending Michaelmas 1666.
„ „ „ 12 „ Dec. 21.

„ „ „ 5 „ Ladyday 1667."

The College had been also dismissed the previous year, August Sth, on the breaking
out of the plague, but Newton must have left Cambridge before that, as his name does

1661-69. LIFE OF SIR ISAAC NEWTON. 27

Plague, he was, on the 1st of October 1667, elected Minor
Fellow, and an apartment called "The Spiritual Chamber,"
assigned to him by the Mastei', — a locality which Mr. Edleston
conjectures to be the ground room next the chapel in the north-
east comer of the great court. A few weeks after this he went
to Lincolnshire, and returned on the 12th February 1667-8.
On the 16th March 1668, he took his degree of M.A., and
was the twenty-third on the list of 148 signed by the Senior
Proctor.^

About this time, and during the period extending from 1666
to 1669, when he succeeded to the Lucasian chair, his studies
were of a very miscellaneous kind, and were doubtless inter-
rupted not only by the appearance and reappearance of the
plague, but by the preparations necessary for taking his degree.
In his common note-book,' which I found among the family
papers, and which, along with a number of problems in
geometry and the conic sections, contains an account of his
expenses from 1665 to 1669, there are many entries which
throw some light upon his social character as well as upon his
studies. During his absence from College in 1665 and 1666,
we find him purchasing Philosophical Intelligences, the History
of the Royal Society, Gunter's Book and Sector from Dr. Fox,
together with magnets, compasses, glass-bubbles, drills, mandrels,
gravers, hones, and hammers. In 1667, he purchased Bacon's

not appear In the list of those who received extra commons for 6^ weeks on the occasion.
"Aug 7, 1665. — A month's commons (beginning Aug. 8th) allowed to all Fellows and
Scholars which now go into the country upon occasion of the pestilence." — (Conclusion
Book.)

" On the continuance of the scourge, we find him with others receiving the allowance
for commons for 12 weeks, in the quarter ending Dec. 21, 166.5, and for 13 weeks ending
Ladyday 1666."— Edleston's Correspondence, ^c. p. xhi. note 8.

1 Thomas Burnet, author of the Theoria Telluris Sacra, and a future friend and cor-
respondent of Sir Isaac.

" This note-book, of which three-fourths is white paper, begins at one end with three
pages of short-hand, which is followed by his expenses. At the other end of the book
there is a Novi Ciibi .... Tahella, and a number of problems in geometry and the
conic sections.

28 LIFE OF SIR ISAAC NEWTON. CHAP. II.

Miscellany, three prisms, and four ounces of putty. ^ He
records his jovial expenses, not only on the occasion of his
taking his two degrees, but " at the tavern several other times."
He acknowledges his having " lost at cards twice ; " but this
is compensated by his liberality to his '' cousin Ayscough," on
whom, and " on other acquaintance," he " spends" considerable
sums, — by his generosity to his sister, for whom he buys
oranges, — and his kindness to D. Wickins, to whom he lends
considerable sums of money. It appears, too, from this note-
book, that Newton went to London on Wednesday the 5th
August 1668, and returned to Cambridge on Monday the
28th September, after an absence of nearly two months ; but
the object of his journey is nowhere mentioned. It is not im-
probable that he went there to purchase lenses, and apparatus
and materials for chemical experiments, — a new branch of
science which seems at this time to have occupied his attention,
and which he continued to prosecute with much zeal during
the most active period of his life. In April 1669, he records
the purchase of lenses in London, and there follows a long list
of chemical substances, headed by mercury, together with a
furnace, and an air-furnace.^

1 Flowers of Putty, an oxide of zinc used in polij^hing lenses and metallic specula.

- As this list of expenses is very interesting, and as the book which contains them has
obviously been preserved by Newton hiinfelf as evidence of the priority of some of his
researches, the following abstract of it is presented to the reader : —

1665.
Received, May 'i3d, whereof I gave my tutor os., . . . .£500

Remaining in my hands since last quarter, . . . . .384

In all, £8 8 4

This account of expenses extends only to six and a half pages, and records many loans.
The following are among the entries : —

Drills, gravers, a hone, a hammer, and a mandrel, . . . .£050

A magnet, . . . . . . 16

Compasses, . . . . . . . . .036

Glass bubbles, . .040

My Bachelor's account, . . . . . . . . 17 6

1661-69.

LIFE OF SIR ISAAC NEWTON.

Towards the end of 1668, Newton carried into effect, on a
small scale, his resolution to " take reflections into considera-
tion." Thinking it " best to proceed by degrees," he first
" made a small perspective to try whether his conjecture would
hold good or not." ^ The telescope was six inches long. The

At the tavern several other times,

Spent on my cousin Ayscough,

On other acquaintance, .

Cloth, 2 yards, and buckles for a

Philosophical Intelligences,

The Hist, of the Royal Society,

Gunter's Book and Sector to Dr.

Lost at cards twice.

At the tavern twice,

I went into the country, Dec. 4

I returned to Cambridge, Feb. 12

Received of my mother, .

My journey.

For my degree to the College,

To the proctor, .

To three prisms, .

Four ounces of putty.

Lent to D. Wickins,

Bacon's Miscellanies,

Expenses caused by my degree,

A Bible binding, .

For oranges for my sister.

Spent on my journey to London,

me in the country,
I went to London, Wednesday,

Monday, September 28,
Lent D. Wickins,

Fox,

1667.
1667

5 10

1 7

and 4s. or 5s. more which my mother gave
August 5th, and returned to Cambridge on

5 10

April 1669.
For glasses in Cambridge.
For glasses in London.
For aquafortis, sublimate, oyle pink, fine silver, antimony, vinegar, spirit of

wine, white lead, salt of tartar, $ . . . . .200

A furnace, . . . . . • . ..080

Air furnace, . . . . . . . . .070

Theatrum chemicum, . . . . . . . .18

Lent Wardwell Ss.. and his wife 28., . . . . . .050

1 See Letter to Oldenburgh, Feb. 1671-2, in Newtoni Opera, by Horsley, torn. iv. p.
295 ; and Letter to a Friend, Feb, 23, 1668-9, in Gregory's Catoptrics, edit. 3d, p. 259 ;
or in the Macclesfield Collections, vol. ii. p. 289.

30 LIFE OF SIR ISAAC NEWTON. CHAP. II.

aperture of the large speculum was something more than an
inch, and, as the eye-glass was a plano-convex lens, with a focal
length of one-sixth or one-seventh of an inch, " it magnified
about forty times in diameter," which he believed was more
than any six-feet refracting telescope could do with distinctness.
Owing to the badness of the materials which he used, and the
want of a good polish, it did not represent objects so distinctly
as a six-feet refractor, yet Sir Isaac was of opinion that it
would discover as much as any three or four feet refractor,
especially if the objects are luminous. He saw with it Jupiter
distinctly round, with his four satellites, and also the horns or
" moonlike phase of Venus," though this last phenomenon
required a nice adjustment of the instrument. He therefore
considered this small telescope as " an ejjitome" of what may
he done by reflections ; and he did not doubt that, in time, a
six-feet reflector might be made winch would perform as much
as any sixty or hundred feet refractor. In consequence of
interruptions. Sir Isaac did not proceed any farther in the
construction of reflectors till the autumn of 1671.

It was during this period of his history, on the 1 8th of May
1669, that Sir Isaac wrote the celebrated letter of advice to
his young friend, Mr. Aston, who, at the age of twenty-seven,
was about to make a tour on the Continent. This " letter" is
a very interesting production. i It does not evince much ac-
quaintance with the ways of the world, but it shows some
knowledge of the human heart, and throws a strong light on
the character and opinions of its author. In his chemical
studies, which, as we have just seen, he had recently com-
menced, his mind was impressed with some belief in the doc-
trines of alchemy, and he certainly pursued his experiments to
a late period of his life, with the hope of eftecting some
valuable transmutations. Among the subjects, therefore, to
which he requests Mr. Aston to pay attention, there are several
which indicate this tendency of his mind. He desires him to

1 See Appbndix, No. I.

1661-69. LIFE OF SIR ISAAC NEWTON. 31

observe the products of nature, especially in mines, with the
circumstances of mining, and of extracting metals or minerals
out of their ores, and refining them ; and, what he considered
as far more important than this, he wishes him to observe if
there were any transmutations out of one species into another,
as, for example, out of iron into copper, out of one salt into
another, or into an insipid body, &c. Such transmutations, he
adds, are above all others worth his noting, being the most
luciferous, and many times lucriferoiis exjyeriments, too, in
philosophy ! Among the particular observations to which he
calls the attention of his friend, is that of a certain vitriol,
which changes iron into copper, and which is said to be kept a
secret for the lucrative purpose of effecting that transmutation.
He is to inquire also whether in Hungary, or in the mountains
of Bohemia, there are rivers whose waters are impregnated
with gold, dissolved by some corrosive fluids like aqua regis ;
and whether the practice of laying mercuiy in the rivers till it
be tinged with gold, and then separating the gold by straining
the mercury through leather, be still a secret or openly prac-
tised. There was at this time in Holland a notorious alchemist
of the name of Bory, who, as Sir Isaac says, was some years
since imprisoned by the Pope, in order to extort from him
secrets of great worth, both " as to medicine and profit," and
who made his escape into Holland, where they granted him a
guard. " I think," adds Sir Isaac, " he usually goes clothed
in green : pray inquire what you can of him, and whether his
ingenuity be any profit to the Dutch ! " We have not been
able to discover the results of Mr. Aston' s inquiries, but what-
ever they were they did not damp the ardour of Newton in his
chemical researches, nor extinguish the hope which he seems to
have cherished, of making " philosophy lucriferous," by trans-
muting the baser metals into gold.

But however fascinating these studies were to our young
philosopher, he did not permit them to interfere with his nobler
pursuits. At the very time when writing to Mr. Aston, we

32 LIFE OF SIR ISAAC NEWTON. CHAP. II.

find him occupied with his flu^ionaiy calculus, and transmitting
to Dr. Barrow his celebrated paper On Analysis hy Equations
with an infinite numher of terms, with permission to communi-
cate it to their mutual friend, Mr. Collins. In announcing this
communication on the 20th June 1669, and promising to
send it by the next opportunity. Dr. Barrow keeps the name of
its author a secret, and merely tells Mr. Collins that he is a
friend staying at Cambridge, who has a powerful genius for such
matters. In his next letter of the 31st July, accompanying
the paper, he expresses the hope that it will not a little delight
him : and, in a third letter to Collins of the 20th August, he
mentions how much he is pleased with tlie favourable opinion
which his correspondent has of it, and adds, that " the name
of the author is Newton, a Fellow of our College, and a yoimg
man, who is only in his second year since he took the degree of
Master of Arts, and who, with an unparalleled genius, has
made very great progress in this branch of mathematics."

1669-73. LIFE OF SIR ISAAC NEWTON. 33

CHAPTER III.

Newton succeeds Barrow in the Lticasian Chair — Hyperbolic Lenses proposed by
Descartes and Others — Opinions of Descartes and Isaac Vossius on Colours — Newton
discovers the Composition of White Light, and the different llefrangibility of the
Rays that compose it — Having discovered the cause of the im])erfection of Refracting
TeleFCopes, he attempts the construction of Reflecting ones — Constructs a second
Reflecting Telescope in 1668, which is examined by the Royal Society, and shown to
the King — Discussions respecting the Gregorian, Newtonian, and Cassegrainian
Telescope — James Gregory tlie Inventor of the Reflecting Telescope — Attempts to
construct one — Newton makes a Speculum of silvered glass — Glass Specula by Short
in 1730, and Airy in 1822 — Hadley constructs two fine Reflecting Telescopes— Tele-
scopes by Bradley, Molyneux, and Hawksbee— Short's Reflecting Telescopes with
Metallic Specula — Magnificent Telescoj)e of Sir William Herschel with a four-fe?t
Speculum — Munificence of George iii — Astronomical Discoveries of Sir Wm. Herschel
— ^Telescopes of Sir J. Herschel and Mr. Ramage — Gigantic Telescope of the Earl of
Rosse with a six-feet Speculum — Progress of Telescopic Discovery — Proposal to send a
fine Telescope to a Southern Climate.

In 1669, when Dr. Barrow had resolved to devote himself
to the studies and duties of his profession, he resigned the
Lucasian Professorship of Mathematics in favour of Newton.
His appointment took place on the 29 th October, and we may
now consider him as having entered on that brilliant career of
discovery, the history of which will form the subject of some of
the following chapters. It had been long known to every
writer on optics, and to every practical optician, that lenses
with spherical surfaces, such as those now in common use, did
not give distinct images of objects. This indistinctness was
believed to arise solely from their spherical figure, in conse-
quence of which the rays which passed through the marginal or
uter parts of the lens were refracted to a focus nearer the lens
lia.n those which passed through its central parts. The dis-
VOL, L c

34 LIFE OF SIR ISAAC NEWTON. CHAP. III.

tance between these foci was called the spherical aberration of
the lens, and various methods were suggested for diminishing
or removing this source of imperfection. Descartes^ had shown
that hyperbolic lenses refracted the rays of light to a single
focus, and we accordingly find the early volumes of the Philoso-
phical Transactions filled with schemes for grinding and polish-
ing lenses of this form. Newton had made the same attempt,
but finding that a change of form produced a very little change
in the indistinctness of the image, he thought that the defect of
lenses, and the consequent imperfection of telescopes, might
arise from some other cause than the imperfect convergency of
the incident rays to a single point. This happy conjecture was
speedily confirmed by the brilliant discoveiy of the different
refrangibility of the rays of light, — a discovery which has had
the most extensive applications to every branch of science, and
(what is very rare in the history of inventions) one to which no
other person has made the slightest claim.

No plausible conjecture, even, had been formed by the pre-
decessors of Newton respecting the nature and origin of colours.
Descartes believed them to be a modification of light depending
on the direct or rotatory motion of its particles. Grimaldi,
Dechales, and others, regarded them as arising from different
degrees of rarefaction and condensation of light. Gregory
defines colour to be the hue (tinctui-a) of igneous corpuscles
emerging from radiant matter,^ and we have already seen that
the views of Barrow on this subject were equally absurd. In
recounting the opinions of preceding writers, Newton alleges
that in all of them the colour is supposed not to be innate in
light, but produced by the action of the bodies which reflect or
refract it. This, however, is not strictly tme, as Isaac Vossius,
in a dissertation which Newton probably never saw, distinctly
maintains that all the colours exist in light itself, or, to use
another of his expressions, that all light carries its colours along

1 Dioptrice, cap. viii. ix. 1629.

2 Optica Promota : Definitioncs, 3. Lond. 1663.

1669-73.

LIFE OF SIR ISAAC NEWTON.

with it.i This, however, was a mere conjecture, which cannot
be regarded as in any way anticipating the great discovery of
Newton, " that the modification of light from which colours
take their origin, is innate in light itself, and arises neither
from reflection, nor refraction, nor from the qualities or any
other conditions of bodies whatever, and that it cannot be
destroyed or in any way changed by them."

After our author had purchased his glass prism at Stour-
bridge Fair, he made use of it in the following manner. Having
made a hole H in his window- shutter sht, and darkened the
room, he admitted a ray of the sun's light er, which after

c~ ~

-:ow

Fig. 2.

refraction at the two surfaces AC, bc of the prism abc, exhibited
on the opposite wall mn what is called the Solar or Prismatic
Spectrum. This spectrum was an elongated image of the sun

1 Isaaci Vossii De Lucis Natura et Proprietate, AmsteL 1662. As the opinions of
Vossius have not been referred to by any of our historians of science the following
passages may be interesting.

" Primus itaque color, si tamen color dicendus sit, is est albus, pelluciditatem proxime
hie accedit. Insunt itaque et lumini omnes colores, licet non semper visibiliter ; nempe
ut flamma intensa alba et unicolor apparet, eadem si per nebula aut aliud deusius
corpus spectetur, varios induit colores. Pari quoque ratione, Lux, licet invisibilis aut
alba ut sic dicam, si per prisma vitreum, aut aerem roridum transeat, similiter varios
colores induit." — P. 6.

" Omnem tamen lucem secum colores deferre et eo colligi potest quod si per lentem
vitream, aut etiam per foramen, lumen in obscurum admittatur cubiculum in muro aut
linteo remotiore manifeste omnes videantur colores, cum tamen in punctis decussationis
radiorum et locis minimum lenti vicinis, nuUus color sed purum tantum compareat
lumen." — P. 64.

" Quapropter non recte ii sentiunt qui colorem vocant Lumen modificatura."— P. 69.

36 LIFE OF SIR ISAAC NEWTON. CHAP. III.

about five times as long as it was broad, and consisted of seven
different colours, Eed^ Orange^ Yellow^ Green, Blue, Indigo,
and Violet. " It was at first," says !N"eA\i;on, " a very pleasing
divertisement to view the vivid and intense colours j^roduced
thereby ;" but this pleasure was immediately succeeded by siu--
prise at various phenomena which were inconsistent with the
received laws of refraction. The " extravagant disproportion
between the length of the spectrum and its breadth," excited
him to a more than ordinary curiosity of examining from whence
it might proceed. He could scarcely think tlmt the various
thickness of the glass, or the termination with shadow or dark-
ness could have any influence on light to produce such an
eflfect ; yet he thought it not amiss first to examine these cir-
cumstances, and he therefore tried what would happen by trans-
mitting light through parts of the glass of diff'erent thickness,
or through holes in the window of different sizes, or by setting
the prism without (on the left hand 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 these cases the same.

Newton then suspected that by some unevenness of the glass,
or other accidental irregularity, the colours might be thus dilated.
In order to try this he took another prism bcd, and placed it
in such a manner that the light passing through them both
might be refracted contrariwise, and thus returned by bcd
into the path erw, from which the first prism abc had diverted
it, for by this means he thought that the regular effects of the
prism ABC would be destroyed by the second prism bcd, and
the irregular ones more augmented by the multiplicity of re-
fractions. The result was, that the light which by the first
prism was diffused into an oblong form mn, was reduced by
the second prism into a circular one w with as much regularity
as when it did not pass through them, so that whatever was
the cause of the length of the image mn, it did not arise from
any irregularity m the prism.

1669-73. LIFE OF SIR ISAAC NEWTON. 37

Sir Isaac next proceeded to examine more critically the
effect that might be produced by the difference in the angles of
incidence, at which rays from different parts of the sun's disc
fell upon the face ac of his prism, and for this purpose he
measured the lines and angles belonging to the spectrum mn,
and obtained the following results

Distance of mn from the hole H,
Length of mn, .
Breadth of mn.
Diameter of the hole h.

22 feet.
13i inches.

. 2t „
• Oi „

Angle of WR with the middle of mn, .

44° 56'.

Angle ABC of the prism,
Refractions at R and r'.

63° 12'.

54° 4'.

" Now, subducting the diameter of the hole from the length
and breadth of the image, there remains 13 inches in the
length and 2f inches in the breadth comprehended by those
rays which passed through the centre of the hole, and conse-
quently the angle of the hole which that breadth subtended
was about 31', answerable to the sun's diameter ; but the
angle which its length subtended was more than five such
diameters, namely, 2° 49'."

With the refractive power of the prism, which he found to
be 1-55, he found the refractions of two rays proceeding from
opposite parts of the sun's disc, so as to differ 31 minutes in
their obliquity, to be such as to comprehend an angle of 31 or
32 minutes.

Although Newton could not doubt the correctness of the
law of the Sines on which these calculations were founded, yet
*' his curiosity caused him again to take his prism, and satisfy
himself by direct experiment that even a motion of the prism
about its axis of four or five degrees, did not sensibly change
the position of the spectrum mn on the wall," so that " there
still remained some other cause to be found out," from which
the spectrum could subtend an angle of 2° 49'.

Having set aside all these explanations of the length of his
spectrum, Newton hazarded the strange suspicion that the rays

38 LIFE OF SIR ISAAC NEWTON. CHAP. Til.

after passing through the prism "might move in curve lines,
and according to their more or less curvity lead to different
parts of the wall," and " it increased his suspicion," he adds,
" when he remembered 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 being communi-
cated to it by that stroke, its parts on that side where the
motions conspire, must press and beat the contiguous air more
violently than on the other, and there excite a reluctancy and
reaction of the air proportionally greater. And for the same
reason, if the rays of light should possibly be (composed of)
globular bodies, and by their oblique passage out of one medium
into another acquire a circulating motion, they ought to feel
the greater resistance from the ambient ether on that side
where the motions conspire, and thence be continually bowed
to the other. But notwithstanding this plausible ground of
suspicion, when I came to examine it, I could observe no such
curvity in them. And besides (which was enough for my
purpose) I observed that the difference betwixt the length of
the image, and the diameter of the hole through which the
light was transmitted, was proportional to their distance."

Having thus gradually removed these different hypotheses,
or suspicions, as Newton calls them, he was led to the experi-
onentum crucis for determining the true cause of the elongation
of the spectrum mn. He placed a board with a hole in 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 the rest. When the hole was near c, for
example, no other rays but the red fell on the wall at n. He
then placed behind the red space at 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 the hole in
the board. He then turned round the first prism abc, so as
to make all the colours pass successively through the two
holes, and he marked their places on the wall. From the

1669-73.

LIFE OF SIE ISAAC NEWTON.

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 arrived at the grand
conclusion, that light was not homogeneous, hut consisted of rays
of different refrangihility.

We have given this full account of Newton's mode of inves-
tigation, in order to show the cautious manner in which he
proceeded ; and were it not for the inconceivable stupidity of
the men who called in question his results, we should have
considered all his suspicions and precautions unnecessary, and
adopted the opinion of Arago, that the compound nature of
ivhite light was clearly involved in the very phenomenon of
the prismatic spectrum, and that the words in which Newton
stated it as a conclusion, were " nothing else than a literal
description or translation of that familiar experiment." ^

Having established this important truth, Newton imme-
diately perceived that the different refrangihility of the rays of

Fig, 3.

light was the real cause of the imperfection of refracting
telescopes. If ll is a convex lens receiving rays sl, sl, the
violet rays in the ivhite ray sl will be refracted in the line ly
to V, the yellow rays to y, and the red rays to r, forming a

1 Phil. Trans, vol. vii. No. 80. Feb. 19, 1672.

40 LIFE OF SIR ISAAC NEWTON. CHAP. III.

violet image of the sun, or any other object from which the
white light proceeds at the point v, a yellow image at y, and
a red one at R, images of intermediate colours being formed at
intermediate points between v and r. If this image is received
on a sheet of white paper at v, or y, or r, it wUl be exceed-
ingly indistinct, and tinged with these different colours. Newton
found that the space vr, which is called the chrmnatic aberra-
' tion, or the aberration of colour^ was in glass the fiftieth part
of the diameter ll of the lens, so that in lenses about six
inches in diameter, such as those used in the telescopes about
150 feet long, of Campani, Divini, and Huygens, the space vr
would be about '17 of an inch. Hence if ll be the object-
glass of a telescope directed to any luminous body, and mm an
eye-glass through which the eye sees magnified the image or
picture of the body between v and r, it cannot see distinctly
all the different images of the body formed there. If it is
adjusted to see distinctly the yellow image at y as it is in the
figure, it will not see distinctly either the red or the violet
images, nor indeed any but the yellow, and that very imper-
fectly, as it is mixed up with hazy images of all the other
colours, producing great confusion and indistinctness of vision.

As soon as Sir Isaac saw this result of his discovery, he left
off his " glass-works," as he called his attempts to improve the
refracting telescope, and, in the autumn of 1668, constructed
the little reflecting telescope which we have already described.
The success of this experiment, small as it was, 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 his speculations on gravity, yet, with all the
ardour of youth, he set himself to the task of executing another
reflecting telescope with his own hands. This telescope, of
which we have given a drawing in the annexed figure, was a better
one than the first ; and, we presume from its not being much
superior either to the first, or to the one executed by his col-
league, he allowed it to lie by him for several years. The

1669-73.

LIFE OF SIR ISAAC NEWTON,

existence of tliese telescopes having become known to some of
the members of the Royal Society, Newton was reciuested to

Fig. 4.

send his instrument to that learned body. This telescope con-
sisted of a concave metallic speculum, the radius of curvature of

42 LIFE OF SIR ISAAC NEWTON. CHAP. III.

which was 12|- or 13 inches, so that " it collected the sun's
rays at the distance of 61 inches." The rays reflected by the
speculum were received upon a plain metallic speculum inclined
45° to the axis of the tube, so as to reflect them to the side of
the tube in which there was an aperture to receive a small tube
with a plano-convex eye-glass, whose radius was one-twelfth of
an inch, by means of which the image formed by the speculum
was magnified 38 times.

Newton did not hesitate to obey the request of the Royal
Society, and it was accordingly sent, and we believe presented
to that distinguished body near the end of 1671. It was also
shown to the King, and a description of it published in the
Philosophical Transactions.^ The instrument itself is carefully
preserved in the Library of the Royal Society, with the inscrip-
tion, —

" THE FIRST HEFLECTING TELESCOPE INVENTED BY SIR ISAAC NEWTON,
AND MADE WITH 1118 OWN HANDS."

Previous to March 16, 1672, a Fellow of Trinity College had
made a similar telescope of nearly the same size, which Newton
found to " magnify more, and also more distinctly," than a six-
feet refractor, and which he considered better than his own. A
description of Newton's instrument in Latin was drawn up and
corrected by Newton, and when signed by Lord Brouncker,
Wren, and Hooke, was sent to Huygens, who expressed his
approbation of it, and suggested the propriety of giving the
concave speculum a parabolic form. Various observations were
made upon the instrument, particularly by Monsieur Auzout and
Monsieur Denys ; and Monsieur Berce claimed for M. Casse-
grain the invention of a telescope which he considered " almost
like Newton's," and " more ingenious." ^ Newton replied to
this commimication, and acknowledging that he had been ac-

1 Phil. Trans, vol. vii. No. 81, p. 4004 March 25, 1672.

2 See Journal dcs Suvans, 1072, pp. 80 and 121 ; and Phil. Trans. No. 83, p 405C,
May 20. 1672.

1669-73. LIFE OF SIR ISAAC NEWTON. 43

quainted with the telescope proposed by Gregory before he had
contrived his own, he points out the superiority of the Grego-
rian to the Cassegrainian form, and of his own to both. This
letter led to a little amiable controversy between Gregory and
Newton on the merits of their reflecting telescopes, in which
neither of them gained the victory. ^

Newton's occupations were at this period too numerous, and
his time too valuable to be spent in mechanical labour ; and he
therefore never resumed the construction of reflecting telescopes.
The Royal Society, however, employed a London optician of the
name of Cox to execute a Newtonian reflector, with a speculum
whose focal length was no less than four feet, but he failed in
polishing the speculum ; and though Sir Isaac himself contem-
plated the construction of another instrument, he seems to have
wholly abandoned the attempt, and to have bequeathed to an-
other age the honour of making his telescope an instrument of
discovery. The want of a good material for the specula seems
to have been the difficulty which perplexed the optician ; and
it would appear from the following observations of Newton
himself, that the specula for the instrument, ordered by the
Royal Society, were to be made of a new material. " You will
gratify me much," says he in a letter to Oldenburg, " by ac-
quainting me with the particular dimensions, fashion, and success

1 Gregory's Catoptrics, App. 261. In this controrersy, Newton never claimed any
credit for the invention of a new form of the reflecting telescope, and was certainly sur-
prised at the notice it excited among persons that either were, or ought to have been,
acquainted with the previous invention of Gregory. In his letter to Mr. Collins, he speaks
in the kindest manner of Gregory. " I doubt not that when Mr. Gregory wrote his Optica
Promota, he could have described more fashions than one of these telescopes, and per-
haps have run through all the possible cases of them, if he had thought it worth his
pains. Because Mr. Cassegrain propounded his supposed invention pompously, as if the
main business was the contrivance of these instruments, I thought fit to signify that that
was none of his contrivance, nor so advantageous as he imagined. And I have now sent
you these fan her considerations on Mr. Gregory's answer, only to let you see that I chose
the most easy and practicable way to make the first trials. Others may try other ways,
nor do I think it material which way these instruments are perfected, so they be per-
fected. — Dec. 10, 1672." See the Macclesfield Collections, vol. ii. pp. 346, 347, or Newtoni
Opera by Ilorsley, vol. iv. p. 288.

44 LIFE OF SIR ISAAC NEWTON. CHAP. III.

of the four-feet tube, which, I presume, Mr. Cox by this time
hath finished. And to inform myself of the advantages of the
steely matter which is made use of, you will much obhge me if you
can procure me a fragment of it. I suppose it is made by melting
steel with a little antimony, perhaps without separating the
sulphureous from the metalline part of that mixture. And so
though it may be very hard, and capable of a good polish, yet
I suspect whether it be so strongly reflective as a mixture of
other metals. I make this inquiry, because if I should attempt
anything farther in the fabric of the telescope, I would first
inform myself of the most advantageous materials. On which
account, also, you would farther oblige me if you can inquire
whether Mr. Cox, or any other artificer, will undertake to pre-
pare the metals, glass, tube, and frame of a foui'-feet telescope,
and at what rates he will do it, so that there may remain no-
thing for me to do but to polish the metals. A gross account
of this will at present suffice, until I send you a particular
design of the fabric of the instrument, if I resolve upon it." ^

Such is a brief account of the first reflecting telescope that
was successfully constructed and applied to the heavens ; but
though we make this admission in its favour, we must also
acknowledge that it was a small and ill-made instrument,
incapable of showing the beautiful celestial phenomena which
had been long seen by the refracting telescopes of Hevelius and
Huygens. No discovery was made by any of the three instru-
ments to which we have referred, and more than fifty years
elapsed before telescopes of the Newtonian form became useful
in astronomy. A similar fate befell the reflecting telescope of
James Gregory, who was the undoubted inventor of that noble
instrument, and whose merits were thrown into the shade by
the display which accompanied the invention of his friend. In
his Optica Promota, published in 1663, Gregory describes a
reflecting telescope, with the view of making telescopes shorter
and more manageable. When compared with other telescopes,

1 July 13, 1672, in the Macclesfield Collections, vol. ii. p. 333.

1669-73. LIFE OF SIR ISAAC NEWTON. 4-5

lie gives it the character of a golden one, as " it has no incon-
veniences, and may have all the properties of the other tele-
scopes, whether dioptric or catoptric." He then goes on to
describe " a telescope of this most perfect kind." It consists
of a parabolic concave speculum, with a hole in its centre,
having near its focus a small elliptic concave speculum. The
image formed by the large parabolic speculum is received by
the small elliptical one, and reflected through the aperture in
the former upon a lens which magnifies it. In the reflecting
telescope proposed by Cassegrain, the image formed by the
larger speculum is received by a small convex speculum, the
eff'ect of which is to shorten the telescope, and prevent the
crossing, or " decussation of the rays," as Newton calls it, in
the focus of the larger speculum.^ Gregory never attempted
to construct this instrument with his own hands, but he em-
ployed Messrs. Reeves and Cox, celebrated glass-grinders, to
execute a concave speculum three feet in focal length, together
with a little concave and a little convex speculum ; but as Mr.
Reeves " could not polish the large concave on the tool, but
merely with cloth and putty," ^ and as Gregory was on the eve

1 Sir Isaac seems to hare been the first person who suggested the idea that vision
might be rendered indistinct by the collision of the rays when they cross one another at
the focus of mirrors or lenses. In speaking of the use of more than one eye-glass in the
Gregorian telescope, he states, that " hy the iterated decussations of the rays, objects
will he rendered less distinct, as is manifest in dioptric telescopes, where two or three
eye-glasses are applied to erect the object." — Letter to Collins, Dec. 10, 1672 ; Maccles-
feld Collections, vol. ii. p. 844. In the course of some experiments on this subject, I
found that the sections of the cone of rays are never so distinct and well-defined aft^r
the rays have crossed as before. — (Treatise on New Phil. Inst. pp. 44 and 193.) And
Captain Kater, in comparing two equal telescopes, the one Gregorian and the other
Cassegrainian, found that the intensity of the light within the focus was nearly double of
what it was without the focus. In other experiments, he found the ratio as 1000 to
788. — Phil. Trant. pp. 13, 14. Mr. Tulley, however, in making similar experiments,
did not confirm the results obtained by Captain Kater. I have found, in confirmation
of these facts, that the negative diflfractive fringes produced by rays which do not cross
one another before they enter the eye, are more distinct than the positive ones which do
cro%i.— Treatise on Optics, Edit, of 1853, p. 117.

2 Dr. Hooke made several experiments with the speculum executed by Mr. Reeves, and
did not find it so bad as Gregory thought. See Newton's Letter to Collins above
referred to.

46 LIFE OF SIR ISAAC NEWTON. CHAP. III.

" of going abroad, he thought it not worth the pains to trouble
himself any farther with it, so that the tube was never made.
Yet," he adds, " I made some trials with a little concave and
convex speculum, which were but rude, seeing I had but tran-
sient views of the object." i

Although Newton did receive through Oldenburg the infor-
mation he requested from Mr. Cox,^ yet he never availed
himself of it in proceeding any farther with metallic reflectors.
In consequence, however, of Gregory having suggested to him
the use of glass specula silvered on the back for burning glasses,
and shown how to make the foci of each surface coincident,
Newton proposed, we believe in 1678, to substitute these
specula instead of metallic ones in the reflecting telescope. In
this manner he attempted to make a telescope four feet long,
and with a magnifying power of 150; but though the glass
was wrought by a London artist, and seemed well finished, yet,
when it was quicksilvered on its convex side, it exhibited all
over the glass innumerable inequalities, which rendered every
object indistinct. He expresses, however, his conviction, that
nothing but good workmanship is wanting to perfect such tele-
scopes, and he recommends their consideration " to the curious
in figuring glasses." This recommendation remained unnoticed
for upwards of fifty years. At last Mr. James Short, a Scotch
artist of consummate skill, executed, about the year 1730, no
fewer than six reflecting telescopes, with glass specula, three of
which were fifteen inches, and three nine inches in focal length ;
but some of them turned out useless from the veins in the
glass. Maclaurin,^ who, with one of nine inches, could read
the Philosophical Transactions very easily at the distance of
130 feet, informs us that they were excellent instruments.
Short, however, found that their light was fainter than he
expected, and from this cause, combined with the difficulty of

1 Letter from Gregory to Collins and Newton, Sept. 26, 1672.

2 Biog. Brit., Art. Newton, p. 3217.

3 Smith's Optics, vol. ii. Remarks, p. 80,

1669-73. LIFE OF SIR ISAAC NEWTON. 47

finishing them, he afterwards limited himself to the use of
metallic specula. ^

The subject of glass specula was resumed in 1822 by Mr.
Airy, one of the distinguished successors of Newton in the
Lucasian chair. Having demonstrated that the aberration
both in jBgure and colour might be corrected in these instru-
ments, he executed more than one ; but though the result of
the experiment was such as to excite hopes of ultimate success,
the construction of such an instrument is still a desideratum in
practical science.

Notwithstanding these failures, we would not discourage the
young artists of the present day from endeavouring to surmount
the difficulties experienced by their predecessors. Discs of glass
can now be obtained entirely free of veins, and what is of great
importance, instead of coating the convex surface with a plate
of mercury and tin, which reflects even less light than speculum
metal, we can now, by the electrotype, deposit pure silver on
the glass,. and give it a reflective power far surpassing that of
any other metal.

Such is a brief history of the attempts which were made by
Newton and Gregory to construct reflecting telescopes. They
were certainly far from being successful ; nor were their con-
temporaries more fortunate, though guided by the light of their
experience.

After the Ijipse of fifty years, however, and several years
before his death, Sir Isaac had the satisfaction of seeing a New-
tonian telescope, six feet long, mounted upon a commodious
stand, and capable of exhibiting some of the most interesting
phenomena in the heavens. A Gregorian telescope, of an infe-
rior size, was executed with similar success, and from that time
the art of making telescopes with metallic reflectors was gra-
dually brought to perfection. The history of these improve-

1 Caleb Smith proposed to correct the colour produced by the two refractions, by a
concave lens placed between the speculum and the small receiver, or by making the
surface of a rectangular glass prism concave.— P/«t7. Trans. 1739, p. 326.

48 LIFE OF SIR ISAAC NEWTON. CHAP. Ill,

ments, and of the grand discoveries in astronomy to which they
led, would of itself form an interesting volume. We shall
endeavour, in a few pages, to present it to our readers.

The person to whom we owe the first step in the improvement
of the reflecting telescope, was John Hadley, one of the inventors
of the Refiecthig Quadrant, which bears his name.^ This gen-
tleman, who was a Fellow of tlie Royal Society, and possessed
of considerable scientific attainments, began his experiments in
1719, and, probably after many failures, completed a telescope
toward the end of 1720. It was shown and presented to the
Royal Society, in whose Journals for January 12, 1721, the fol-
lowing notice of it occurs.: — " Mr. Hadley was pleased to show
the Royal Society his reflecting telescope, made according to our
President's (Sir Isaac Newton) directions in his Optics, but
curiously executed by his own hand, the force of which was
such as to enlarge an object near two hundred times, though
the length thereof scarce exceeds six feet ; and having shown
it he made a present thereof to the Society, who ordered their
hearty tlianks to be recorded for so valuable a gift." The instru-
ment consisted of a metallic speculum, about six inches in
diameter, and its focal length was five feet two inches and a
half. Its plane speculum was made of the same metal, about
the 1 5th of an inch thick, and it had six eye-pieces, three con-
vex lenses l-3d, 3-lOths, and ll-40ths of an inch, magnifying
190, 208, and 230 times, two concave lenses magnifying 200
and 220 times, and an erecting eye-piece of three convex lenses,
magnifying about 125 times. It had also a small refracting
telescope as a tinder, which, we believe, was first suggested by
Descartes, and the whole was mounted upon a stand, ingeniously
and elegantly constructed.2 The celebrated Dr. Bradley, and
the Rev. Mr. Pound of Wanstead, compared it with the great
Huygenian refractor 123 feet long, and they saw with the re-
flector, though less brightly, " whatever they had hitherto disco-

1 See Prof. Rigaud's Biorrraphical Account of John Hadley, Efq., pp 7 11.
- Phil Trans, vol. xxxii. No. 37C, March and April, 1V23, p. .^01.

1669-73. LIFE OF SIR ISAAC NEWTON. 49

vered with the Huygenian, particularly the transits of Jupiter's
satellites, and their shadows over the disc of Jupiter, the black
list in Saturn's ring, and the edge of the shadow of Saturn cast
on his ring. They also saw with it several times the five satel-
lites of Saturn." ^ Mr. Hadley himself and others likewise saw
the preceding phenomena together with the belts of Saturn, and
the first and second satellites of Jupiter, as bright spots on the
body of the planet.^

After executing another Newtonian telescope of the same
size, Mr. Hadley directed his attention to those of the Gregorian
form, upon which he made great improvements. In 1726 be
communicated to Dr. Desaguliers an account of the instrument
as perfected by himself, with tables showing the relative pro-
portions of its different parts ; and in 1734 he made an addi-
tional communication to the same writer, in reference to the use
of a double eye-glass, for " preventing the objects being coloured
fnear the edges of the field." ^ Not content with the labours of
[his own hands, Mr. Hadley, who was now Vice-President of
Hhe Eoyal Society, was desirous of enabling astronomers and
opticians to manufacture these valuable instruments, the former
for use in their observatories, and the latter for public sale.
He accordingly inspired Dr. Bradley with the desire of con-
structing these instruments, and with his directions " he suc-
ceeded pretty well, and would probably have perfected one of
them, had he not been obliged suddenly to remove from the
place where he then dwelt, and been since diverted from it by
|other avocations." Soon afterwards, however. Dr. Bradley with
\Mt. Samuel Molyneux, renewed the attempt at Kew, by making
[an instrument about 26 inches long ; but notwithstanding Dr.
j Bradley's experience and Mr. Hadley's frequent instructions,
i& long time elapsed before they could " tolerably succeed." At

5t, however, they completed to their satisfaction a telescope of
[the Newtonian form of the above focal length. They afterwards

1 Phii. Trans. July and August 1723, p. 382.

2 Gregory's Catoptrics, pp. 250, 285. 8 jud., p. 385.
VOL. I. D

50 LIFE OF SIR ISAAC NEWTON. CHAP. III.

made a pretty good one of seven inches, and one of eight feet,
the largest that had yet been made.^ The first of these instru-
ments was elegantly fitted up on a highly ornamented stand,
and presented by Mr. Molyneux to his Majesty John v. of
Portugal. 2

Hitherto no optician but Mr. Hawksbee had ventured to
construct these instruments for sale.' He executed a good one
of about 3 J feet in focal length,^ and other two of six and
twelve feet, and he was the first person, as Molyneux informs
us, " who had attempted it without the assistance of a fortune,
which could well bear the disappointment."

Having acquired, by his own experience and Mr. Hadley's
instructions, a sufficient knowledge of the art, Mr. Molyneux
communicated the whole process* to Mr. Edward Scarlet, his
Majesty's optician, and to Mr. Heame, a mathematical instru-
ment maker, and both these artists attained to such perfection
in constructing them, that they manufactured them for public
sale. In this way the Reflecting Telescope came into general
use, and, principally in the Gregorian form, it has been an article
of trade with every regular optician.

While the English opticians, with the aid of Molyneux and
Hadley, were thus practising the new art of grinding and
polishing specula, Mr. James Short of Edinburgh, without any
such aid, was devoting to the subject all the energies of his
youthful mind. In the year 1732, and in the 226. year of his
age, he began his labours ; and to such perfection did he carry
the art of grinding and polishing metallic specula, and of
giving them the true parabolic figure, that with a telescope of
15 inches in focal length, he and Mr. Bayne, Professor of Law

1 The Hon. Samuel Molyneux and Hadley in Smith's Optics, vol. ii. p. 302, § 782.

2 Ibid., p. 363, § 913.

3 This telescope, according to Dr. Smith, was so excellent that it was scarcely inferior
to Hadley's of 6 feet 2i inches in length. It bore a power of 226, as determined by Mr.
Hawksbee, Mr. Folkes, and Dr. Jurin. See Smith'.s Oleics ; Remarks, p. 79.

* This process, drawn up partly by Molyneux and partly by Hadley, is printed in Dr.
Smith's Optics, vol. ii. p. 301.

1669-73. LIFE OF SIE ISAAC NEWTON. 51

in the University of Edinburgh, read the Philosophical Trans-
actions at the distance of 500 feet, and several times, particu-
larly on the 24th of November and the 7th of December 1734,
they saw the five satellites of Saturn together, an achievement
beyond the reach of Hadley's six-feet telescope. Mr. Short
had constructed several instruments, 9, 6, 4, and 2-^ inches
in focal length. With those four inches long he saw the
satellites of Jupiter very well, and read in the Philosophical
Transactions at the distance of 125 feet. With the six-inch
ones he read at the distance of 1 60 feet, and with the nine-
inch ones at the distance of 160 feet. The celebrated Colin
Maclaurin compared one of the six-inch ones with one of the
best London ones of 9 -3^ inches, and found that it exceeded it
in brightness, distinctness, and magnifying power. It surpassed
also another London one, 11^ inches in focal length.^ After
Short had established himself in London in 1742, he received
£630 for a twelve-feet reflector from Lord Thomas Spencer.
In 1752 he executed one for the King of Spain for £1200 ;
and a short time before his death, which took place in 1768,
he finished the specula of the magnificent telescope which was
mounted equatorially for the Observatory of Edinburgh, by his
brother Thomas Short. The King of Denmark off'ered twelve
hundred guineas for this instrument, through which we have
often seen the leading celestial phenomena, but not till the
large speculum had been greatly injured in consequence of
having been repolished by an inferior artist.^

Notwithstanding these great improvements on the Eeflecting
Telescope, no discovery of importance had yet been achieved by
them. The ordinary refractors of Huygens, and those of Cam-
pani in the hands of Cassini, though they laboured under all
the imperfections of coloured light, had made the latest dis-

1 Maclaurin in Smith's Optics, vol. ii., Remarks, p. 81.

2 This telescope was removed from the Observatory upon the establishment of the
Astronomical Institution, and is, we believe, now lying dismantled in some garret of
the city.

^2 LIFE OF SIR ISAAC NEWTON. CHAP. III.

coveries in the heavens ; and nearly three quarters of a century-
had elapsed without any extension of our knowledge of the
Solar and Sidereal Systems. This, however, was only one of
those stationary intervals during which human genius holds its
breath, in order to take a new and a loftier flight. The power
of the Refracting Telescope, extended to the unmanageable
length of above two hundred feet, had been strained to the very
utmost, and the Reflectors, vigorous and promising in their
infancy, were about to attain an efliciency and magnitude which
the most sanguine astronomer had never ventured to anticipate.
It was reserved for Sir William Herschel and the Earl of Rosse
to accomplish this great work, and by the construction of
telescopes of gigantic size to extend the boundaries of the Solar
System — to lay open the hitherto unexplored recesses of the
sidereal world, and to bring within the grasp of reason those
nebular regions to which imagination had not ventured to soar.
Anxious to observe with his own eyes the wonders of the
planetary system, and, fortunately for science, unable to pur-
chase a telescope for himself. Sir William Herschel resolved, in
1774, to construct one with his own hands. With this in-
strument, which was a Newtonian reflector of five feet, he saw
distinctly the ring of Saturn and the satellites of Jupiter.
Dissatisfied with its performance, he afterwards executed two
hundred specula of seven feet focal length, one hundred and fifty
of ten feet, and above eighty of twenty feet ! In 1781 he began
a thirty-feet aerial reflector, with a speculum three feet in
diameter, but as it was cracked in the operation of annealing,
and as another of the same size was lost in the fire from a
failure in the furnace, his hopes were disappointed. In minds
like his, however, disappointment is often a stimulus to higher
achievements, and the double accident which befell his specula
suggested, no doubt, the idea of making a still larger instrument,
and of obtaining pecuniaiy aid for its accomplishment. He
accordingly conveyed, through Sir Joseph Banks, to the King
his intention to execute such a telescope, and his Majesty, with

1669-73. LIFE OF SIR ISAAC NEWTON. 53

the munificent spirit of a great sovereign, instantly offered to
defray tlie whole expense of its construction. Encouraged by
this noble act of liberality, Sir William Herschel began in 1785,
and completed in 1789, his gigantic telescope, forty feet in
focal length, with a speculum forty -seven and a half inches in
diameter ! Its tube, about forty feet long and five wide, was
made of iron, and the observer, suspended in a moveable seat
at the mouth of it, examined, with what is called the front vieiv,
the celestial objects to which it was directed. This noble in-
strument, now dismantled, stood in the lawn of Sir William
Herschel's house, and some of our readers may remember, like
ourselves, its extraordinary aspect when visiting the great
astronomer himself, or resting in the Crown Hotel at Slough,
or journeying on their way to Windsor.

It is due to the memory of George iii., that the friends of
science should cherish it with respect and gratitude. By en-
abling Sir William Herschel to construct his colossal tube, and
to spend the whole of his time in applying it to the heavens,
he was entitled to share in the glory of his discoveries ; and
we owe it to historical truth to say, that none of the sovereigns
who either preceded or followed him have an equal claim on
the homage of astronomers. If, in his imperial rule, he some-
times transcended the limits of constitutional government, let
us remember that he left the throne more secure and glorious
than he found it. If he ventured, on some occasions, to thwart
the counsellors of his choice, we may find some apology for the
exercise of a high prerogative in the factious character of the
age, and in the acknowledged incapacity of his advisers ; — and
if he lost a transatlantic empire by persisting to levy tribute
from its people, he followed the advice of distinguished coun-
sellors, and was but the instrument of a higher power in
establishing a mighty nation veined with Saxon blood, and
nerved with British spirit, — destined to give lessons of civilisa-
tion to the Eastern World — to afford a home to science un-
patronized — to religion in persecution, and to patriotism in exile.

54 LIFE OF SIR ISAAC NEWTON. CHAP. III.

Stimulated by such patronage, the genius and perseverance
which created instruments so transcendent in magnitude, were
not likely to be baffled in their practical application. In the
examination of the starry heavens, the ultimate object of his
labours, Sir William Herschel exhibited the same exalted quali-
fications ; 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 antiquity, and as enduring as the objects
with which it will be for ever associated. Nor was it in the ardour
of the spring of life tliat these triumphs were achieved. He had
reached the middle of his appointed 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
nebulas and groups of celestial bodies, were added in hundreds
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. ^

When Sir WilHam Herschel's great telescope was taken down
in 1822, a telescope of 20 feet in focal length, and with an
aperture of 18 J- inches, was erected in its place by his son. Sir
John Herschel. This instrument, with three mirrors of the
same size, was carried to the Cape of Good Hope, and it was
with it that Sir John made those valuable observations which
have added so greatly to our knowledge of Sidereal Astronomy.

About the same time, the late Mr. John Ramage, a merchant

I For an account of the Decline of Science in England, here alluded to, we refer the
reader to Sir John Herschel's Treatise on Sound, to Mr. Airy's Rcpoi-t on Astronomy, in
the Report of the British Association for 1833, and to Mr. Babbage's interesting volume,
On the Decline of Science. See also Quarterly Review, October 1830, and North British
Review, vol. xiv. p. 235.

1669-73. LIFE OF SIR ISAAC NEWTON. 55

in Aberdeen, devoted much of his attention to the construction
of large Newtonian reflectors. He ground and polished specula
of 13i, 15, and 21 inches in diameter. One of these was
erected at the Royal Observatory of Greenwich, in 1820,^ with
a focal length of 25 feet, and a speculum 15 inches in diameter ;
another of the same size at Sir John Ross's Observatory, near
Stranraer ; — and the large speculum of 21 inches is, we believe,
in the Observatory of Glasgow.^

The long interval of half a century seems to be the period
of hybernation during which the telescopic mind rests from its
labours, in order to acquire strength for some great achieve-
ment : Fifty years elapsed between the dwarf telescope of New-
ton and the large instruments of Hadley : Other fifty years
rolled on before Sir William Herschel constructed his magnifi-
cent telescope ; and fifty years more passed away before the
Earl of Rosse produced that colossal instrument which has
already achieved such brilliant discoveries.

This distinguished nobleman began his experiments so early
as 1828, and he ground and polished specula fifteen inches, two
feet, and three feet in diameter, before he commenced the Her-
culean attempt of executing a speculum six feet in diameter, and
with a focal length ^i fifty feet. The speculum was cast on the
13th April 1842, ground in 1843, polished in 1844, and, in
February 1845, the telescope was ready to be tried. The focal
length of the speculum is fifty-four feet. It weighs four tons,
and, with its supports, it is seven times as heavy as the four-
feet speculum of Sir William Herschel. The speculum is placed
in one of the sides of a cubical wooden box s, Fig. 6, about
eight feet wide ; and to the opposite end of this box is fastened
the tube, which is about fifty feet long, eight feet in diameter
in the middle, but tapering to seven at the extremities, and

1 See Transactions of the Astronomical Society, vol. ii. p. 413.

2 A fine reflecting teles^cope, with a speculuna two feet in diameter, and a focal length
of twenty feet, has been recently constructed by Mr. Lassels, who has made with it several
important discoveries within the limits of our own system.

LIFE OF Sm ISAAC NEWTON.

CHAP. III.

furnished with diaphragms 6i feet in aperture. The tube is
made of deal staves an inch thick, hooped with strong iron
clamp rings, and it carries at its upper end, and in the axis
of the tube, the small oval speculum a, six inches in its lesser
diameter.

The telescope, as shown in the annexed figure, is established
between two lofty castellated piers sixty feet high, and is raised
to different altitudes by a strong chain cable b attached to the
top of the tube. This cable passes over a pulley t on the frame

Fig. 5.— Lord Rosse's Telescope from the Soutb-East.

F down to a windlass shown at u in Fig. 6, on the ground, which
is wrought by two assistants. To the frame f are attached,
at X, X, chain guys fastened to the counterweights e, e. The
telescope is balanced by these counterweights suspended by
chains d, d, which are fixed to the sides of the tube, and pass
over large iron pulleys c, c.

To the eastei-n pier is fixed a strong semicircle of cast-iron

1669-73.

LIFE OF SIR ISAAC NEWTON.

vv, about eighty-five feet in diameter. The telescope is con-
nected with this circle by a strong racked bar w, with friction-
rollers attached to the tube by wheel-work, so that by means of
a handle near the eye-piece, the observer can move the telescope
along the bar on either side of the meridian to the distance of
an hour for an equatorial star.

Fig. 6. — Lord Rosse's Telescope from the North-West.

On the western pier are erected the stairs and galleries for
the observers. The Jirst gallery, shown at h, h below the tube,
M^. 5, commands an altitude of 42°. It is a light but strong

58 LIFE OF SIR ISAAC NEWTON. CHAP. III.

framing of wood, which slides between two ladders i, i, fixed
to the southern face of the j^iers. It is counterpoised by a
weight, and raised to the height required by a windlass K.
Upon its upper plane is a railway upon which the observing
gallery l can be moved about 24 feet east and west by means
of two wheels turned by a winch m near the observer. Other
three galleries, n, o, p, command all altitudes above 42°, and
within 5® of the zefiith. They are each carried by two beams
Q, Q, which run between pairs of grooved wheels r, r, and these
beams, with their respective galleries, are drawn forward when
the wheels are turned by a veiy ingenious piece of mechanism.
These galleries hold twelve persons, and strangers are not a little
startled when they find themselves suspended, midway between
the piers, over a chasm 60 feet deep.^

We have enjoyed the great privilege of seeing and using this
noble instrument, one of the most wonderful combinations of
art and science which the world has yet seen. We have, in the
morning, walked again and again, and ever with new delight,
along its mystic tube, and, at midnight, with its distinguished
architect, pondered over the marvellous sights which it discloses,
— the satellites, and belts and rings of Saturn, — the old and new
ring, which is advancing with its crest of waters to the body of
the planet, — the rocks, and mountains, and valleys, and extinct
volcanoes of the moon, — the crescent of Venus, with its moun-
tainous outline, — the systems of double and triple stars, — the
nebulae and starry clusters of every variety of shape, — and
those spiral nebular formations which baffle human compre-
hension, and constitute the greatest achievement in modern dis-
covery.

Such is a brief description of the gigantic telescope completed
by the Earl of Rosse. In order to form a correct idea of its
effective magnitude, we must compare it with other instruments,
as in the following table, in which the specula are supposed to
be square in place of round. : —

1 A box containing a second speculum is shown at T.

1669-73.

LIFE OF SIR ISAAC NEWTON.

Ties of Makers,

Diameter of Speculum.

Area

of Surface.

Newton,

1 inch.

1 square inch

. 2-3r „ . .

5-6

Iladley.

4-6 „

5 „ . .

Ilawksbee,

9 „ . .

Ramage,

. 21 „ . .

441

Lassels,

2 feet.

576

Lord Rosse,

2 „ . .

516

3 „ . . .

1296

Herschel,

4 „ . .

2304

Lord Rosse,

6 ,. . .

6184

Next in interest to the telescopes "^of Lord Rosse are those
of M. Foucault, who deposits a film of pure silver upon the
spherical surface of a disc of glass. After the silver surface has
been polished by the hand, he modifies the figure by local re-
touches, and converts the sphere into an ellipsoid, and then into
a paraboloid, so as to remove the spherical aberration. By
this method he has produced a telescope with a speculum thirteen
inches in diameter, and eight feet in focal length, which separates
the two small stars which compose the blue star of y Andro-
medse, a result obtained by M. W. Struve with the great achro-
matic of Palkowa.

In looking back on what the telescope has accomplished since
the time of Newton, and in reflecting on the vast depths of
ether which have been sounded ; — on the number of planetary
bodies which have been added to our system, and on the exten-
sive fields of sidereal space which have been explored, can we
hesitate to believe it to be the Divine plan that man shall yet
discover the whole scheme of the visible universe, and that it is
his individual duty, as well as his high prerogative, to expound
its mysteries and to develop its laws 1 Over the invisible world
he has received no commission to reign, and into its secrets he
has no authority to pry. It is over the material and the visible
that he has to sway the intellectual sceptre, — it is among the
structures of organic and inorganic Joeing that his functions of
combination and analysis are to be chiefly exercised. However
great have been the achievements of the past, and however

60 LIFE OF SIR ISAAC NEWTON. CHAP. III.

magnificent the instruments to which we owe them, the limits
of telescopic vision have not been reached, and space has yet
marvellous secrets to surrender. A reflector ten feet in diameter
will be due to science before the close of the century, and a disc
of flint-glass,^ 29 inches in diameter, awaits the command of
some liberal government, or some munificent individual, to be
converted into an achromatic telescope of extraordinary power.

In cherishing these sanguine expectations, we have not for-
gotten that the state of our northern atmosphere must set some
limit to the magnifying power of our telescopes. In a variable
climate, indeed, the vapours and local changes of temperature,
and consequent inequalities of refraction, off"er vaiious obstruc-
tions to astronomical research. But we must meet the difficulty
in the only way in which it can be met. The astronomer can-
not summon the zephyrs to give him a cloudless sky, nor com-
mand a thunderstorm to clear it. He must transport his
telescope to the purer air of Egypt or India, or climb the flanks
of the Himalaya or the Andes, to erect his watch-tower above
the grosser regions of the atmosphere. In some of those brief
yet lucid intervals, when distant objects present themselves in
sharp outline and minute detail, discoveries of the highest value
might be grasped by the lynx-eyed astronomer. The resolution
of a nebula, — the bisection of a double star, — the detection of
new asteroids ; — the details of a planet's ring, — the evanescent
markings on its disc, — the physical changes on its surface, and
perchance the display of some of the dark worlds of Bessel,
might be the revelations of a moment, and would amply repay
in national glory the transportation of a huge telescope to the
shoulder or to the summit of a lofty mountain. ^

1 This disc of flint-glass was executed by Messrs. Chance Brothers and Company, of
the Smethwick Glass-works, and was rewarded with a council medal of the Great Exhibi-
tion. — See Reportt of the Juries, p. 529.

2 This proposal, which was first made by the author in September 1841. is likely to
be now carried into effect. A committee of the British Association, and of the Royal
Society, have applied to Government for the necessary funds.

1670-76. LIFE OF SIR ISAAC NEWTON. 61

CHAPTER IV.

Newton writes Notes on Kinkhuysen's Algebra— and on Harmonic and Infinite Series —
Delivers Optical Lectures at Cambridge — Is elected a Fellow of the Royal Society —
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 — with Linus— with Gascoigneand Lucas— The Influence of these
Disputes on his Mind — His Controversy with Dr. Hooke and Monsieur Huygens, aris-
ing from their Attachment to the XJndulatory Theory of Light — Harassed with these
Discussions he resolves to publish nothing more on Optics — Intimates to Oldenburg
his Resolution to withdraw from the Royal Society from his inability to make the
"Weekly Payments — The Council agree to dispense with these Payments— He is allowed
by a Royal Grant to hold his Fellowship along with the Lucasian Chair without taking
Orders— Hardship of his situation in being obliged to plead Poverty to the Royal So-
ciety—Draws up a Scheme for extending the Royal Society, by paying certain of its
Members — The Scheme was foimd among his Papers — Soundness of his Views relative
to the Endowment of Science by the Nation— Arguments in support of them.

While Newton was constracting his Reflecting Telescope,
and discussing with Gregory and others the question of its
superiority to instruments of the Gregorian and Cassegrainian
form, his mind was directed to a variety of other subjects. Dr.
Barrow had requested him, through Collins, to write some notes
to be appended to a Latin translation from the Dutch, of Kink-
huysen's Algebra, a task which he readily undertook, and which
occupied some considerable portion of his time during the years
1669 and 1670. He at first did not think the work « worth
the pains of a formal comment," and returned the book with
his notes, " intermixed with the author's discourse," requesting
Collins not to mention his name, but merely to say that " it
was enriched by another author." In thanking him for his
valuable additions, Collins intimated that the part on surd
numbers had been " too lightly handled," and requested New-

62 LIFE OF SIR ISAAC NEWTON. CHAP. IV.

ton to point out in several books on surds which he sent to
him, such passages as might be added to Kinkhuysen, to supply
the defect. Newton kindly offered to make the necessary
additions, and having learned from his correspondent that his
" pains" in this matter " would be acceptable to some very
eminent grandees of the Royal Society, who must be made
acquainted therewith," he got back his MSS., and added only
two or three examples more, as upon revising the papers he
" judged it (the part on surds) not so imperfect as he thought
it had been."^

His attention had also been directed by Collins to problems
on the summation of harmonic series, and in the determination
of the rate per cent, in annuity problems, when all the other
quantities were given. In sending the solution of the problems,
he gives Collins permission " to insert it in the Philosophical
Transactions, so it be without his name to it." " For I see
not," he adds, " what there is desirable in public esteem were
I able to acquire and maintain it. It would perhaps increase
my acquaintance, the thing which I chiefly study to decline."

In the month of July 1670, he had intended, during the
Duke of Buckingham's installation as Chancellor of the Univer-
sity of Cambridge, to pay a visit to his friends in London, and
to give Mr. Collins " a verbal acknowledgment of his unde-
served favours ;" but he was prevented " by the sudden sur-
prisal of a fit of sickness, which not long after (God be thanked)
I again recovered of"

During the winter of this year, Newton had begun to " me-
thodize his Discourse of Infinite Series, ^ designing to illustrate
it with problems," but he was " suddenly diverted from it by
some business in the country," and was not able to resume the

1 Letters to Collins from 1669 to September 27, 1670.— Macclesfield Correspondence,
vol. ii.

2 This work was never finished. It was published by Horslej', under the title of
Geometria Analytica, from three diflFerent MSS.— See Newtoni Opera, torn. i. pp. 391-518..
A translation of it had been published by Colson in 1736.

1670-76. LIFE OF SIE ISAAC NEWTON. 63

subject till towards the end of the year, when he was prevented
by other avocations from preparing it for the press.

Although our author had read a course of lectures on Optics,
in the University of Cambridge, in the years 1669, 1670, and
1671, containing his principal discoveries regarding the different
refrangibility of light, and towards the end of 1671 was pre-
paring a series of twenty of them for the press, yet it is a
singular fact that these discoveries should not have become
public through the conversation or correspondence of his pupils.
The members of the Boyal Society even had acquired no know-
ledge of them till the beginning of February 1672, and it was
chiefly on his Reflecting Telescope that his reputation in that
body was founded. So great indeed was the interest which it
excited, that Dr. Seth Ward, Bishop of Salisbury, who had
written some able works on Astronomy, and filled the Savilian
Chair of Astronomy at Oxford, proposed Mr. Newton as a
Fellow of the Royal Society on the 23d December 1671. In
a letter to its secretary, Mr. Oldenburg, of the 6 th January,
he expressed his satisfaction with this event in the following
words : — " 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." He
was accordingly elected on the 11th January, on which day the
Society, with the view of securing his invention of the telescope
from foreign piracy, agreed to transmit a drawing and account
of it to Huygens at Paris. The notice of his election, and the
thanks of the Society for the communication of his telescope,
were contained 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 replying to this letter,
Newton very justly expressed his surprise to see " so much
care taken about securing an invention of which I have hitherto

64 LIFE OF SIR ISAAC NEWTON. CHAP. IV.

had so little value, and therefore since the Royal Society is
pleased to think it worth the patronizing, I must acknowledge
it deserves much more of them for that, than of me, who, had
not the communication of it been desired, might have let it
still remain in private, as it hath already done some years."

Thus encouraged by the Royal Society, Newton lost no time
in making other communications to them. In his very next
letter to their secretary, dated 18th January 1672, he an-
nounces his optical discoveries in the following 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 on account of a philosophical dis-
covery, which induced me to the making of the said telescope,
and which 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 " oddest and most considerable detection" was the dis-
covery of the dififerent refrangibility of the rays of light, which
it was necessary to explain in a previous chapter, as having
been made before the construction of his telescope. It was
communicated in a letter to Oldenburg on the 6th of February
1672, and excited great interest when read on the 8th February
to " that illustrious company." The " solemn thanks of the
meeting were voted to its author for his very ingenious dis-
course ;" and it was immediately printed in the 80th Number
of their Transactions, namely, on the 19 th February, 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." At the same time a com-
mittee, consisting of Dr. Seth Ward, Bishop of Salisbury, Mr.
Boyle, and Dr. Hooke, was appointed to peruse and consider it,
and to give in a report upon it to the Society.

The kindj^ess of this distinguished body, and the anxiety

1670-76. LIFE OF SIR ISAAC NEWTON. 65

which they had ah-eady shown for Newton's reputation in the
affair of his telescope, excited on his part a reciprocal feeling,
and he accepted of their proposal to print his discourse in the
following humble terms : — " 'Twas an esteem," he says, " of
the Royal Society, for candid and able judges in philosophical
matters, which encouraged me to present them with that dis-
course of light and colours^ which since it has been so favour-
ably accepted of, I do earnestly desire you to return them my
cordial thanks. I before thought it a great favour to have
been made a member of that honourable body : but T am now
more sensible of the advantage. For believe me, Sir, I do not
only esteem it a duty to concur with them in the promotion
of real knowledge, but a great privilege, that instead of ex-
posing discourses to a prejudiced and censorious 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 strait and
narrow for public view. I designed it only to those that know
how to improve upon hints of things, and therefore, to shun
tediousness, omitted many such remarks and experiments as
might be collected by considering the assigned laws of refrac-
tion, some of which I believe, with the generality of men,
would yet be almost as taking as any of those 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 record it (if it be so thought fit) in the ensuing Transactions."

Having in the preceding chapter given an account of the
leading doctrine of the diff'erent refrangibility of the rays of
light, and of the attempts to improve the reflecting telescope
which that discovery suggested, we shall now endeavour to
make the reader acquainted with the other discoveries respect-
ing colours, which he at this time communicated to the Royal
Society.

VOL. I. B

LIFE OF SIR ISAAC NEWTON.

CHAP. IV.

We have already seen that a beam of white light emitted
from the sun, and refracted by a prism, is decomposed by its
action into seven different colours, which compose what is called
the Prismatic Spectrum, and which is nothing more than an
elongated image of the sun, its length being Jive times its
breadth, and the coloured spaces having the proportions shown
in the annexed figure.

When this spectrum is distinctly formed by a good prism, so
so that the different colours are clearly separated, Newton
found that any particular colour, such as red,
Ked I was not susceptible of any change either by

Orange.

Tellow.

Green.

Blue.

Indigo.

Violet.

refraction through prisms, or reflection from
mirrors, or from natural bodies, nor by any
other cause that he could observe, notwith-
standing his utmost endeavours to change it.
It might become fainter or brighter, but its
colour never changed. Its refrangibility, too,
was equally unchangeable, and hence he drew
the conclusion that the same degree of refrangi-
bility always belonged to the same colour, and
the same colour to the same degree of refrangi-
bility.

But while the colours in the spectrum are
original and simple, such as red, orange, yellow,
green, blue, indigo, and violet, other colours may
be compounded of these, "for a mixture of yeUow
*'^" '' and blue makes green, and red and yelloiv makes
orange, and orange and yellowish green makes yelloiv.'''' These
compound colours, however, may be separated by the prism into
their simple colours, and hence we are enabled by the prism to
decompose all such colours, and however similar they may be to
the primitive ones, their difference may always be discovered by
the different refrangibility of their elements.

But, as Newton remarks, " the most surprising and wonder-
ful composition is that of whiteness. No one sort of rays is

1670-76.

LIFE OF SIR ISAAC NEWTON.

alone capable of exhibiting it. It is ever compounded, and for
its composition all the primary colours in their due proportion
are required." In order to prove this doctrine, which is called
the Recomposition of white light, he employed three different
methods. When the beam of white light rr. Fig. 8, was
separated into its component colours, as in the spectrum mn,
he received the refracted pencil r' on a second prism bcd, held

Fig. 8.

either close to the firsts or a little behind it, and by the oppo-
site refraction of this prism they were all refracted back into a
beam of perfectly white light bw, which projected a white
circular spot on the wall at w, exactly similar in form and in
colour to the spot formed there by the beam rr, before the
prism intercepted it.

Another mode of recomposing white light, which Newton
tells us he " often beheld with admiration," is to cause the spec-
trum to fall upon a large lens at some distance from the prism,
and then to converge aU the colours into a spot, and mix them
again as they were in the light before its incidence on the
prism. The light thus reproduced is " entirely and perfectly
white," and does not " at all sensibly differ from the direct
light of the sun, unless when the glasses used were not suffi-
ciently clear." Hence our author concludes, " that whiteness
is the usual colour of light ; for light is a confused aggregate
of rays endued with all sorts of colours, as they are promiscu-
ously darted from the various parts of luminous bodies." When
there is a due proportion of the ingredients, that is, of all the

68 LIFE OF SIR ISAAC NEWTON. CHAP. IV.

simple colours, whiteness is generated, but if any one colour
predominate, the light will incline to that colour, as in the
yellow flame of a candle, the blue flame of brimstone, and the
various colours of the fixed stars.

From a consideration of these facts, our author regards it as
very evident how colours are produced by the prism. Since
such of the rays constituting white light as differ in colour,
diffier proportionally in refrangibility, they must in virtue of
their unequal refraction be severed and dispersed into an oblong
form, as in Fig. 7, in regular succession from the least refracted
red to the most refracted violet. " And for the same reason it
is," says Newton, " that objects, when looked upon through a
prism, appear coloured. For the diffbrm rays, by their un-
equal refraction, are made to diverge towards several parts of
the retina, and there express the images of things coloured, as
in the former case they did the sun's image upon a wall."

Having established these principles, Newton applies them to
the explanation of several interesting phenomena. He shows
that the colours of the primary and secondary rainbow are
prismatic spectra, produced by the refraction of the drops of
water. He explains the odd phenomena of lignum nephriticum,
leaf gold, fragjnents of coloured glass, and other bodies, which
appear in one position of one colour, and of another in another,
in consequence of their disposition to reflect one sort of light
and transmit another. He assigns the reason of Hooke's beauti-
ful experiment, with two wedge-like transparent vessels, the one
filled with red, the other with a blue liquor. Although they
are each very transparent, yet when the two are put together
they are opaque ; for since the one transmits only red, and the
other only blue, no rays whatever can pass through both of
them. And without giving more instances, he concludes with
this general one, " That the colours of all natural bodies have
no other origin than this ; that they are variously qualified to
reflect one sort of light in greater plenty than another. For if
we illuminate these bodies with imcompounded light of different

1670-76. LIFE OF SIR ISAAC NEWTON. 69

colours, they always appear of the colour of the light cast upon
them, the colour being most vivid in the light of their own day-
light colour. Minium^ for example, though red, appears indif-
ferently of any colour, though most luminous in red; and Use,
though blue, appears indifferently of any colour cast upon it,
though most luminous in blue. Hence, since minium reflects
most copiously the red rays, it must appear red when illumi-
nated with daylight, that is, wdth all sorts of rays promiscuously
blended, and for the same reason hise appears blue.

No sooner were these important discoveries given to the
world, than they were criticised and assailed with a degree of
virulence and ignorance which have not often been combined in
scientific controversy. The Royal Society unfortunately con-
tained few individuals of pre-eminent talent capable of appre-
ciating the value of his discoveries, and of entering the lists
against his envious and ignorant assailants. While they held
his labours in the highest esteem, they regarded his discoveries
as fair subjects of discussion, and their secretary regularly com-
municated to him, and even published in their Transactions,
almost all the papers which were written in opposition to his
views.

The first communication on this subject was the suggestion
of four experiments with the prism, which seems to have been
made by some friend at Cambridge, as Newton communicated
them to the editor of the Philosophical Transactions, with his
own observations.^ This letter was followed by a communica-
tion from a Jesuit, Ignatius Pardies, Professor of Mathematics
in the Parisian College of Clermont, containing animadversions
upon the new Theory of Colours. Although Newton in his
original discourse had demonstrated the reverse, yet the French
professor pretended that the elongation of the sun's image arose
from the unequal incidence of the different rays on the first
face of the prism ; that the mixture of diSerently coloured

1 The communication is dated 13th April 16T2, and is published in the Transactions,
No. 82, p. 4059, April 22, 16T2.

70 LIFE OF SIR ISAAC NEWTON. CHAP. IV.

powders was not white, but dun and grey ; and that opacity
was not produced when the two coloured liquors were mixed in
the same vessel. Newton answered these shallow objections in
the most satisfactory manner ;^ but this disciple of Descartes,
unwilling to be vanquished, took up a new position, and main-
tained that the elongation of the sun's image by the prism,
might be explained by the diffraction of light on the hypothesis
of Grimaldi, or by the diffusion of undulations on the hypothesis
of Hooke.2 Newton replied to these silly speculations on the
11th of June ; but he contented himself with reiterating his
original experiments, and confirming them by more popular
arguments.^ Pardies replied on the 9th July, in terms highly
complimentary to Newton.** He expressed himself satisfied
with Newton's exi3lanations, acknowledged that his only diffi-
culty had been wholly removed, and that he cherished the
warmest gratitude for the kindness with which his annotations
had been examined and answered.

About this time Newton seems to have been peculiarly sensi-
tive about the reception of his Doctrine of Colours. On the
8th of July, a month after he had written his second Reply to
Pardies, he published in the Philosophical Transactions, with
his name, " A Series of Queries, propounded by Mr. Isaac
Newton, to be determined by experiment, positively and directly
concluding his new Theory of Light and Colours, and here re-
commended to the industry of the lovers of Experimental Philo-
sophy, as they were generously imparted to the Publisher in a
letter of the said Mr. Newton."^ This paper consists of eight
queries, which are merely the different propositions he had
established put into that form as if they were still matters of
doubt, and it concludes with expressing the wish of the author,
" that all objections be suspended taken from Hypotheses, or
any other heads than these two ; of showing the insuflBciency

1 Phil. Trans. No. 84. p. 4091, June 17, 1672.

2 Phil. Trans. No. 85, p. 6012, July 15, 1672. » Ibid. p. 5014. ♦ Ibid. p. 5018.
5 Phil. Trans. No 84, p. 4080, June 17, 1672. This paper is part of a letter to Olden-
burg, dated July 6, 1672, from Stoake Park, Northamptonshire.

1670-76. LIFE OF SIR ISAAC NEWTON. 71

of experiments to determine these Queries, or prove any other
parts of my theory by assigning the flaws and defects in my
conclusions drawn from them ; or of producing other experi-
ments which directly contradict me, if any such may seem to
occur." In order to "invite and gratify foreigners" to con-
sider and put to trial these Queries, the publisher " delivers Mr.
Newton's letter in the language also of the learned."

This challenge to foreigners on the part of Oldenburg, sum-
moned into the field a new combatant, in the person of Francis
Linus, a physician in Liege, who, on the 6th October 1674,
addressed a letter to a friend in London, entitled, " Animad-
versions on Newton's Theory of Light and Colours."^ He
asserts that he ha»s often observed the same difference between
the length and breadth of the spectrum ; but that he never
found it so when the sky was clear and free of clouds near
the sun. The difference only appeared when the sun either
shone through a white cloud, or enlightened some such clouds
near him. The elongation of the spectrum was therefore not
affected by the true sunbeams, " and consequently the theory of
light grounded on the experiment cannot subsist." In support
of these gratuitous assertions, Linus appeals to frequently re-
peated experiments on the refractions and reflections of light
which he had exhibited nearly thirty years ago, *' together
with divers other experiments on light, to that worthy promoter
of experimental philosophy. Sir Kenelm Digby, who coming
into these parts to take the Spa waters, resorted oftentimes to
my darkened chamber, and took notes upon them ;" and he
adds, that if Newton had used the same industry as he did,
" he would never have taken so impossible a task in hand," as
" to endeavour to explicate the aforesaid difference between the
length and breadth of this coloured spectrum, by the received
laws of refraction." When this letter was shown to Newton he
refused to answer it ; but Linus was referred to his answer to
Pardies, and assured that the experiments on which he animad-

1 Phil. Tratis. No. 110, p. 217.

72 LIFE OF SIR ISAAC NEWTON. CHAP. IV.

verted were made in clear days when there was no bright cloud
in the heavens. The Dutch philosopher, however, was not
satisfied with this reply. He confesses in a second letter to
liis friend, that " if the assertions be admitted, they do indeed
directly cut off what he had said of Mr. Newton's being de-
ceived by a bright cloud ;" but he endeavours to prove that
Newton did not make the experiment in a clear day, because
Newton describes the ends of the spectrum as semicircular,
" and these semicircular ends are never seen in a clear day !"
The rest of the letter abounds with the most erroneous state-
ments, indicating the grossest ignorance, and calcidated to irri-
tate even the patient mind of Newton.

Oldenburg again attempted to prevail upon Newton to answer
these observations, but he once more declined, on the ground
that the dispute referred merely to simple matters of fact,
which could only be decided before competent witnesses. The
entreaties of Oldenburg, however, prevailed, and " lest Mr.
Linus should make the more stir," this great man condescended
to write a grave reply to reasonings utterly contemptible, and
to assertions wholly unfounded. In this answer, dated Novem-
ber 13, 1G75, and which Linus, who died on the 15th No-
vember, probably never saw, Newton gives the most minute
and simple instructions for producing the prismatic spectrum.
He mentions the size of the hole, " about the bigness of a
pease," the position of the prism close to the hole, the mode of
turning the prism round till the spectrum is placed in its
stationary position, when the rays are equally refracted on both
sides of the prism, and the nature and order of the colours.
He tells him also that the experiment will not succeed well if
the day is not clear, and he begs that " when Mr. Line has
tried this he will proceed to try the experimentum crucis,
which," he adds, "may be done, though not so perfectly, even
without darkening a room, or the expense of any more time
than half a quarter of an hour." ^

1 Phil. Trans. No. 121, p. 503.

1670-76. LIFE OF SIR ISAAC NEWTON. 73

After the death of Linus, his pupil, Mr. Gascoigne, entered
the field, and declared that Linus had shown to various persons
in Liege his experiment, proving the spectrum to be circular,
and that Mr. Newton could not be more confident on his side
than they were on the other, being fully " persuaded, that un-
less the diversity of placing the prism, or the bigness of the
hole, or some other such circumstance, be the cause of the
difference between them, Mr. Newton's experiment will hardly
stand." ^ Pleased with " the handsome genius " of Mr. Gas-
coigne's letter, Newton replied again, ^ exerting himself to dis-
cover the reason why the elongated spectrum was not as visible
to others as it was to himself. With this view, he describes
the three different kinds of images that may be seen upon the
wall when a prism refracting the sun's rays is turned round
its axis. The first of these is the regular elongated coloured
spectrum ; the second a round white image formed by reflection
from one of the faces of the prism ; and the third, an image
formed by two refractions and one reflection, which, with a good
equi-angular prism, would be a round white image of the
aperture, but more or less elongated and coloured, if the two
refracting angles were more or less inequal. From this it be-
comes very probable that Linus never saw the real prismatic
spectrum.^

As Mr. Gascoigne had not the means of making the experi-
ment thus pointed out, he requested Mr. Anthony Lucas of
Liege to make it for him. This ingenious individual, who
succeeded Linus in the mathematical chair at Liege, confirmed
the leading results of Newton, in so far as the prismatic spec-

1 Phil. Tram. No. 121. p. 503. 2 jMd. No. 123, p. 556.

s A short time before the commencement of this controversy, Linus communicated
to the Royal Society a paper entitled Optical Assertions concerning the Rainbow, which
appeared in their Transactions, No. 117, p. 386. How such a paper could have been
published by so learned a body seems very incomprehensible. Linus was celebrated as
a dial-malier. Mr. Charles Ellis mentions one of his dials at Liege, in which the hours
were distinguished by touch, and says that they were " the originals of those formerly
in our Privy Gardens."— P/»?7. Trans. No. 283, 1703, vol. xv. p. 1418.

74 LIFE OF SIR ISAAC NEWTON. CHAP. IV.

trum was concerned ; but he refused to acknowledge the truth
of his theory, and made a number of experiments with coloured
silks and coloured fluids, which he considered to be subversive
of it. His experiments on the length of the spectrum, how-
ever, possess a peculiar interest. With a prism having an
angk of 60°, and a refractive power of 1-500, he formed the
spectrum at the distance of eighteen feet from the window.
The hole in the shutter was sometimes one-fifth and sometimes
one-tenth of an inch, the distance of the prism from the hole
about two inches, and the darkness of the room equal to that
of the darkest night when the hole was shut. Under these
circumstances, he never could find the spectrum longer than
thrice the diameter of its breadth, or, at most, three and a half
times that diameter when the refractions on both sides of the
prism were equal ; whereas Newton found it to be five times
that diameter, with a prism whose refracting angle was 63" 12'.
In taking into consideration this new difficulty, Newton
acknowledges that a difference of 3° 12' in the refracting angle
of the prism is too little to reconcile the two results, and he
conjectures that Mr. Lucas may have set down the round num-
ber of 60° as the angle of his prism, in the same manner as
he set down its refractive power, or the ratio of the sines, as
two to three, or 1-500. "Then," he adds, "if it be two or
three degrees less than 60°, if not still less, all this would take
away the greatest part of the diflference between us." In order,
however, to determine the point experimentally, he measured
the length of the spectrum with prisms of different angles, and
obtained the following results : — In the first column of the
following table, he gives the six angles of two prisms which he
used, and " which were measured as exactly as he could by
applying them to the angle of a sector ^ In the second he
gives in inches the length of the image made by each of these
angles, its breadth being two inches, its distance from the prism
eighteen feet and four inches, and the breadth of the hole in
the window-shutter one-fourth of an inch. We have added a

1670-76. LIFE OF Sm ISAAC NEWTON. 75

third column, showing the ratio of the length to the breadth of
the spectrum.

Batio of its Length
Angles of the Prism, Length of Image. to its Breadth.

56° 10' 7| inches. 3| to 1.

The first Prism, -l 60 24 SJ „ 4| to 1.

!56° 10'
60 24
63 26

f5i' 0'

1, <62 12

lea 48

lOi „ 6^ to 1.

7i „ 3§ tol.

The second Prism, -{ 62 12 lOJ „ 5^^ to 1.

lOf „ 6§ tol.

On a clearer day, with the second prism, he found the
lengths of the spectrum to be as follows, about one-fourth of an
inch greater than before : —

(54° 0'

7f inches.

3| to 1.

The second Prism,

■J62 12

10^ „

5i to 1.

163 48

5| to 1.

In noticing the other experiments of Lucas with differently-
coloured silks, which he placed in a line, and viewing both
through a prism and when placed at the bottom of a square
vessel of water, Newton found that "unconcerned persons"
always saw them in a line as if they had all suffered the same
refraction. He does not, however, point out their insufficiency
to prove an equality of refraction, but thanks Mr. Lucas for
taking so much pains in examining them, " and so much the
more, as he was the first that had sent him an experimental
examination of them." He even goes so far as to say that, in
a little Treatise on the subject, written before his first com-
munication to the Royal Society, he had actually written down
the principal of the experiments which Mr. Lucas had now
sent him.

We have been thus minute in describing the experiments of
Lucas and Newton on the length of the spectrum, because they
have a close connexion with the determination of the different
dispersive powers of bodies, which was one of the greatest dis-
coveries of the following century, and led to the invention of
the achromatic telescope. There are only two ways in which

76 LIFE OP SIR ISAAC NEWTON. CHAP. IV.

we can account for the shortness of the spectrum observed by
Lucas. His eyes may have been to some extent insensible to
violet and blue light, and therefore the spectrum would appear
to him much shorter than it really was. If we cut off from
Newton's spectrum one and a half inches, to reduce it to Lucas's,
we cut off the whole of the indigo and violet spaces ; and,
unless from an imperfection of \'ision, Lucas could not have
failed to see these colours in an apartment so very dark as his.
If he had no such imperfection, it becomes highly probable that
his prism was made of glass of a low dispersive power. New-
ton's prisms may have been of flint-glass, and Lucas's of crown-
glass ; and it is a remarkable circumstance, that in all these
controversies the nature of the glass is never once mentioned.
Had Newton been less confident than he was, that all other
prisms must give a spectrum of the same length as his, in re-
lation to its refracting angle and index of refraction, the inven-
tion of the achromatic telescope would have been the necessary
result. The objections of Lucas drove Newton to make ex-
periments which he never contemplated, namely, to measure
accurately the lengths of spectra formed with prisms of diff'erent
angles and different refractive powers ; and had the Dutch
Professor maintained his opinions with more obstinacy and
perseverance, he would have conferred a distinguished favour
upon science, and rewarded Newton for all the vexation which
had arisen from the minute discussion of his optical discoveries.

Thus terminated the disputes with Pardies, Linus, Gas-
coigne, and Lucas, and we think it can scarcely be doubted
that Newton found it a more difficult task to detect the origin
of his adversaries' blunders, and to expose their fallacy, than to
establish the great truths which they had attempted to overturn.

Harassing as such a controversy was to a philosopher like
Newton, yet it did not touch those deep-seated feelings which
characterize the noble and generous mind. It was with igno-
rance and incapacity only that he had to strive. No personal
invective ruffled his equanimity ; — no vulgar jealousy roused

1670-76. LIFE OF SIR ISAAC NEWTON. 77'

his indignation ; — no charge of plagiarism called in question
his veracity or his honour. These aggravations of scientific
controversy, however, he was destined to endure, and in the
disputes which he was called to maintain against Hooke,
Huygens, and Leibnitz, the agreeable consciousness of grappling
with minds of kindred power was painfully embittered by the
personal feelings which were thrown into the contest.

Dr. Robert Hooke, bom in 1635, was about seven years
older than Newton, and was one of the ninety-eight original
or unelected Fellows 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 de-
voted himself with fixed purpose to any particular branch of
knowledge. His numerous and ingenious inventions, of whicli
we cannot speak too highly, gave to his studies a practical
character, unfitting him for that continuous labour whicli
physical researches so imperiously demand. The subjects of
light and colours, however, seem to have deeply occupied his
thoughts before Newton descended into the same arena, and
there can be no doubt that he had made considerable progress
in their study. With a mind less divergent in its pursuits,
and more fixed in its purpose, he might have unveiled the
mystery in which both these subjects were enveloped, and pre-
occupied the intellectual throne which was destined for his
rival ; but the infirm state of his health, the peevishness of
temper to which it gave rise, the number of unfinished inven-
tions 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 seed, it was not easy to conceal the
mortification which their success inspired. In the arbitra-
ments of science, it has always been a difficult task to adjust

.78 LIFE OF SIR ISAAC NEWTON. CHAP. IV.

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 its re-
sults, 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 the unfinished
labours, and demonstrate the imperfect speculations of his rival
or 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 un-
})ublished 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. Wlien Newton
presented his Reflecting Telescope to the Royal Society, Dr.
Hooke not only criticised the instrument with undue severity,
but announced, what was never realized, 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."

Descartes had long ago maintained that an ethereal medium
pervaded all transparent bodies ; — that light consists in the
action of this medium ; — that the ether is less implicated in the
parts of solid bodies ; — that it moves more freely in them, and
transmits light more readily through them, so as to accelerate
the rays in a certain proportion ; — that refraction arises from
this acceleration, and has the sines of incidence and refraction
proportional ; — that light is at first uniform ; — that its colours
are some disturbance or new modification of its rays by refrac-

1670-76. LIFE OF SIR ISAAC NEWTON. 79

tion or reflexion ; — that the colours of a prism are made by
means of tke quiescent medium accelerating some motion of
the rays on one side where red appears, and retarding it on
the other side where blue appears, and that there are but these
two original colours, or colour-making modifications of light,
which, by their various degrees or dilutings, as Hooke calls
them, produce all intermediate ones.

These views were adopted by Dr. Hooke, who " changed
Descartes' pressing or progressive motion of the medium to a
vibrating one ; — the rotation of the globuli to the obliquation
of pulses, and the accelerating their rotation on the one hand,
and retarding it on the other, by the quiescent medium to pro-
duce colours, to the like action of the medium on the two ends
of his pulses for the same end."^

Such were Hooke's opinions of the nature of light when
Newton published his Theory of Colours, and it was through
this theoretical medium that he viewed Newton's discoveries,
when he sent his observations upon them to the Eoyal Society,
on the 15th February 1672. Dr. Hooke was thanked "for
the pains he had taken in bringing in such ingenious reflec-
tions ;" but it was not " thought fit to print the two papers
together, lest Mr. Newton should look upon it as a disrespect
in printing so sudden a refutation of a discourse of his which
had met with so much applause at the Society but a few days
before."

It is not easy to follow the train of thought which runs
through the observations of Dr. Hooke. While he praises " the
niceness and curiosity" of Newton's experiments, and expresses
an entire agreement with him as to the truth of those which he
brought forward, founded on hundreds of trials made by him-
self, yet he " cannot see in his hypothesis of solving the pheno-
mena of colours thereby, any undeniable argument to convince

1 This view of Descartes' theory and of Hooke's opinions, is given by Newton in his
letter to Oldenburg, dated 21st December 1675, General Diet. vol. vii. p. 783, or Maccles-
field Correspondence, vol. ii. p. 378.

80 LIFE OF SIR ISAAC NEWTON. CHAP. IV.

liim of its certainty." He considers them as proving his own
hypothesis, which he endeavours, without much success, to ex-
plain and establish. This, indeed, seems to be the principal
object of his paper, but even if he had succeeded, the truth of
his theory would not have invalidated in the slightest degree
the doctrines of Newton. " I most readily agree," says he,
" with them (Newton's experiments) in every part thereof, and
esteem it (his hypothesis) very subtle and ingenious, but I
cannot think it to be the only hypothesis, nor so certain as
mathematical demonstration." In remonstrating with Newton
*' on his wholly laying aside the thought of improving tele-
scopes and microscopes by refractions," he is more successful ;
but though this assertion, that the difficulties of removing the
effects of colour are not insuperable, has received ample con-
firmation, yet the result was not obtained by any of the con-
trivances which he pretended to possess.

Newton lost no time in replying to Hooke's communication,
and he expressed to Oldenburg the gratification which he felt,
" that so acute an objector as Hooke had said nothing that
could enervate any part of his theory." On the 11th July
1672, he transmitted to Oldenburg an elaborate answer to
Hooke,^ expressing his conviction that both of them "had a
sincere endeavour after knowledge, without valuing uncertain
speculations for their subtleties, or despising certainties for their
plainness." After admitting that he had deduced the " cor-
poreity of light" from his theory of colours, he asserts that the
properties of light were in some measure capable of being ex-
plained, not only by that theory, but by many other mechanical
hypotheses, and that " he had therefore declined them all, and
spoken of light in general terms, considering it abstractedly as
something or other propagated every way in straight lines from
luminous bodies, without determining what that thing is."
Conscious of the ingenuity and mental power of his opponent,
Newton left him no loop-hole for escape, but replied to ever}^

1 Newtoni Opa-a, torn. iv. pp. 322-S42.

1670-76. LIFE OF SIR ISAAC NEWTON. 81

objection with a precision and force of argument which Hooke
found to be unanswerable. In this remarkable discussion New-
ton pointed out the true character of experimental philosophy,
and the duties of those who cultivate it when rival theories
demand their attention. He has shown that the properties of
light may be investigated, and its physical laws determined
without any other principle than that it is " something pro-
pagated every way in straight lines," and that discoveries are
not to be valued from their coincidence with the theoretical
views of him who made them, or their repugnance to those of
his opponents. The discovery of an important fact, or a new
law, may confirm one theory and shake another, but he is not
a friend to truth who would over-estimate it in the one case, or
depreciate it in the other. The true philosopher who forgets
his own reputation amid the triumphs of advancing science, and
who confides in a theory as a branch of eternal truth, will be
the last to spurn from him even experimental results, that may
put his own views to the torture. It is the self-seeking sciolist
alone who pilfers a laurel at the expense of truth, or the intel-
lectual coward who dreads the ordeal, and questions the decision
of experiment and observation. Should the eye of youthful
genius rest upon these pages, w^e would counsel him to ponder
over the reply to Hooke, and to remember, in the ardour of his
pursuit, that Science has a court of appeal in which posterity
is the arbiter.

It would have been well for the progress of science and the
tranquillity of its friends, if experiment and observation had
been, more than they have, our guides in philosophical inquiry.
Even in the present day the disciples of Hooke, who " split
|)ulses" with more success than he did, and whose theory of light
lias attained a lofty pre-eminence, have not scrupled to imitate
their master in measuring optical truths by the undulatory
standard, and in questioning and depreciating labours, that it
cannot explain, or that run counter to its deductions. There
is fortunately, however, a small remnant in the Temple o|

voi^ I. • F

82 LIFE OF SIR ISAAC NEWTON. CHAP. IV.

Science, who, while they give to theory its due honours and its
l)roper place, are desirous, as experimental philosophers, to
follow in the steps of their great Master.

After silencing the most powerful of his adversaries, Newton
was unexpectedly summoned to defend himself against a new
fneray. The celebrated Christian Huygens, an eminent mathe-
matician and natural philosopher, who, like Hooke, had main-
tained the undulatory theory of light, transmitted to Oldenburg
on the 14th January 1673, a letter from Paris, containing some
eunsiderations on Newton's Theory of Light ; but though his
knowledge of optics was of the most extensive kind^ his ob-
jections were as groundless, and his speculations as erroneous
as those of his less enlightened countrymen. Attached to the
undulatory hypothesis, he seems, like Dr. Hooke, to have viewed
the theory of Newton as calculated to overturn it, and he
therefore objects to its two leading doctrines, namely, the com-
position of white light by the union of all the colours, and the
generality of the doctrine of their different refrangibilities. The
objection which he urges against the theory of whiteness is, that
it may be j^roduced equally well by yellow and hlue, and " he
does not see why Mr. Newton doth not content himself with
these two colours, as it will be much more easy to find a
hypothesis by motion that will explicate these two differences,
than for so many diversities as there are of other colours ; and
till he hath found this hypothesis, he has not taught us what it
is wherein consists the nature and difference of colours, but only
this accident (which certainly is very considerable) of their dif-
ferent refrangibility." He then proposes that the experiment
should be tried of stopping all the colours but yellow and blue
and green, and then mixing them on paper to see if they make
the paper white, '' as well as when they all give Mght." Nay,
he adds the following extraordinary opinion, as if it were a new
and happy thought. " I even doubt," says he, " whether the
lightest place of the yellow colour may not all alone produce
that effect, and I mean to try it at the first eonveniency ; for

1670-76, LIFE OF SIR ISAAC NEWTON. 83

this thought never came into my mind but just now. Mean-
time you may see that if these experiments do succeed it can no
more be said that all the colours are necessary to compound
white ; and that 'tis very probable that all the rest are nothing
but degrees of yelloiv and blue more or less changed."

On the subject of the difference of refrangibility, he is equally
wrong, though with more reason for his error. He remarks,
that the picture formed in a dark room by an object-glass of
twelve feet, is too distinct and too well defined to be *' pro-
duced by rays that would stray the fiftieth part of the aperture ;
so that (as I believe I have told you heretofore) the difference
of the refrangibility doth not, it may be, always follow the
same proportion in the great and small inclinations of the rays
upon the surface of the glass." ^

To these extraordinary objections, Newton replied on the 3d
April 1673,^ and also in another paper which immediately fol-
lows the observations of Huygens, the first of these answers
having been, as we are informed by the editor, mislaid, other-
wise it should have also immediately followed the letter of
Huygens. In these answers, Newton shows that the yellows
and hliies which could produce white^ are not simple but com-
pound ; and he explains more minutely how the existence of an
aberration equal to the fiftieth of the aperture, is compatible
with the distinctness of a picture formed by a twelve-feet ol>
ject-glass. Huygens, still dissatisfied with the explanations so
Datiently given to him, informs Oldenburg that he has still
•'matter to answer them, but seeing that Newton maintains his
opinion with so much concern, he list not to dispute." Newton
was not pleased with this criticism upon his explanations, and
says in his letter to Oldenburg, — " As for Mr. Huj'-gens' ex-
pression, I confess it was a little ungrateful to me to meet
with objections which had been answered before, without

1 Phil. Trans. toI. viii. No. 96, p. 6086, July 1693.
* Phil. Trans. No. 97, p. 6108.

84 LIFE OF SIR ISAAC NEWTON. CHAP. IV.

having the least reason given me why those answers were in-
sufficient."^

But tliough Huygens appears in this controversy as a ralli
and unreasonable objector to the Newtonian doctrine of colours,
it was afterwards the destiny of Newton to play a similar part
against the Dutch philosoplier. When Huygens published his
beautiful law of double refraction, founded on the finest experi-
mental analysis of the phenomena, though presented as a result
of the undulatory theory, Newton not only rejected it, but sub-
stituted for it another law entirely incompatible with the ex-
periments of Huygens, which Newton himself had praised, but
with those of all succeeding philosophers.^

Although Hooke and Huygens were now driven from the
field, and the views of Newton established upon an impregnable

^ Letter to Oldenbui^. without a date, but probably in April 1673.

2 It is curious to observe how little accurate knowledge of the great optical dis-
coveries of the age was possessed by Leibnitz. In a letter addressed to Huygens, dated
8th September 1679, he says, — " 1 hear from Mr. de Mariotte that you are about; to give
U8 your Dioptrics, so long wished for. 1 have a great desire to know beforehand if you
are satisfied with the ratio of refraction proposed by Descartes. I confess that I am
neither wholly satisfied with it, nor with the explanation of Mr. Format, given in the
third volume (Lett. 51) of Descartes' Letters." — Ch. Hugenii Excrcit. Math., torn. i. pp.
7, 8 : lett. iv. Hag. Com. 1833. Huygens made no reply to this question, though he an-
swered Leibnitz's letter on the 22d November. In reply to this letter, Leibnitz repeats
the same question, confessing that he was neither satisfied with the ratio of Descartes,
nor that of lermat deduced from an opposite supposition. To this question he adds, —
" I wish to know also if you believe that the irregularity of refraction, — for example,
that which Mr. Newton has remarked, — ought to hurt telescopes considerably ?' — Ibid.
lett. vi. p. 17. An answer to this question was given by Huygens in a subsequent letter,
for we find Leibnitz, in a letter dated 20th June 1680, expressing his satisfaction that
Huygens had formed the same opinion of the " pretended demonstration of the laws of
refraction given by Descartes." — Ibid, lett viii. p. 20. No reply is made to the question
about Newton's doctrine of the cause of the imperfection of refracting telescopes ; but
ten years afterwards, when Leibnitz had received from Huygens a copy of his Traite de
la Lumiere, we find the following curious passage in his letter to Leibnitz, dated 24th
August 1690 : — " I have said nothing respecting colours in my Traits de la Lumiere,
finding this subject very difiBcult, and particularly from the great number of different
ways in which colours are produced. Mr. Newton promised something on the subject,
and communicated to me some very fine experiments which he had collected. It seems
that you have also thought on the subject, and apparently to some purpose." — Ibid.
lett. xi. pp. 27, 28.

1G70-7G. LIFE OF SIK ISAAC NEWTON. 85

basis, yet these prolonged and exciting controversies ruffled his
temper, and disturbed his tranquillity. Even the satisfaction
of humbling all his antagonists he did not regard as a compen-
sation for the time he had wasted, and the intellectual labour
which he had thrown away. " I intend," says he to Olden-
burg, " to be no farther solicitous about matters of philosophy ;
and therefore I hope you will not take it ill if you never find
me doing anything 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 farther 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, of the 9th December
1675, he observes, — "I was so persecuted with discussions
arising out 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." Nor was this a temporary reso-
lution arising from some disagreeable expressions of a personal
nature, which often embitter controversy even in its most
temperate form. Nearly a year after his complaint to Leibnitz,
he uses the following remarkable expressions in a communica-
tion to Oldenburg : — " I see I have made myself a slave to
philosophy ; but if I get free of Mr. Linus's business, I will
resolutely bid adieu to it eternally, excepting what I do for my
private satisfaction, or leave to come out after me ; for I see a
man must either resolve to put out nothing new, or to become
a slave to defend it,"^

In this state of mind, perplexed, as we shall presently see,
with some pecuniary difficulties, and feeling, as he expressed it
to Collins in 1674, "that mathematical speculations were at
least dry, if not somew^hat barren," there is reason to believe

1 This letter is dated November 18, 1676, and was written after receiving an account
of the experiments of Lucas. — Maccksjidd Correspondence, vol. ii. p. 405,

86 LIFE OF SIE ISAAC NEWTON. CHAP. IV.

that Newton, " who, in the usual course of things, would
vacate his Fellowship in a few months, had seriously thought of
directing his mind to the study of law." In an obituary
notice of the Rev. Robert Uvedale, Rector of Langton, in Lin-
colnshire,^ it is stated that his grandfather, Mr. Uvedale, when
one of the Divinity Fellows of Trinity College, Cambridge, had
become candidate for the Law Fellowship in that College when
made vacant, on the 14th February 1673, by the death of
Dr. Crane ; — that Mr. Newton was his competitor ; — that Dr.
Barrow, as Master of Trinity, decided it in favour of Mr.
Uvedale ; and that the ground of his decision was, that thougli
Mr. Uvedale and Mr. Newton were at that time equal in literary
attainments, yet he must give the Fellowship to Mr. Uvedale
as the senior. Mr. Edleston^ is disposed to consider this story
as mythical, and he thinks that the real facts of the case were,
that Uvedale was appointed to a Law Fellowship, and that
Newton would have been glad to have had one. This opinion
he rests on the ground that the tenure of the Law Fellowship
could scarcely be considered compatible with the duties of the
Lucasian chair, and " he believes that it would argue much
misconception of the characters of the two great men con-
cerned, to suppose them capable of being parties to a lax inter-
pretation of the statute which they had sworn to obey." We
can hardly admit the force of this argument in opposition to
the precise statements, even if traditionary, of the Uvedale
family. The necessities of Newton, and the ardent friendship
of Barrow, might have induced the one to adopt a lax inter-
pretation of the Lucasian statutes, and the other to accept the
Fellowship, had it been in his power, without any great loss of
character ; and we are the more inclined to adopt this opinion,
when we know that in modern times the same statutes have
been imperfectly observed.

While Newton was harassed with these discussions, and

1 Gentleman's Magazine, 1799, Supplement, pp. 1186 and 999.

2 (Jorrespondence, if^c, pp. xlviii, xlix. note, 38.

1670-76. LIFE OF SIR ISAAC NEWTON". 87

chagrined, it may be, with the loss of the Law Fellowship, he
came to the resolution of resigning his place in the Royal
Society. On the 8th of March 1673, he writes in the follow-
ing terms to Oldenburg :— " Sir, — I desire that you will procure
that I may be put out from being any longer a member of the
Royal Society ; for though I honour that body, yet, since I see
I shall neither profit them, nor (by reason of this distance) can
partake of the advantage of their assemblies, I desire to with-
draw." Oldenburg expressed his surprise i "at his resigning
for no other cause than his distance, which he knew as well at
the time of his election ; " and he probably then intimated to
him, that he would apply to the Society to excuse him his
weekly payments. That such an intimation was made, appears
from Newton's letter to Oldenburg, dated June 23, 1673, in
which he says, — " For your proffer about my quarterly pay-
ments, I thank you, but I would not have you trouble yourself
to get them excused, if you have not done it already." Nothing
farther seems to have been said on the subject till the 28t]i
January 1675, when Mr. Oldenburg mentioned " to the Society,
that Mr. Newton was now in such circumstances that he desired
to be excused from the weekly payments."^ Upon which " it
was agreed to by the council that he should be dispensed with,
as several others were." It does not appear, from any docu-
ments we have seen, what the change of circumstances was to
which Oldenburg alludes, but Mr. Edleston thinks it probable
that it refers to the expected vacating of his Fellowship, from
his being appointed to the Lucasian chair, which, in the usual
course of things, would expire in the following autumn. This
anticipated event, however, did not take place, for, on the 27th
April 1675, he obtained a patent from the Crown, permitting
tlie Lucasian Professor to hold a Fellowship, without being
obliged to go into orders.

1 This appears from a memorandum on the back of Newton's letter to him.

2 The admission-money to the Royal Society was £2, and the payments one shilling
a week.

88 LIFE OF SIE ISAAC NEWTON. CHAP. IV.

This permission seems to have been obtained on the applica-
tion of Newton ; and Mr. Edleston is of opinion, that the
draught of it in Newton's own hand, among the Lucasian
papers, was composed by himself, and that his visit to London
in February may have been connected with this application to
the Crown. When the grant was submitted to the King, the
following memorandum, found also in Newton's handwriting,
was recorded at Whitehall on the 2d March 1674 : — " His
Majesty, being willing to give all just encouragement to learned
men who are and shall be elected into the said Professorship, is
graciously pleased to refer this draught of a patent unto Mr.
Atturney-Generall to consider the same, and to report his
opinion what his Majesty may lawfully do in favour of the said
Professors, as to the indulgence and dispensation proposed and
desired." The original draught, which has been published by
Mr. Edleston, was adopted, excepting in two unimportant par-
ticulars, and there is a copy of it in the archives of Trinity
College, with the heading, — Indulgentia Regia PYofessorl
Mathematico concessa, dig^iissimo vivo Magistro Isaaco Neiv-
tono^ hujus Collegii Socio, istud munus tvMC temporis oheunte.

It is obvious, we think, from these proceedings, that the
change in Newton's circumstances must have been of a dis-
tressing nature, otherwise he would hardly have permitted
Oldenburg to apply to the Royal Society for a remission of his
weekly payments. At no period of his life had he any regard
for money, and, as he was always punctual and accurate in his
pecuniary concerns, it is very probable, that when the income
of his Fellowship ^ and the Lucasian chair were united, he may
have resumed his payments to the Royal Society.^ If he did

I In reference to an application from Francis Aston for a dispensation similar to that
received by Newton, Dr. Barrow, then Master of Trinity, in declining to grant it, says,
— " Indeed a Fellowship with us is now so poor, that I cannot think it worth holding by
an ingenuous person upon terms liable to so much scruple." — Edleston's Correspondence.
p 1.

3 In a volume of MSS. in the British Museum relating to the Royal Society, there is,
as Mr. Weld informs us, a sheet containing the names of Fellows who will probably paj/.

1670-76. LIJ?^ OF SIR ISAAC NEWTON. 89

not do this, it could not have been from poverty, as we find
him in 1676 subscribing forty pounds to the new Library of
Trinity College.

But however this may be, it cannot fail to be remarked,
especially by foreigners, as a singular example of the illiberality
of England to her scientific institutions, that a Society, founded
by the sovereign, and bearing the name of Royal, should have
been established without any provision for the support of its
members, for carrying on scientific inquiries, or for the publica-
tion of its Transactions. Nor is it less remarkable, that an
Institution so useful to the country, so bright with immortal
names, and so fitted to promote the intellectual glory of the
nation, should have been continued under royal patronage for
nearly two hundred years without any attempt being made to
extend its usefulness, by placing it in the same advantageous
position as the Academy of Sciences in Paris, and other similar
institutions in the metropolitan cities of Europe.

If Newton did not feel it a hardship to pay a weekly pittance
into the treasury of the Royal Society, he must have felt it a
degradation to plead poverty for its remission. His colleagues
in the Society, and men of science in a succeeding age, on whom
the wealth of this world is never abundantly bestowed, must
have often smarted under the injustice of paying for the publi-
cation of discoveries which it cost them much time, and
frequently much money, to complete. Of all the taxes upon
knowledge this is the most oppressive, and not the less oppres-
sive that it is exacted from the feelings and patriotism of its
victims.

There is reason to believe that Newton took this view of his
own position, and of the inefficiency of any scientific body con-
stituted upon the voluntary principle ; and it is not improbable,

and give yearly one entertainment lo the Society. Opposite the names of Dr. Grew,
Hooke, and Newton, are the words, "No pay, but will contribute experiments." The
date of this list, if it has any, is not mentioned. See Baily's Life of Flamsteed, p. 90.
note, and Weld's Hist, of the Royal Society, voL i. p. 250, note.

90 LIFE OF SIR ISAAC NEWTON. CHAP. IV.

that he committed to writing his opinions on this subject at the
time when he had resolved to withdraw from the Society. In
support of this opinion, we have great pleasure in submitting
to the reader a very remarkable document in ISewton's hand-
writing, which we found among the family papers at Hurts-
bourne Park, entitled " A Scheme for Establishing the Royal
Society." We give it without abridgment or change, as the
opinions of so competent a judge on the subjects which ought
to occupy the attention of a national institute, and on the best
method of making it efficient in promoting the advancement of
profound science and of useful knowledge, cannot fail to be
appreciated by every class of readers. ^

((

SCHEME FOR ESTABLISHING THE ROYAL SOCIETY.

" Natural Philosophy consists in discovering the frame and
operations of Nature, and reducing them, as far as may be, to
general Rules or Laws, — establishing these rules by observa-
tions and experiments, and thence deducing the causes and
effects of things ; and for this end it may be convenient, that
one or two (and at length perhaps three or foui-) Fellows of the
Royal Society, well skilled in any one of the following branches
of Philosophy, and as many in each of the rest, be obliged by
pensions and forfeitures (as soon as it can be compassed), to
attend the meetings of the Royal Society. — The Branches
are —

" 1. Arithmetic, Algebra, Geometry, and Mechanics, with
relation to the figures, surfaces, magnitudes, forces, motions,
resistances, weights, densities, centres of gravity, and other
mathematical aflFections of solids and fluids ; — the composition
of forces and motions ; — the shocks and reflexions of solids ; —
the centrifugal forces of revolving bodies ; — the motion of pen-

1 We found six copies of this scheme, one of which is more complete than the other?.
The first paragraph of the copy given in the text is wanting in the less perfect copies, but
in other respects they are nearly the same. There is no date upon any of the copies.

1670-76. LIFE OF SIE ISAAC NEWTON. 91

(lulums, projected and falling bodies ; — the mensuration of time
and distance ; — the efficacy of the five powers, the running of
rivers ; — the propagation of light and sound, and the harmony
and discord of tunes and colours.

"2. Philosophy relating to the Heavens, the Atmosphere,
and the surface of the Earth, viz.. Optics, — Astronomy, —
Geography, — Navigation, and Meteorology ; and what relates
to the magnitudes, distances, motions, and centrifugal forces of
the heavenly bodies ; and to the weight, height, form, and
motions of the Atmosphere, and of the things therein, and to
instruments for observing the same ; and to the figure and mo-
tions of the Earth and Sea.

" 3. Philosophy relating to animals, viz., their species, — quali-
ties, — passions, — anatomy, diseases, &c., and the knowledge of
the frame and use of their Stomachs, — entrails, blood-vessels,
heart, lungs, liver, spleen, glands, juices, and organs of sensa-
tion, motion, and generation.

" 4. Philosophy relating to vegetables, and particularly the
knowledge of their species, parts, leaves, flowers, seeds, fruits,
juices, virtues, and properties, and the manner of their genera-
tion, nutrition, and vegetation.

" 5. Mineralogy^ and Chemistry, and the knowledge of the
nature of Earths, Stones, Corals, Spars, Metals, semi-metals,
Marchasites, Arseniates, Bitumens, Sulphurs, Salts, Vitriols,
Rain- Water, Springs, Oils, Tinctures, Spirits, Vapours, Fumes,
Air, Fire, Flames and their parts. Tastes, Smells, Colours,
Gravity, Density, Fixity, Dissolutions, Fermentations, Coali-
tions, Separations, Congelations, Liquefactions, Volatility, Dis-
tillation, Sublimation, Precipitation, Corrosiveness, Electricity,
Magnetism, and other qualities ; — and the causes of subterrane-
ous Caves, Rocks, Shells, Waters, Petrifactions, Exhalations,
Damps, Heats, Fires, and Earthquakes, and the rising or falling
of Mountains and Islands.

" To any one or more of these Fellows, such Books, Letters,

1 Written by mistake Meteorology ; but in one of the other copies it is Mineralogy.

92 LIFE OF SIR ISAAC NEWTON. CHAP. IV.

and things as desei've it, may be referred by the Royal Society
at their meetings from time to time ; and as often as any such
Fellowship becomes void, it may be filled up by the Royal Society
with a person who hath already invented something new, or
made some considerable improvement in that branch of philoso-
phy, or is eminent for skill therein, if such a person can be
found For the reward will be an encouragement to Inventors ;
and it will be an advantage to the Royal Society to have such
men at their meetings, and tend to make their meetings numer-
ous and useful, and their body famous and lasting."

It is very evident, from this interesting document, that
Newton was desirous of converting the Royal Society into an
institution like that of the Academy of Sciences in Paris ; but
we have not been able to learn that he ever communicated this
plan either to the Society itself, or to any of its membera.
During the last twenty years, and long before we could have
known the views of so competent a judge, we have cherished
the same desire, and embraced ever}^ opportunity of pressing it
upon the notice of the public.^ Several years ago we com-
municated Sir Isaac Newton's scheme to Sir Robert Peel, and
it was so far carried into effect by the establishment of the
Museum of Practical Geology, which is neither more nor less
than an enlargement of the Mineralogical, Geological, and
Chemical sections of an Academy of Sciences, or a National
Institute. The services of all the members of this important
body are of course at the entire disposal of the State, though its
members are frequently employed in other duties than those
which strictly belong to their office. If mineralogy, geology,
and chemistry, therefore, have obtained a national establish-
ment for their improvement and extension, — astronomy, me-

1 See especially the (Quarterly Review, October 1830, vol. xliii. pp. 305-342 ; Edinburgh
Jieniew, January 1835, vol. Ix. p. 363 ; Edinburgh Journal of Science, passim.- North
British Review, vol. iv. pp. 410-412 ; vol. vi, p. 506; vol. xiv. pp. 231-288 ; from the last
of which articles some of the paragraphs in the text are transferred.

1670-76. LIFE OF SIR ISAAC XEWTON. 93

chanics, natural history, medicine, and literature, and the arts,
are entitled to the same protection. If any real objections
exist to such an establishment, they can be founded only upon
two causes ; — on the unwillingness of existing voluntary societies
to be merged in a general institution, and on the apprehension
that the expense would be a burden to the state. Men will always
be found who oppose every change, however salutary, and who
regard the reform of existing institutions as dangerous inno-
vations. In political and educational questions, the rights and
interests of individuals often obstruct the march of civilisation,
but in matters of science and literature, such rights have
neither been conferred nor claimed. Were the Royal, the
Astronomical, the Geological, the Linnsean, the Zoological, and
the Geographical Societies, together with the Society of Civil
Engineers, and the Museum of Practical Geology, all united into
an Academy of Sciences, and divided into distinct sections as in
France, the really working members would occupy a more dis-
tinguished position, while the nobility and gentry would pre-
serve all their rights and privileges as honorary members.^
Tlie Royal Society of Literature, and the Antiquarian Society,
would readily coalesce into the Academy of Belles Lettres, and
the existing Royal Academy would form the Academy of the
Fine Arts, divided, as in France, into the three sections of
Painting, Sculpture, and Engraving. In the magnificent grove
acquired by Prince Albert and the Royal Commissioners at
Kensington Gore, a Palace of Arts would be reared for the
Institute, and there would be one library, one museum, and one
record of their weekly proceedings. Each member of the now
insulated societies would listen to the memoirs and discussions
of the assembled Academy, and science and literature would
thus receive a new impulse from the number and variety of
their worshippers.

The second difficulty to which we have referred, namely, the
expense of endowment, scarcely merits our consideration. A

J Corresponding to the Acad^micicns Lilyres of the Academy of Sciences in Paris.

94 LIFE OF SIK ISAAC NEWTON. CHAP. IV.

very large sum is annually expended by the State in support of
the existing societies, and a considerable number of those who
would be members of the General Institute, already enjoy the
liberality of Government. But, independently of these con-
siderations, the organization of a National Institute would be a
measure of real and direct economy. The inquiries connected
with the arts, whether useful or ornamental, which are required
by the Government, have hitherto been carried on by Com-
mittees of Parliament ; and had we a return of all the sums
annually spent in scientific inquiries, and for scientific purposes,
the amount would be found to exceed greatly that of the
annual expense, however liberal, of a National Institution.
Every question connected with ship-building, with our steam
navy, our light-houses, our harbours, our railways, our mines,
our fisheries, our sanitary establishments, our agriculture, our
statistics, our fine and useful arts, would be investigated and
reported upon by a Committee of Academicians ; and while the
money of the State would thus be saved, the national resources
would be augmented, and all the material interests of the
country, under the combined energies of her Art and her
Science, would advance with a firm and accelerated step.

But there are grounds higher than utilitarian, on which we
would plead the national endowment of science and literature.
In ancient times, when knowledge had a limited range, and
was but slightly connected with the wants of life, the sage
stood even on a higher level than the hero and tlie lawgiver,
and History has preserved his name in her imperishable record,
when theirs have disappeared from its page. Archimedes lives
in the memory of thousands who have forgotten the tyrants of
Syracuse, and the Roman consul who subdued it. The halo
which encircled Galileo under the tortures of the Inquisition,
extinguishes in its blaze even the names of his tormentors ;
and Newton's glory will throw a lustre over the name of Eng-
land, when time has paled the light reflected from her warriors.
The renown of military achievements appeals but to the country

l(;70-76. LIFE OF SIR ISAAC NEWTON. 95

which they benefit and adorn : It lives but in the obelisk of
g-ranite : It illuminates but the vernacular page. Subjugated
nations turn from the proud monument that degrades them,
and the vanquished warrior spurns the record of his humiliation
or his shame. Even the patriot traveller makes a deduction
from military glory, when he surveys the red track of desola-
tion and of war, and the tears which the widow and the orphan
shed corrode the inscription that is written in blood. How
different are our associations with the tablet of marble, or the
monument of bronze, which emblazon the deeds of the sage
and the philanthropist ! Their paler lustre irradiates a wider
sphere, and excites a warmer sympathy. No trophies of war
are hung in the temple which they adorn, and no assailing foe
desecrates its shrine. In the anthem from its choir the cry of
human suffering never mingles, and in the procession of the
intellectual victor, ignorance and crime are alone bound to his
car. The achievements of genius, on the contrary, could the
wings of light convey them, would be prized in the other
worlds of our system, — in the other systems of the universe.
They are the bequests which man offers to his race, — a gift to
universal humanity — at first to civilisation — at last to barbarism.
Views like these must have influenced the mind of Newton,
when, in an elaborate document which he left in duplicate be-
hind him, he recommended the systematic endowment of
Science. Were the British Parliament to try this question at
its bar, and summon as witnesses the wisest of their race, what
name, or vvhat constellation of names, could countervail against
the High Priest of Science, when he proposes to rebuild its
Temple upon a broader basis, and give its arches a wider span,
and its domes a loftier elevation ! ;.

9G LIFE OF SIR ISAAC NEWTON. CHAP. V.

CHAPTER V.

Mistake of Newton in supposing the Length of the Spectra to be the same in all Bodies —
And in despairing of the Improvement of Refracting Telescopes — In his Controversy
VFith Lucas he was on the eve of discovering the different Dispersive Powers of Bodies
— Mr. Chester More Hall makes this Discovery, and constructs Achromatic Telescopes,
but does not publish his Discovery — Mr. DoUond re-discovers the Principle of the
Achromatic Telescope, and takes out a Patent — Principle of the Achromatic Tele-
scope explained — Dr. Blair's Aplanatic Telescope — Great Improvement on the Achro-
matic Telescope by the Flint-Glass of Guinant, P'raunhofer, and Bontemp? — Mistake
of Newton in forming his Spectrum from the Sun's Disc — Dark Lines in the Spectrum
— Newton's Analysis of the Spectrum incorrect — New Analysis of the Spectrum by
Absorption, &c., defended against the Objections of Ilelmholiz, Bernard, and others
—Change in the Refrangibility of Light maintained by Professor Stokes— Objections
to his Theory.

The two great doctrines of the different refrangibility of the
rays of light, and of the composition of white light, ])y mixing
all the rays of the spectrum, having been established by Newton
on an impregnable basis, we come now to describe some of the
other results which he obtained regarding the prismatic spec-
trum and its colours, to point out the errors which he com-
mitted, to show the influence which they had on the progi'ess
i)f optics, and to give an account of the remarkable discoveries
which have been made in this branch of science during tlie last
and the present century.

There are few facts in the history of optics more singular
thsft that Newton should have believed that all bodies when
shaped into prisms produced prismatic spectra of equal length,
or separated, or dispersed the red and violet rays to equal dis-
tfinces, when the mean refraction, or the refraction of the
middle ray of the spectrum, was the same. This opinion,
which he deduced from no direct experiments, and into which

1676. LIFE OF SIR ISAAC NEWTON. 97

no theoretical views could have led him, seems to have been
impressed on his mind with all the force of an axiom. In one
of his experiments he had occasion to counteract the refraction
of a prism of glass by a prism of water ; and had he completed
the experiment, and studied the result of it when the mean
refraction of the two prisms was the same, he could not have
failed to observe that the prism of water did not correct the
colour of the prism of glass, and would have thus been led to
one of the most important truths in optics, — that different
bodies have different dispersive powers, or produce prismatic
spectra of different lengths, when their mean refraction is the
same. It is curious to observe, as happened in this experiment,
what trifling circumstances often arrest the philosopher when
on the very verge of a discovery. Newton had mixed with the
water which he used in his prism a little sugar of lead^ in
order to increase the refractive power of the water ; but the
sugar of lead having a higher dispersive power than water,
made the dispersive power of the water prism equal to that of
the prism of glass ; so that if Newton had completed the ex-
periment, the use of the sugar of lead would have prevented
him from making an important discovery, which was almost in
his possession. Had he, on the contrary, increased the angle
of his water prism till it produced the same deviation of
the mean ray of the spectrum, he would have found that the
one prism did not correct the colour of the other, and that the
glass had a greater dispersive power than the water, and gave
a longer spectrum.

Nor is it less extraordinary that the same discovery escaped
from his grasp during his controversy with Lucas. When the
Dutch philosopher and his numerous friends who saw his ex-
periments, pronounced his spectrum to be only 3|^ times its
breadth, Newton found it to be at least five times its breadth ;
and it is strange that neither party ever thought that this might
arise from using different kinds of glass, and never made the
least inquiry regarding the material of which their prism was

VOL. L G

98 LIFE OF SIR ISAAC NEWTON. CHAP. V

made. It is highly probable that Lucas's prism had a very low
dispersive power, which would account for the great difference
between his spectra and those of Newton, but whether this was
the case or not, Newton, under the blind conviction that all
spectra must, cceteris paribus, be of equal length, pronounced
'" the improvement of telescopes by refractions to be desperate,"^
and thus checked for a long time the progress of this branch
of science.

About two years after the death of Sir Isaac, an individual
unknown to fame, broke the spell in which the subject of the
spectrum had so long been bound. In the year 1729, Mr.
Chester More Hall, of More Hall in Essex, while studying the
mechanism of the human eye, was led to suppose that tele-
scopes might be improved by forming their object-glass with
two lenses of different refractive powers. He published no
memoir on the subject, and has not even left behind him any
record of the steps by which he arrived at such a conclusion.
It is probable that he may have adopted David Gregory's idea
of combining lenses of different density, and as crown and flint-
glass differed most in this respect, that in combining them be
discovered the great difference in their dispersive powers, and
was thus led to the invention of the achromatic telescope. Mr.
Hall employed working opticians to grind his lenses, and
furnished them with the proper radii of their surfaces for cor-
recting the colour arising from the difference of refrangibility
in the rays, and the aberration occasioned by the spherical

1 Optics, Prop. vii. Book ii. p. 91. In his reply to Hooke, who justly "reprehended
him for laying aside the thoughts of improving optics by refractions," he seems to modify
his opinion by saying that ho tried what might be done " by two or more glasses or
crystals, with water or some other fluid between them." " But what the results by
tlieory or by trials hare been, he might possibly find a more proper occasion to declare."
This was written in 1672, and we can therefore say with certainty that 1 e fai'ei in this
attempt, as it was in 1684 that he pronounced the case to be desperate. It is a curiou»
circumstance that David Gregory, in his Lectures delivered in Edinburgh in 1684, sug-
gests that, in imitation of the human eye, the object-glasses of telescopes might be com-
posed of media of different density. In Brown's translation of Gregory, the sense of the
passai^e is not brought out. See Gregory's Catoptrics, Prop. xxiv. Schol. pp. 110, 111.

CHAP. V. LIFE OF SIR ISAAC NEWTON. 99

figure of the lenses. Mr. Bass, a well-known working optician,
was one of his assistants, and it was probably through him
that the knowledge of Mr. Hall's invention has been preserved.
About the year 1733 he had completed several achromatic
object-glasses, which bore an aperture of more than 21 inches,
though their focal length did not exceed twenty inches. One
of these telescopes, which in 1798 was in the possession of the
Rev. Mr. Smith of Charlotte Street, Rathbone Place, was ex-
amined by several gentlemen of scientific eminence, and found
to be a genuine achromatic telescope.

Many years after the death of Mr. More Hall, Mr. John
DoUond and others had turned their attention to the improve-
ment of telescopes. Euler, believing the eye to be achromatic,
had attempted, but in vain, to discover a combination of
media, by which the object-glasses of telescopes could give
colourless images. Klingenstierna had endeavoured to show
that refraction without colour might be produced according to
the laws of refraction laid down by Newton himself ; but none
of these philosophers made a single step towards the great dis-
covery which was made by Mr. Dollond, when the previous
labours of Hall were unpublished. In 1758, he communicated
to the Royal Society an account of his experiments on the
different refrangibility of light. In this valuable paper, he
proved that glass had a greater dispersive power than water,
and attempted to make achromatic object-glasses by enclosing
water between two lenses of glass. In this attempt he found
the spherical aberration difiicult to correct, and he was there-
fore led to try crown and flint glass, which he found to have
such different dispersive powers, that he was at once able to
make achromatic object-glasses. In order to secure his right
to this invention, Dollond took out a patent ; but in conse-
quence of its having been discovered that the same invention
had been made before, some of the London opticians tried the
question at law, and produced in court the telescope of Mr.
Hall. It was in vain to deny the prior claims of Mr. Hall ;

100

LIFE OF SIR ISAAC NEWTON.

CHAP. V.

but as it was certain that Dollond was unacquainted with his
labours, and as no achromatic telescope had ever been exposed
to sale, Lord Mansfield justly decided the case in favour of
DoUond.i

It is not easy to explain to the general reader the principle
of the Achromatic Telescope ; but we think it may be appre-
hended from an inspection of the annexed diagram. In crown
glass the index of refraction is 1-526 for red rays, and 1-547
for violet rays. If l L then be a convex lens of crown glass, it
will refract the violet rays more than the red, the former in the
direction l r, and the latter in the direction l v, so that r will
be the focus of red, and v that of the violet rays. If we now
place behind it a concave lens c c of the same kind of glass
and the same curvature, it will by its opposite and equal refrac-
tions unite again the rays L R, l v, in the direction l Z, so as
to form a white ray ; but in this case the compoimd lens acts
like a piece of plane glass, or rather like a watch glass which

I. c

Fig. 9.

has no focus. But if we make the concave lens c c of flint
glass with less curvature than l l, then since it has a greater
refractive and dispersive power than the lens l l of crown glass,
it will, notwithstanding its inferior curvature, unite the rays
L R, L V, and leave such a balance of refraction in favour of the
lens L L, that the rays will be united, and a colourless image

1 See Tilloch'fl Philotophic4a Magatine, Nov. 1789, vol. ii. p. 177.

CHAP. V. LIFE OF SIR ISAAC NEWTON. 101

formed at o, so that the double object-glass l l c c will be an
achromatic one.

If the prismatic spectrum formed by crown and flint glass
had been exactly the same, that is, if the coloured spaces in
each were of the same length, telescopes constructed upon the
preceding principle would have been perfect, in so far as colour
is concerned ; but this is not the case, and consequently in the
very best achromatic telescopes, there is left what has been
called a secondary spectrum, consisting of green and purple
colours, which appear on the border of the images of all lumin-
ous objects.

This secondary or residual spectrum, arising from what has
been called the irrationality of the coloured spaces in the two
equal spectra of crown and flint glass, may be corrected by an
ingenious contrivance discovered by Dr. Blair. He found that
muriatic acid produced a prismatic spectrum, in which the
coloured spaces were nearly the same as in crown glass, and
that he could increase its low refractive and dispersive power,
by mixing it with metallic solutions, so as to fit it for being
used like flint glass for correcting the colour of the crown glass
without balancing its refraction. This increase in its refractive
and dispersive powers, did not alter the proportion of the
coloured spaces in its spectrum, so that it was capable of giving
a perfectly colourless image, when placed as a concave lens
between two convex ones of crown glass. The metallic solution
used by Dr. Blair was muriate of antimony, and in the lens
which he constructed, the rays of diff'erent colours were bent
from their rectilineal course with the same equality and regu-
larity as in reflexion. To this telescope he gave the name of
Aplanatic. According to the testimony of Professor Robison,
those he examined surpassed greatly the best ordinary achro-
matic telescopes ; but they have been found difficult to con-
struct, and in so far as we know, there is not in existence a
single aplanatic telescope.

The Achromatic Telescope, on the contrary, even with the

102 LIFE OF SIR ISAAC NEWTON. CHAP. V.

imperfection of its secondary spectrum, has undergone great
improvements, and promises to rival Reflectors in excellence and
power. By the labours of Guinand, Fraunhofer, and M. Bon-
temps, discs of flint glass of 12, 15, 24, and even 29 inches
in diameter, have been made, and we hope soon to see the
largest of them converted into a magnificent telescope. The
disc of 24 inches has been converted into a telescope by the
Rev. Mr. Craig of Leamington.!

But while Newton overlooked the remarkable property of the
prismatic spectrum, on which the improvement of Refracting
Telescopes depends, he committed other considerable mistakes
in his examination of the spectrum. It does not seem to have
occurred to him that the Solar Spectrum was not the spectrum
from which the properties of the sun's rays ought to be deduced,
and that the relations of the coloured spaces must depend on
the angular magnitude of the luminous body, or of the aperture
from which the spectrum is obtained. Misled by an apparent
analogy between the length of the coloured spaces and the
divisions of a musical chord,^ which he ascertained " by an
assistant whose eyes were more critical than his own," he
adopted that division as representing the proportion of the
coloured spaces in every dispersed beam of light. Had he
studied the prismatic spectrum in Mercury and Jupiter by the
same instruments, he would have obtained quite diff'erent
results. In Mercury, where the sun's apparent magnitude is
very large, he would have seen a spectrum without any green,
and having red, orange, and yellow at one end, white in the
middle, and blue and violet at the other end. In Jupiter, on
the contrary, he would have obtained a ^spectrum in which the
coloured spaces were much more condensed, and the pure
colours more separated. The Solar spectrum described by
Newton, has an intermediate character between these two
extremes, and had he examined it under the same circumstances

1 See my Treatise on Optics, new edit. p. 506.

2 Optics, Part ii. Prop. iii. p. 110.

CHAP. V. LIFE OF SIE ISAAC NEWTON. 103

in winter and in summer, he would have found the analysis of
the beams more perfect in summer, on account of the sun's
diameter being less. We are entitled, therefore, to assert, that
neither the number nor the extent, nor the limits of the
coloured spaces, as given by Newton, are those which belong to
the true prismatic spectrum.

Had Newton received upon his prism a beam of light
transmitted through a very narrow aperture, he would have
anticipated Wollaston and Fraunhofer in their fine discovery of
the lines in the prismatic spectrum. In 1802, Dr. Wollaston,
by transmitting the light of the sky through an aperture the
twentieth of an inch wide, discovered six fixed dark lines in the
spectrum, one in the red, one in the orange, one in the blue,
and one in the violet spaces. Without knowing of Wollaston's
observations, the late celebrated M. Fraunhofer of Munich, dis-
covered in sun light, nearly 600 lines, the largest of which
subtended an angle of from 5" to 10". We have found this
angle to increase enormously by atmospherical absorption, as
the sun passes from the meridian to the horizon, and in a
long series of observations we have observed upwards of two
thousand lines in the prismatic spectrum formed from the
sun's rays.

From his analysis of the Solar spectrum, by examining with
the prism its separate colours, Newton concluded, that to the
same degree of refrangihility ever belonged the same colour, and
to the same colour ever belonged the same ref Tangibility, and
hence he inferred that red, orange, yellow, green, blue, indigo,
and violet, were primary and simple colours. This proposition
is true in so far as the analysis of the spectrum by the prism
is concerned ; but we have found another species of analysis,
by which the colours of the spectrum may be decomposed.
Though we cannot separate the green rays in the spectrum into
yellow and blue by the refraction of prisms, yet if we possessed
any solid or fluid which had a specific attraction for blue rays,
that is, which absorbed them during the passage of the green

104 LIFE OF SIR ISAAC NEWTON. CHAP. V.

light through the medium, and allowed the yellow rays to pass,
we should then analyse the green into its component elements
as efiectually as if we separated them by the prism. We have
in this way subjected the colours in the spectrum to the
analysis of a great variety of solid and fluid bodies of different
colours, and we have found that in every part of the spectrum,
the colours are more or less changed or decomposed by
absorption.

The simplest way of observing these changes is to receive
the spectrum in the eye by looking through the prism at a
narrow line of light from the sky. If we now interpose be-
tween the eye and the prism a plate of purplish blue glass,
about the twentieth of an inch thick, we shall see the prismatic
spectrum with its bright colours completely metamorphosed.
The red part of the spectrum is divided into two red spaces,
separated by a dark inteiTal. 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 follow the blue and the violet,
the last of which has suffered little or no diminution. Now, in
this experiment, the Uue glass has 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, places it beyond a
doubt that the orange and green colours in this spectrum are
component colours, the former consisting of red and yellow, and
the latter of yellow and blue rays of the very same refrangi-
bllity. If we compare the two red spaces seen through the
blue glass, with the red spaces seen without the blue glass, it
will appear that the 7'ed 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 light ; and hence
we conclude that the red of this spectrum contains a slight

GUAP. V.

LIFE OF SIR ISAAC NEWTON.

105

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.

By varying the absorptive media, I have found that red
light exists in the yellow space, and we have ocular evidence,
that in the violet space red light is combined with the hhie
rays. From these and other facts, which it would be out of
place here to enumerate, I have been led to the conclusion that
the 'prismatic spectrum consists of three different spectra, viz., red,
yellow, and blue, all having the same length, all superposed,
and each having its maximum intensity at the point where it
predominates in the combined spectrum. Hence it follows : —

1. That 7'ed, yellow, and blue, rays of the same refrangi-
bility exist at every point of the spectrum of intensities, repre-
sented by the ordinates of the curve of intensity in each separate
spectrum.

2. That the colour of the spectrum at any one point will be
that of the predominant ray modified by the smaller quantities
of the other two rays ; and,

3. That if we could absorb the two predominant rays at any
one point of the spectrum, in such quantities as when mixed
with the remaining or unabsorbed ray, would make white light,

|we should be able to insulate white light indecomposable by the
'ism.

This view of the structure of the spectrum will be under-
?Btood from the annexed diagrams, where Figs. 10, 11, and 12,
represent the three separate spectra, which are shown in their
combined state in Fig. 13. In all these figures, the point m
is the red or least refrangible extremity of the spectrum, and n
^the violet or most refrangible extremity. The maximum inten-
sity of each spectrum is opposite e, y, and B, the intensity
linishing to nothing at the extremities m and n. When
lese three spectra are superposed, they will exhibit the colours
lown in Fig. 1 3, in which we have inserted the three curves
rhich represent the intensities in each spectrum.

106

LIFE OF SIR ISAAC NEWTON.

CHAP. V.

iillK

i l! i l lli !;i i Hli|i!'l"ii''i"':i

Fie 10.

Fig. 11.

Fig. 12.

^^Bllilii

Fig. 13.

CHAP. V. LIFE OF SIR ISAAC NEWTON. 1 07

In order to explain how the seven colours, observed by-
Newton, are produced by the three primitive colours, we shall
take the case of the orange, as shown in Fig. 13, where the
three ordinates ax, hx, ex, will indicate the relative intensities
of the three colours, combined at any point x of the spectrum.
Thus let

The ordinate for red light be ax = iQ
„ yellow tx = 16

„ blue ex = 2

Then ax + bx + ex = 48 rays.

Hence the point x will be illuminated with forty-eight rays,
namely, thirty of red, sixteen of yellow, and two of blue light.
Now, as there must be certain quantities of red and yellow
light, which, when combined with two blue rays, will form
white, let us suppose that white light, whose intensity is ten,
will be formed by three red, five yellow, and two blue rays,
then it follows that the point x will be illuminated with

Red rays, 30 — 3 or 27 rays.

Yellow rays, . . . . 16 — 5 or 11 ,,
White light + 3 red + 5 yellow + 2 blue, or 10 , ,

Orange = red + yellow + white, . =48 rays.

That is, the point x will have the colour of orange rendered
brighter by a mixture of white light. The blue rays conse-
quently which exist at x will not communicate any blue tinge
to the prevailing orange.

In submitting to the scientific world this new analysis of
light, by absorption, we were fully aware of the difiiculties
which we had to encounter, and we anticipated the opposition
which would be made to it. " Even in physical science," we
said,^ " it is an arduous task to unsettle long-established and
deeply-rooted opinions ; and the task becomes Herculean when
these opinions are intrenched in national feeling, and associated
with immortal names. There are cases, indeed, where the

1 Edinhxirgh Transaetions, 1831, vol. xii. p. 124.

108 LIFE OF SIR ISAAC NEWTON. CHAP. V.

simple exhibition of new truths is sufficient to dispel errors
the most deeply cherished, and the most venerable from their
antiquity ; but it is otherwise with doctrines which depend on
a chain of reasoning where every step in the inductive process
is not rigorously demonstrative ; and of this we require no
other proof than is to be found in the history of Newton's
optical discoveries, and particularly in the opposition they
experienced from such distinguished men as Dr. Hooke and
Mr. Huygens."

The preceding analysis of the spectrum embraces three pro-
positions, which, to a certain extent, are independent of each
other.

.1. That the colours of the coloured spaces may be changed
by absorbing media, acting by reflexions and transmissions.

2. That in pure spectra, white light can be insulated.

3. That the Newtonian spectrum of seven colours consists of
three equal primary spectra, red, yellow, and blue superposed,
having their maximum intensity of illumination at different
points, and shading to nothing at their extremities.

The/7*5^ of these propositions may be true, even though we
could not insulate white light at any point of the spectrum ;
and both the first and second may be true, without our being
able to demonstrate that the three spectra have the same length,
and diminish in intensity from their maxima to their extremities.

The general proposition that the colours of the spectrum are
changed by absorption, has been questioned by three classes of
critics, — by Mr. Airy,^ M. Melloni,^ and Mr. Draper,^ who
have never repeated our experiments, but made some very
imperfect ones of their own ; — by Dr. Whewell,* and the Abb^
Moigno,^ who have made no experiments at all ; — and by M.

1 PMl. Mag. vol. xxx. p. 73.

2 Bibl. Univers. AoQt 1847.

8 Silliraan's Journal, vol. iv. p. 388. 1847.

* Hist, of Inductive Sciences, vol. ii. p. 361 ; and Edinburgh Review, vol Ixvi. p. 136 ;
and vol. Ixxiv. p. 288.
6 Ripertoire d'Optiquc, torn. ii. p. 469.

CHAP. V. LIFE OF SIR ISAAC NEWTOK 109

Helmholtz^ in Prussia, and M. Bernard ^ in France. "We have
replied to the three first of these writers, and shall now make
a few observations on the results obtained by MM. Helmholtz
and Bernard.

M. Helmholtz has candidly stated, in contradiction of Mr.
Airy, that " the changes of colour" which we have described,
as produced by absorption, " are for the most part sufficiently
striking to be observed without difficulty :" and he adds, that
" a careful repetition of at least the most important of my
experiments, carried out in exact accordance with my method,
and with every precaution hitherto deemed necessary, has
indeed taught me that the facts which he affirms to have ob-
served, are described with perfect accuracy."

The change of colour^ thus admitted as a physical fact, M.
Helmholtz ascribes to two causes : —

1. To the possible admixture of rays scattered from the
prism, and the other transparent bodies used in the experiment ;
and

2. To the mixture of complementary colours produced by
the action of the other colours of the spectrum on the retina.

The first of these, as M. Helmholtz almost admits, is wholly
uninfluential, and the second, if it does disturb the colorific
impressions on retinae tender and sensitive, had no such effect
on ours.

If the subjective perception of colour, when we view the
spectrum, or make experiments in which more than one colour
reaches the eye, is capable of masking the colours under exami-
nation, then all that has been written on colours, thus seen,
must be erroneous, and all the gay tints of art or of nature are
but false hues under the metamorphosis of a subjective per-
ception. We must not now pronounce a rose to be red, and
its leaves green, till we have stared at them through a chink,
or torn them from their foot-stalk ! The phenomena of ab-

1 PoggendorflTs Annalen 1852, No. 8.

2 Ann. de Chim. et de Phys. torn. xxxt. p. 385, &c.

110 LIFE OF SIR ISAAC NEWTON. CHAP. V.

sorption which we have described we have seen, just as Newton
saw his seven colours in the spectrum, and Hooke his composite
tints in the soap-bubble ; and now that our eyes have nearly
finished their work, we are not dfsposed to mistrust, without
reason, such good and faithful servants.^

The observations of M. Bernard, who has repeated only a few
of our experiments, difter very little from those of M. Helmholtz.
He maintains that the conversion of the blue space into viQlet
arises from the light being diminished. If the colours of the
spectrum thus change, as he maintains, by their becoming
fainter, we would desire to ask at what degree of illumination
are we to see the spectrum in its true colours ? Colour cannot
depend upon refrangibility, if the blue space is converted into
violet either by diminution of light or absorption ; and there-
fore the doctrine of M. Bernard is as fatal to Newton's as to
ours. If M. Bernard's experiment be correct, it only proves
that the blue rays, when enfeebled, lose their power over the
retina sooner than the red.

The Newtonian doctrine, " that the degree of refrangibiUty
proper to any particular sort of rays is not mutable by refrac-
tion, nor reflection, nor by any other cause, "^ has been recently
questioned by Professor Stokes, one of the distinguished suc-
cessors of Newton in the Lucasian chair. Mr. Stokes^ found
that the chemical rays in the violet space, between the lines g
and H of the spectrum, produce, in a solution of sulphate of
quinine, light of a shy-blue colour, which he assumes to have
the refrangibility of that portion of the spectrum. By refracting

1 The changes of colour in the spectrum at diflFerent seasons of the year, and the dif-
ferent hours of the day, and when formed from different portions of the illuminated sky,
as well as from the direct light of the sun, are very remarkable. We have mentioned
one or two of them in the Edinburgh Review, vol. Ixxiv. p. 284. Jan. 1842. One of
these observations is as follows : — " October 23, 1832. 11th, The yellow comes distinctly
up to V, and a little beyond it ; i.e., the blue has been all absorbed in the green space of
Fraunhofer's spectrum from e to p." In another observation on the 5th February 1833,
the green space was wholly yellow.

2 Letter to Oldenburg, Feb. 6, 1672, in Phil. Trans. No. 80, p. 3081, § 3.

3 Phil. Trans. 1852.

CHAP. V. LIFE OF SIR ISAAC NEWTON. Ill

this light through a prism, he converts the sky-hlue rays into a
spectrum of all colours, and all refrangibilities. Hence he con-
cludes, that the sky-hlue light having the fixed refrangibility
due to its locality between g and h, is changed by refraction
into all the other colours, with their respective refrangibilities.
If this conclusion be admitted, our doctrine of the severance of
colour and refrangibility is placed beyond a doubt. We have
in the first experiment sky-hlue light with the refrangibility of
violet light between g and H ; and, in the second experiment,
we have the same hlue light changed by refraction into all the
colours of the spectrum.

We cannot, however, avail ourselves of this last fact, for,
after a careful consideration of Mr. Stoke's important re'sults,^
we cannot but regard the sky-hlue light as a phosphorescence,
produced in the quinine solution by the chemical rays, which,
like all other phosphorescences, is decomposable by the prism.

1 See my Treatise on Optics, new edition, pp. 182, 183.

112 LIFE OF SIR ISAAC NEWTON. CHAP. V:

CHAPTER VI.

Newton on the cause of the Moon's Libration— Is occupied with the subject of planting
Cider Trees — Sends to Oldenburg his Discourse on Light and Colours, containing his
Hypothesis concerning Light — Views of Descartes and Hooke, who adopt the Hypo-
thesis of an Ether, the Vibrations of which produce Light — Rejected by Newton, who
proposes a Modification of it, but solely as an Illustration of his Views, and not as a
Truth— Light is neither Ether, nor its Vibrating Motion— Corpuscles from the Sun
act upon the Ether — Hooke claims Newton's Hypothesis as contained in his Micro-
grajihia — Discussions on the Subject — Hooke's Letter to Newton proposing a Private
Discussion as more suitable — Newton's Reply to this Letter, acknowledging the Value
of Hooke's Discoveries — Oldenburg the Cause of the DiflFerences between Hooke and
Newton — Newton's Letter to Boyle on the Subject of Ether — His Corjecture on the
Cause of Gravity — Newton supposed to have abandoned the Emission Theory — Dr.
Young's Supposition incorrect— Newton's mature Judgment in favour of the Emission
Theory.

In the years 1675 and 1676, when Newton was engaged
in his fruitless controversy with the Dutch professors, his mind
was directed to a great variety of subjects. Collins^ informs
his correspondent, James Gregory, that he had not written to
Newton or even seen him for these eleven or twelve months ;
that he did not wish to trouble him, as he was " intent upon
chemical studies and practices," and that Newton and Barrow
had <' begun to think mathematical speculations at least dry,
if not somewhat barren." His attention was at this time oc-
cupied with the subject of the moon's libration. In a letter to
Oldenburg in 1673, in reference to Huygen's work on Central
Forces, he mentions that " he had sometimes thought that the
moon's libration might depend upon her conatus from the sun
and earth compared together, till he apprehended a better
cause." This better cause he communicated in 1675 to Nicholas

1 October 19, 1675. Maccksjlcld Corretpondence, vol. ii. p. 280.

1675-76. LIFE OF SIR ISAAC NEWTON. 113

Mercator, who published it in the following year in his Astro-
nomical Institutions.^ Galileo had discovered and explained
the diurnal libration, arising from the spectator not viewing the
moon from the centre of the earth, but it was reserved for
Newton to explain the libration in longitude, v/hich Hevelius,
its discoverer, had ascribed to the displacement of the centre of
the moon's orbit from the centre of motion. He showed that
it was occasioned by the inequalities of the moon's motion in
an elliptic orbit round the earth, combined with the uniformity
of her motion round her axis. In the same letter to Mercator
he showed that the libration in latitude arose from her axis of
rotation being inclined 88° 17' to the ecliptic.

About this time we find Newton occupied with a subject
very different from his usual pursuits — taking an interest, like
a country gentleman, in the planting of fruit trees for the
manufacture of cider. It does not appear how his attention
was directed to this subject. A reference is made to it in a
letter to Oldenburg, in November 1676; but we have been
fortunate enough to find among his papers a previous letter to
the same gentleman, in September, which we need make no
apology for inserting here.

" Septemher 2, 1676.

" Sir, — I have now made what inquiry I can into the state
we are in for planting, and find there are some gentlemen
that of late have begun to plant, and seem to incline more and
more to it, but I cannot hear of any professed nurseryman we
have. Our gardeners find more profit in cherry trees, and so
stock their ground almost wholly with them. The chief of
them plant some fruit trees, but it is to find the gentry with
plants : to whom I am apt to think your proposition will
prove a very reasonable one, considering the new humour of
planting that begins to grow among them. But in order to

1 "Harum . . . librationum causas Hypothesi elegantissima explicavit nobis vir cl.
Isaac Newton, cujus humanitati hoc et aliis norainibus plurimum debere me lubens pro-
Iji fiteor." — Mercator'3 Instilutiones Astronomicce, p. 286.

VOL. L H

114 LIFE OF SIR ISAAC NEWTON. CHAP. VI.

promote the design, I am desired to inquire what sort of trees
your friend can furnish us with, at what rates, which way they
can most conveniently be conveyed to so gi-eat a distance, and
what may be the charges of carriage. Also, whether they are
to be sent in cions or grafts ; the first being more convenient
for carriage, and so rather to be wished, unless those trees be
found best which are grafted on their native soil. I perceive
the gardener I mentioned (Mr. Blackley by name) would gladly
embrace the proposal, and provide himself with more ground
than he has, for a nurseiy, to stock his neighbours, if he found
he can have good sorts of trees, and the carriage make them
not too dear.

" But, upon discoursing with people, I find we lye under one
great difliculty ; which is an opinion generally taken up here,
that Red Streaks (the famous fruit for cyder in other parts)
will not succeed in this country. The tree thrives well here,
and bears as much fruit, and as good to look as in other coun-
tries ; but the cyder made of it they find harsh and churlish,
and so this fruit begins here to be generally neglected, and
other fruit, and which they find does pretty well, but the cyder
will not keep above a year, whereas that made of Red Streaks
in other parts will keep three years or more. The ill success
of Red Streaks here, I perceive, is generally imputed to the
soil ; but since the tree thrives, and bears as well here as in
other parts, I am apt to think it is in the manner of making the
cyder. For upon inquiry of the gardiners, I cannot find that
they mixed any other fruit with the Red Streaks, which I
have been told they do in the cyder countries, and am apt to
believe it necessary ; the juice of the finer fruit, on the one
hand, sweetening and ripening the harsh juice of the Red
Streaks, as that juice, on the other hand, by its slow ripening,
makes the cyder keep long. Sir, if this prejudice we have
against Red Streaks could be removed, it would much promote
the design of planting, and double the benefit of it to us by
bettering the cyder ; and therefore I make bold to desire you

1675-76. LIFE OF SIR ISAAC NEWTON. 115

to inform me, if you know of any practical description of
making cyder, printed in any author ; and if not, to desire you,
if it lye in your way at any time, to inquire, about the manner
of making and ordering of it. For which end give me leave
to make these queries : — What sort of fruit are best to be
used, and in what proportion they are to be mixed, and what
degree of ripeness they ought to have 1 Whether it be material
to press them as soon as gathered, or to pare them "? Whether
there be any circumstances to be observed in pressing them 1
or what is the best way to do it 1 If you can direct us to, or
procure for us a short narrative of the way of making and
ordering cyder in the cyder countries, which takes in a resolu-
tion of these, or the most material of these queries, you will
oblige your humble servant,

"Is. JSTewton."

" S^- If my last letter be not yet sent to Mr. Lucas, I de-
sire you would, for preventing any suspicion of insincerity, in-
sert this parenthesis (as is well known here) between the words
[and written a tractate on that subject], and [wherein I had set
down] in the latter part of my letter."^

In November 1676, Newton addresses another letter to
Oldenburg in the following terms : —

" I am desired to write to you about procuring a recom-
mendation of us to Mr. Austin, the Oxonian planter. We hope
your correspondent will be pleased to do us that favour as to
recommend us to him, that we may be furnished with the best
sort of cider fruit-trees. We desire only about 30 or 40 graffs
for the first essay, and if these prove for our purposes, they will
be desired in greater numbers. We desire graffs rather than
sprags, that we may the sooner see what they will prove. They

1 Newton's letter had been forwarded to Mr. Lucas, and therefore the sentence doaa
not appear in it.— See Phil. Trans. No. 128, p. 703.

116 LIFE OF SIR ISAAC NEWTON. CHAP. VI.

are not for Mr. Blackley, but some other persons about Cam-
bridge." 1

The friend mentioned in one of these letters, and the cor-
respondent in the other, was the Rev. Dr. John Beal, Rector
of Yeovil, in Somersetshire, who, in imitation of his father and
great-grandfather, had distinguished himself by his zeal in the
plantation of orchards for the making of cider. -^

But though thus occasionally occupied with other subjects,
lie was at this time diligent in the prosecution of his optical
researches. On the 13th November 1675, he intimated to
Oldenburg, " that he 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. But, however, I have one discourse by me on
that subject, written when I sent my first letter to you about
colours, and of which I then gave you notice. This you may
command when you think it may be convenient, if the custom
of reading weekly discourses still continues." Mr. Oldenburg
having been desired by the Society to thank him for this offer,
and to desire him to send this discourse as soon as he pleased,
Newton again writes to him on the 30th November, "that he
intended to have sent the papers this week, but that upon re-
viewing them it came into his mind to write another little
scribble to accompany them." This little scribble was his
" Hypothesis," to which we shall presently refer.

The discourse above referred to was produced in manuscript
on the 9th December 1675, with the title of— "A Theory of
Light and Colours, containing partly an Hypothesis to explain
the properties of light discoursed of by him in his former papers,
partly the principal phenomena of the various colours exhibited
by thin plates or bubbles, esteemed to be of a more difficult
consideration, yet to depend also on the said properties of

1 Edleston's Correspondence, App. No. xvi. p. 260.

2 He wrote a work entitled, Herefordshire Orchards a Pattern for England, 1656.
See Birch's Hist, of the Royal Societv, vol. iv. p. 235.

1675-76. LIFE OF SIR ISAAC NEWTON. 117

light." This paper was introduced by the following letter to
Oldenburg, which possesses considerable interest.

" Sir, — I have sent you the papers I mentioned, by John
Stiles. Upon reviewing them I find some things so obscure as
might have deserved a further explication by schemes ; and
some other things I guess will not be new to you, though
almost all was new to me when I wrote them. But as they
are, I hope you will accept of them, though not worth the
ample thanks you sent. I remember in some discourse with
Mr. Hooke, I happened to say that I thought light was re-
flected, not by the parts of glass, water, air, or other sensible
bodies, but by the same confine or superficies of the ethereal
medium which refracts it, the rays finding some difl&culty to
get through it in passing out of the .denser into the rarer
medium, and a greater difficulty in passing out of the rarer
into the denser ; and so being either refracted or reflected
by that superficies, as the circumstances they happened to be in
at their incidence make them able or unable to get through it.
And for confirmation of this, I said further, that I thought the
reflexion of light, at its tending out of glass into air, would not
be diminished or weakened by di'awing away the air in an air-
pump, as it ought to be if they were the parts of air that re-
flected ; and added, that I had not tried this experiment, but
thought he was not unacquainted with notions of this kind.
To which he replied, that the notion was new, and he would
the first opportunity try the experiment I propounded. But
upon reviewing the papers I sent you, I found it there set down
for trial ; which makes me recollect that about the time I was
writing these papers, I had occasionally observed in an air-
pump here at Christ's College, that I could not perceive the re-
flexion of the inside of the glass diminished in drawing out the air.
This I thought fit to mention, lest my former forgetfulness, through
my having long laid aside my thoughts on these things, should
make me seem to have set down for certain what I never tried.

118 LIFE OF SIR ISAAC NEWTON. CHAP. VI.

" Sir, — I had formerly purposed never to write any hypo-
thesis of light and colours, fearing it might be a means to
engage me in vain disputes ; but I hope a declared resolution
to answer nothing that looks like a controversy, unless possibly
at my own time upon some by-occasion, may defend me from
that fear. And therefore, considering that such an hypothesis
would much illustrate the papers I promised to send you, and
having a little time this last week to spare, I have not scrupled
to describe one, so far as I could on a sudden recollect my
thoughts about it ; not concerning myself, whether it should
be thought probable or improbable, so it do but render the
paper I send you, and others sent formerly, more intelligible.
You may see by the scratching and interlining it was done in
haste ; and I have not had time to get it transcribed, which
makes me say I reserve a liberty of adding to it, and desire
that you would return these and the other papers when you
have done with them. I doubt there is too much to be read
at one time, but you will soon see how to order that. At the
end of the hypothesis you will see a paragraph, to be inserted
as is there directed. I should have added another or two, but
I had not time, and such as it is I hope you will accept it. —
Sir, I am your obedient servant, " Is. Newton.*'

The Hypothesis,! to which this letter is introductory, pos-
sesses many points of historical interest. Descartes was the
first philosopher who maintained the existence of an ether, a
medium more subtle than air, filling the interetices of air, and
occupying the pores of glass and all transparent bodies. He
considered the ether to be composed of a continued series of
molecular globules, along which a motion was propagated con-
stituting light and colour. ^ Dr. Hooke, who adopted the

^ See Appendix, No. II.

- Dr. Whewell states that Descartes regarded light as " consisting of small particles
emitted by the luminous body," but Mr. Vernon ITarcourt (Letter to Lord Brougham,
p. 32) has shown the incorrectness of this opinion. See (Euvres de Descartes, torn. vii.
pp. 393, 240.

l(;75-76. LIFE OF SIR ISAAC NEWTOX. 119

general view of Descartes, maintained that " the parts of bodies
when briskly agitated excite vibrations in the ether which are
propagated every way from these bodies in straight lines, and
cause a sensation of light by beating and dashing against the
bottom of the eye ; something after the manner that vibrations
in the air cause a sensation of sound by beating against the
organs of hearing."^ In his reply to Hooke, on the 11th of
July 1673, Newton distinctly states that this, which he calls
the fundamental supposition in Hooke's hypothesis, " seems
itself impossible ; namely, that the waves or vibrations of any
fluid can, like the rays of light, be propagated in straight lines,
without a continual and very extravagant spreading and bend-
ing every way into the quiescent medium where they are
terminated by it. / am mistaken if there he not both experi-
ment and demonstration to the contrary.''

In thus summarily rejecting Hooke's hypothesis, Newton
suggests a modification of it, or a form in which it will be better
fitted to account for the phenomena, or to use his own ex-
pression, — " The most free and natural application of this
hypothesis I take to be this — that the agitated parts of bodies,
according to their several figures, sizes, and motions, do excite
vibrations in the ether of various depths or sizes, which being
promiscuously propagated through that medium to our eyes,
eff'ect in us a sensation of light of a white colour ; but if by
any means those of unequal sizes be separated from one
another, the largest beget a sensation of a red colour, the least
;or shortest of a deep violet, and the intermediate ones of inter-
mediate colours."^ Now this modification of Hooke's hypo-
thesis has been very erroneously regarded as an expression of
Sir Isaac's own views, whereas he merely gives it as a better
form of a hypothesis, the fundamental position of which he
pronounces impossible, and contrary both to experiment and
demonstration. In judging of Sir Isaac's Hypothesis of 1675,

1 Newtoni Opera, torn. iv. pp. 325, 326.

2 Phil. Trans. 1672, No. 88, p 6088.

120 LIFE OF SIR ISAAC NEWTON. CHAP. YI.

it is necessary to keep this in view, as it appears to be quite
clear that this hypothesis is not what he believes, but what he
found it necessary to draw up for the information of many of
his friends. " Having observed," he says, " the heads of some
great virtuosos to run much upon hypotheses, as if my dis-
courses wanted a hypothesis to explain them by, and found
that some, when I could not make them take my meaning,
when I spoke of the nature of light and colours abstractedly,
have readily apprehended it when I illustrated my discourse
with an hypothesis ; for this reason I have here thought fit to
send you a description of the circumstances of this hypothesis,
as much tending to the illustration of the papers I herewith
serfd you."

In order to prevent any misapprehension of his meaning, he
goes on to say, " that he shall not assume either this or any
other hypothesis ;" yet while he is describiug this hypothesis
" he shall sometimes, to avoid circujnlocution, and to represent
it more conveniently, speak of it as if he assumed it, and pro-
pounded it to he believed.'''

With this caution, he supposes an ethereal medium rarer than
air, subtler, and more elastic, not one uniform matter, but
" compounded of various ethereal spirits or vapours, with the
l^hlegmatic body of ether. The whole frame of nature may be
nothing but various contextures condensed by precipitation, and
after condensation, wrought into various forms, at first by the
immediate hand of the Creator, and ever since by the power of
nature ; which, by virtue of the command, increase and multiply,
became a complete imitator of the copies set her by the proto-
plast." " Thus," he adds, " perhaps may all things be origi-
nated from ether." Newton then proceeds to describe an
electrical experiment, which afterwards excited much interest
in the Society. He laid upon a table a round piece of glass
about two inches broad, set in a brass ring, so as to keep the
glass about the sixth of an inch from the table, the air being
enclosed on all sides by the ring. Havmg placed some small

1G75-76. LIFE OF SIE ISAAC NEWTON. 121

pieces of paper within the ring, and rubbed the glass briskly
with some rough substance, the pieces of thin paper began to
be attracted and fly about even after the friction had ceased.
From this result he conceived that some subtle matter lying
condensed in the glass was rarefied by friction as Avater is
rarefied into vapour by heat, and by " moving and circulating
variously, actuates the pieces of paper till it returns into the
glass and be re-condensed there." He next supposes that this
ether may be imbibed by the earth, and also copiously by the
sun, in order to preserve his shining, and keep the planets from
receding farther from him ; that is, to increase his " gravitating
attraction, which may be caused by the continual condensation
of some very subtle gummy or unctuous substance difiused
through the ether." And as if he were amusing himself with
the extravagance of his speculations, he adds, " And they that
will may a^so suppose that this spirit aff'ords, or carries with
it thither, the solary fuel, and material principle of light, and
that the vast ethereal spaces between us and the stars are for a
sufficient repository for this food of the sun and planets !" If
we laugh at Kepler's firm belief that the earth and other planets
are enormous living animals taking their daily and nightly
alternations of sleeping and waking, we may be allowed to
smile when Newton condescends to feed them with the nectar
and ambrosia of the ethereal domains. In the same extrava-
gance of speculation he supposes that the soul may have an
immediate power over the whole ether in any part of the body,
producing, by processes which he invents, the swelling and
shrinking of the muscles, and the animal motions which result
from it.

In passing from " the effects and uses of ether " to the
" consideration of light," he supposes that light " is neither
ether, nor its vibrating motion, but something of a different
kind propagated from lucid bodies," such as "multitudes of
small and swift corpuscles of various sizes springing from
shining bodies, at great distances, one after another, but yet

1:22 LIFE OF Sm ISAAC NEWTON. CHAP. VI.

without any sensible interval of time." That it is different
from the vibrations of the ether, lie infers from the existence
of shadows^ and the colours of thin plates. His next supposi-
tion is, " that light and ether mutually act upon one another,
ether in refracting light, and light in warming ether ; " and,
after some farther observations on this mutual action, he goes
on to explain the manner in which refraction and reflexion are
produced upon this hypothesis, and the cause of transparency,
opacity, and colour. His discourse concludes with an applica-
tion of the hypothesis to the colours of thin plates, to the in-
flexion of light, and to the colours of natural bodies, — subjects
to which we shall presently direct the reader's attention.

After the reading of the first part of this discourse on the
9th December, Mr. Hooke said, " that the main of it was con-
tained in his Micrographia, which Mr. Newton had only carried
farther in some particulars." When this remark was com-
municated to Newton, he seems to have been greatly oftended,
and, on the 21st December, he wrote a letter to Oldenburg,
pointing out the difference between his hypothesis and that of
Dr. Hooke. Although "he is not much concerned at the
liberty of Mr. Hooke's insinuation," yet he wishes to " avoid the
savour of having done anything unjustifiable or unhandsome "
to him. He therefore separates the part of the hypothesis that
belongs to Descartes and others, and leaves to Hooke the merit
of having changed Descartes' progressive motion of the ether
into a vibrating one, — "the rotation of the globuli to the
obliquation of pulses, and the accelerating their rotation on the
one hand, and retarding it on the other, by the quiescent
medium to produce colours, to the like action of the medium
on the two ends of his pulse for the same end." He gives
Hooke the credit also of explaining the phenomena of thin
plates, and also the colours of natural bodies, fluid and solid. ^
In the other two paragraphs of the letter, he details more

1 Newtoni Optra, torn. iv. pp. 378-381 ; or Birch, vol. iii. p. 278.

1675-76. LIFE OF SIE ISAAC NEWTON. 123

specifically the difference between his explanations and those of
his rival. 1

These controversial discussions seem to have annoyed Hooke
as much as they did Newton, and, instead of publicly replying
to the two last communications of Newton, he addressed a
letter to him, which, with Newton s answer, we had the good
fortune to discover among the family papers. These letters
are highly interesting ; and we are persuaded that those who
have had occasion to animadvert on the conduct of Hooke, will
peruse this letter with much satisfaction.

Robert Hooke — " These to my much esteemed friend, Mr.
Isaack Newton, at his chambers in Trinity College in
Cambridge.

" S^, — The hearing a letter of yours read last week in the
meeting of the Royal Society, made me suspect that you might
have been some way or other misinformed concerning me ; and
this suspicion was the more prevalent with me, when I called
to mind the experience I have formerly had of the like sinister
practices. I have therefore taken the freedom, which I hope
I may be allowed in philosophical matters to acquaint you of
myself. First, that I doe noe ways approve of contention, or
feuding or provmg in print, and shall be very unwillingly
drawn to such kind of warre. Next, that I have a mind very
desirous of, and very ready to embrace any truth that shall be
discovered, though it may much thwart or contradict any
opinions or notions I have formerly embraced as such. Thirdly,
that I do justly value your excellent disquisitions, and am ex-
tremely well pleased to see those notions promoted and im-
proved which I long since began, but had not time to compleat.

^ In a paper entitled "Objervations," -which accompanied this letter, but which was
not printed, Newton says that Hooke, in his Micrograjihia, had " delivered many -very
excellent things concerning the colours of thin plates, and other natural bodies, which he
had not scrupled to make use of as far as they were for his purpose."

124 LIFE OF SIR ISAAC NEWTON. CHAP. VI.

That I judge you have gone farther in that affair much than I
did, and that as I judge you cannot meet with any subject more
worthy your contemplation, so I believe the subject cannot meet
with a fitter and more able person to inquire into it than your-
self, who are every way accomplished to compleat, rectify, and
reform what were the sentiments of my younger studies, which
I designed to have done somewhat at myself, if my other more
troublesome employments would have permitted, though I am
sufficiently sensible it would have been with abilities much
inferior to yours. Your design and mine are, I suppose, both
at the same thing, which is the discovery of truth, and I sup-
pose we can both endure to hear objections, so as they come
not in a manner of open hostility, and have minds equally in-
clined to yield to the plainest deductions of reason from experi-
ment. If, therefore, you will please to correspond about such
matters by private letters, I shall very gladly embrace it ; and
when I shall have the happiness to peruse your excellent dis-
cours.e (which I can as yet understand nothing more of by
hearing it cursorily read), I shall, if it be not ungrateful to you,
send you freely my objections, if I have any, or my concur-
rences, if I am convinced, which is the more likely. This way
of contending, I believe, to be the more philosophical of the
two, for though I confess the collision of two hard-to-yield con-
tenders may produce light, [yet] if they be put together by the
ears by other's hands and incentives, it will [produce rathjer
ill concomitant heat, which serves for no other use but ....
kindle — cole. S"", I hope you will pardon this plainness of,
your very affectionate humble serv*,

" 1675-6. Robert Hooke."

To this letter Newton sent the following reply : —

" Cambridge, February 5, 1675-6.
" Dr. Sir, — At the reading of your letter I was exceedingly
pleased and satisfied with your generous freedom, and think

1675-76. LIFE OF SIR ISAAC NEWTON. 125

you have done what becomes a true philosophical spirit. There
is nothing which I desire to avoyde in matters of philosophy
more than contention, nor any kind of contention more than
one in print ; and, therefore, I most gladly embrace your pro-
posal of a private correspondence. What's done before many
witnesses is seldom without some further concerns than that
for truth ; but what passes between friends in private, usually
deserves the name of consultation rather than contention ; and
so I hope it will prove between you and me. Your animad-
versions will therefore be welcome to me ; for though I was
formerly tyred of this subject by the frequent interruptions it
caused to me, and have not yet, nor I believe ever sliall re-
cover so much love for it as to delight in spending time about
it ; yet to have at once in short the strongest objections that
may be made, I would really desire, and know no man better
able to furnish me with them than yourself. In this you will
oblige me, and if there be any thing else in my papers in which
you apprehend I have assumed too ,...'.. If you please to
reserve your sentiments of it for a private letter, I hope you
[will find that I] am not so much in love with philosophical

productions but that I can make them yield But,

in the mean time, you defer too much to my ability in search-
ing into this subject. What Descartes did was a good step.
You have added much several ways, and especially in con-
sidering the colours of thin plates. If I Jmve seen farther, it is
hy standing on tJie shoulders of giants. But I make no ques-
tion you have divers very considerable experiments beside those
you have published, and some, it's very probable, the same
with some of those in my late papers. Two at least there are,
which I know you have often observed, — the dilatation of the
coloured rings by the obliquation of the eye, and the apparition
of a black spot at the contact of two convex glasses, and at the
top of a water-bubble ; and it's probable there may be more,
besides others which I have not made, so that I have reason to
defer as much or more in this respect to you, as you would to

126 LIFE OF SIR ISAAC NEWTON. CHAP. VI.

me.^ But not to insist on this, your letter gives me occasion
to inquire regarding an obsei*vation you was propounding to
me to make here of the transit of a star near the zenith. I
came out of London some days sooner than I told you of, it
falling out so that I was to meet a friend then at Newmarket,
and so missed of your intended directions ; yet I called at youi-
lodgings a day [or] two before I came away, but missed of you.
If, therefore, you continue ...... to have it observed, you

may, by sending your directions, command your

humble servant, " Is. Newton."

These beautiful letters, emulous of good feeling and lofty
principle, throw some light on the character and position of
two of the greatest of our English philosophers, and we cannot
read their mutual confessions and desires without an anxious
hope that two such men may never again be placed in a state
of intellectual collision. In alluding to the sinister practices
of some intermeddling friend, and to the evil consequences of
two hard-to-yield contenders being put together by the ears
by other's hands and incentives, Hooke evidently refers to his
colleague, Mr. Oldenburg. It was not unlikely that the secre-
tary to the Royal Society, and its Curator and Professor of
Mechanics, might have occasional grounds of difference without
any imputation upon their social or moral character ; but this
official jealousy, whatever was its amount, was increased in a
high degree during the disputes between Hooke and Hevelius
on the subject of plain and telescopic sights, and between Hooke
and Huygens respecting the invention of pendulum clocks.
These disputes were running high about the time when New-
ton's discourse on colours was before the Royal Society, and
in both of them Oldenburg took a keen and active part against
Hooke. It was, therefore, no improbable supposition, that in
communicating to Newton what Hooke had said at the Society,

1 In his Optics, published many years after this, in 1704, Newton does not give Ilooke
the credit of having made these observations.

1675-76. LIFE OF SIE ISAAC NEWTON. 127

Oldenburg liad given it too high a colouring, or even artfully
misrepresented it. In a subsequent dispute, in 1686, about
the law of gravity, when Newton made some severe animadver-
sions on Hooke's claim, Dr. Halley informs him in reply, that
" he feared Mr. Hooke's manner of claiming the discovery had
been represented in worse colours than it ought.'''' With his
usual good feeling, Newton thus expressed his regret : " Now
that I understand he was in some respects misrepresented to me,
I ivish I had spared the postscript in my last''

When Hooke, in the case more immediately before us,
stated " that the main of Newton's discourse was contained in
his Micrographia, which he had only carried further in some
particulars," he did not do justice to the valuable communica-
tion of his rival ; but, on the other hand, we have it on the
evidence of Newton himself, that he did not, in his discourse,
give Hooke the same credit for his discoveries which he after-
wards did in the letter that he addressed to him. It has been
too much the practice of the admirers of Newton to assail the
memory of Hooke with ungenerous animadversions, and un-
manly abuse. M. Biot has even ventured to describe him as
" a bad man," as if he added to the intellectual fame of New-
ton by the moral depreciation of his rival. We cannot give
our sanction to so harsh a judgment. Under a due sense of
the imperfections of our common nature, and influenced by the
charity which thinketh no evil, we may find in the physical
constitution and social position of Hooke, and to a certain
extent in the injustice of his enemies, some apology for that
jealousy and quickness of temper which may have been more
deeply regretted by himself than it was felt by others.

After the publication of his " Hypothesis, explaining the
Properties of Light," Newton seems to have been conversing
with Robert Boyle on its application to chemistry, and on the
28th February 1679, he addressed a letter to him on the
subject, in fulfilment of a long deferred promise. The views
which he here presents to his friend, he characterizes as in

128 LIFE OF SIR ISAAC NEWTON. CHAP. VI.

digested and unsatisfactory to himself, and he adds, that " as
it is only an explication of qualities that is desired," he " sets
down his apprehensions in the form of suppositions." He sup-
poses a subtle and elastic ether to pervade all gross bodies, and
to stand rarer in their pores than in free space, being so much
the rarer as their pores are less. The ether within solid and
fluid bodies diminishes in density towards their surface, while
the ether without all such bodies dimini^jhes in density towards
their surface. According to this theory there is a certain space
within solid and fluid bodies; and a certain space without tliem,
which Newton calls " the space of the ether's graduated rarity."
On these suppositions he tries to explain the inflexion of light
in passing through this space, the colours of minute particles,
and of natural bodies, the repulsion and attraction of bodies
coming into contact, the action of menstrums upon bodies, the
phenomena of effervescence and ebullition, and the transmuta-
tion of gross substances into aerial ones. He conceives the
confused mass of vapours, air, and exhalations, which we call
the atmosphere, to be nothing else but the particles of all sorts
of bodies of which the earth consists, separated from one an-
other, and kept at a distance by the said principle, and he con-
cludes this remarkable speculation with a conjecture about the
cause of gravity.

" I shall set down," he says, " one conjecture more, which
came into my mind even as I was writing this letter ; it is
about the cause of gravity. For this end I will suppose ether
to consist of parts diff'ering from one another in subtlety by in-
definite degrees ; that in the pores of bodies there is less of
the grosser ether in proportion to the finer, than in open
spaces ; and consequently, that in the great body of the earth
there is much less of the grosser ether in proportion to the
purer, than in the regions of the air ; and that yet the grosser
either in the air aff'ects the upper regions of the earth, and the
finer ether in the earth the lower regions of the air, in such a
manner, that from the top of the air to the surface of the earth,

1G75-79. LIFE OF SIR ISAAC NEWTON. 129

and again from the surface of the earth to the centre thereof,
the ether is insensibly finer and finer. Imagine now any body
suspended in the air or lying on the earth ; and the ether
being by the hypothesis grosser in the pores which are in the
upper parts of the body, than in those which are in its lowest
parts, and that grosser ether being less apt to be lodged in these
pores than the finer ether below, it will endeavour to get out
and give way to the purer ether below, which cannot be without
the bodies descending to make room above for it to go out into."^
The Hypothesis of Newton, and his other speculations re-
garding ether, have led some writers to suppose that he liad
abandoned the corpuscular or emission theory, in which light is
supposed to be produced by material particles projected from
luminous bodies, and that he had adopted views not very dif-
ferent from those of the supporters of the undulatory theory.
This opinion has been entertained chiefly on the authority of
Dr. Thomas Young, in his theory of light and colours.^ In in-
troducing this theory, he remarks, that "a more extensive
examination of Newton's writings has shown me, that he was
in reality the first that suggested such a theory as I shall en-
deavour to maintain ; and that his own opinion varies less from
this theory than is now almost universally supposed."'^ "I
shall collect," he adds, "from Newton's various writings, such
passages as seem to be most favourable to its admission (Dr.
Young's theory), and although I shall quote some papers which
may be thought to have been partly retracted at the publica-
tion of the ' Optics,' yet I shall borrow nothing from them that
can be supposed to militate against his maturer judgment''' In
another place he states in language still more explicit, " that
Neioton considered the operation of an ethereal medium as abso-
lutely necessary to the production of the most remarkable effects
of lights

1 Letter to Boyle, Newtoni Opera, torn. iv. pp. 385-395.

2 Phil. Trans. 1801 ; or, Lectures on Natural Philosophy, vol. ii. p. 614.

3 Ibid. vol. i. p. 477.

VOL. L I

130 LIFE OF SIR ISAAC NEWTON. CHAP. VI.

In direct contradiction to these statements, we Lave already
found Newton distinctly maintaining "that light is neither
ether nor its vibrating motion, but something of a different
kind propagated from lucid bodies," such as " multitudes of
small and swift corpuscles of various sizes springing from shin-
ing bodies ;" and when in order to please his friends and illus-
trate his views, he invents a speculation " not propounded to be
believed," he cannot be regarded as maintaining views at all
approximating to the undulatory theory. We cannot under-
stand how Dr. Young could overlook the language of caution
in which he everywhere guards himself against its being sup-
posed that he believes even in the existence of an ether, —
language, too, so precise, that the honest meaning of its author
cannot be misinterpreted.

The matured judgment of Newton, of which Dr. Young
speaks, and against which his quotations directly militate, is
given in the following explicit passage, published in 1717, in
the second edition of his Optics, revised by himself.^

" Are not aU hypotheses erroneous in which light is supposed
to consist in pression or motion propagated through a fluid
medium ] For in all these hypotheses the phenomena of light
have been hitherto explained by supposing that they arise
from new modifications of the rays, which is an erroneous
supposition.

"If light consisted only in pression propagated without
actual motion, it would not be able to agitate and heat the
bodies which refract and reflect it. If it consisted in motion
propagated to all distances in an instant, it would require an
infinite force every moment in every shining particle to generate
that motion. And if it consisted in pression or motion propa-
gated either in an instant or in time, it would bend into the
shadow. For pression or motion cannot be propagated in a
fluid in right lines, beyond an obstacle which stops part of the

1 Optics, edit. 3d, 1720, pp. 336, 3^3.

1675-79. LIFE OF SIR ISAAC NEWTON. 131

motion, but will bend and spread every way into the quiescent
medium which lies beyond the obstacle. ...

" And it is as difficult to explain by such hypotheses how
rays can be alternately in fits of easy reflexion and easy trans-
mission ; unless perhaps one might suppose that there are in all
space two ethereal vibrating mediums, and that the vibrations
of one of them constitute light, and the vibrations of the other
are swifter, and as often as they overtake the vibrations of the
first, put them into those fits. But how two ethers can be
different through all space, one of which acts upon the other,
and by consequence is reacted upon, without retarding, shatter-
ing, dispersing, and compounding one another's motions, is
inconceivable. And against filling the heavens with fluid
mediums, unless they be exceeding rare, a great objection arises
from the regular and very lasting motions of the planets and
comets in all manner of courses through the heavens. For
thence it is manifest that the heavens are void of all sensible
resistance, and by consequence of all sensible matter."

That this passage contains the mature and the latest judg-
ment of Newton on the subject of light cannot be doubted. All
the quotations from Newton referred to by Dr. Young bear the
date of 1672 and 1675, and the letter to Boyle the date of
1679; but the preceding passage was published in 1704, 1717,
and 1721, in the lifetime of Newton, when it was in his power
to alter or retract it. But in addition to this argument, we
have the evidence of Leibnitz in a letter to Huygens, dated 26th
April 1694, that Newton at that time was more convinced than
ever of the truth of the emission theory. " I have learned,"
says Leibnitz, " from Mr. Fatio,^ by one of his friends, that Mr.
Newton and he have been more than ever led to believe that
light consists of bodies which come actually to us from the sun,
and that it is in this way that they explain the different refran-
gibility of light and colours, as if there were primitive bodies

1 Fatio D'huilUer, the particular friend of Newton.

132 LIFE OF SIR ISAAC NEWTON, CHAP. VI.

which always kept their colours, and which come materially
from the sun to us. The thing is not impossible, but it appears
to me difficult to understand how by means of these little an-ows
which, according to them, the sun darts, we can explain the
laws of refraction."'

1 Huygenii Exfrcitat'miet Maihematico', ^c, Fascic. i. p. 173.

1675. LIFE OF SIR ISAAC NEWTON. 133

^ CHAPTER VII.

Newton's Hypothesis of Refraction and Reflexion — Of Transparency and Opacity —
Hypothesis of Colours — The Spectrura supposed to he divided like a Musical String —
Incorrectness of this Speculation — Hooke's Observations on the Colours of thin Plates
explained by the Vibrations produced in the Ether by the luminous Corpuscle —
Hooke claims this Theory as contained in his Micrographia — Newton's Researches on
the Colours of Thin PIh tes— Previous Observations of Boyle — Hooke's elaborate Expe-
riments on these Colours— His Explanation of them— Dr. Young's Observations upon
them — Newton acknowledges his Obligations to Hooke — Newton's Analysis of the
Colours seen between two OVject-Glasses— Corrections of it by MM. Provostayes and
Desains — Newton's Theory of Fits of easy Reflexion and Transmission — Singular Phe-
nomenon in the Fracture of a Quartz Crystal — Newton's Observations on the Colours
of Thick Plates — Recent Experiments on the same Subject.

In the preceding chapter we have given an account of the
first part of Newton's discourse on light and colours, read on
the 9th December 1675, and explaining his hypothesis concern-
ing " ether and ethereal substances, and their effects and uses."
In the second part of the portion read at the same meeting he
proceeds to " the consideration of light" as connected with the
supposed ether, that is to the cause of refraction, reflexion,
transparency, and opacity.

Regarding the ether as more dense in free space than in solid
bodies, and as diminishing in density towards their surface both
from without and from within, Newton supposes the incurva-
tion or bending of a ray of light, incident on such a surface, in
one direction to produce refraction, and in another to produce
reflexion, to be effected within " the space of ether's graduated
rarity," or " physical superficies." In the case of refraction,
from air to glass, the ray passes from denser into rarer ether,

13-1: LIFE OF SIR ISAAC NEWTON. CHAP. VII.

and is incurvated from the perpendicular in its passage through
the physical superficies ; whereas in reflexion from a dense me-
dium, such as glass into air, it is incurvated upw^ards or towards
the glass, and the incurvation may be such that the ray does
not emerge but suffer total reflexion.

In order to account by the agency of ether for the simulta-
neous refraction and reflexion of light incident upon the same
surface of glass or water, Newton supposes " that ether in the
confine of two mediums is less pliant and yielding than in other
places, and so nmcli the less pliant (or, ' more rigidly tenacious')
by how much the mediums diff'er in density." When light
therefore, that is small corpuscles, falls upon " this rigid resist-
ing ethereal superficies, it puts it into a vibrating motion, so
that the ether therein is continually expanded and compressed
hy turns.'" When a ray of light is incident upon it " while it
is much compressed, it is too dense and stiff to let the ray pass
through, and so reflects it ; but the rays that are incident upon
it at other times, when it is either expanded by the interval
of two vibrations, or not too much compressed or condensed, go
through and are refracted^

When the ether is of the same rarity in every pore, or when
the ether is evenly spread by its continual vibrations into all
the pores when they do not exceed a certain size, the light will
pass freely through the body, or the body will be transparent.
But when the pores exceed a certain size, the density of the
ether will be greater than that which surrounds it, and the
light being refracted or reflected at its supei-ficies, the body will
be opaque.

On the 1 6th December the second portion of Newton's dis-
course was read, in which he applies his hypothesis to the
(explanation of colours. For this purpose he supposes the
particles of light to have dift'erent degrees of " bigness, strength,
or power," red having the largest, and violet the least degree of
any of these qualities. When light, therefore, is incident on
the " refracting superficies," the smallest particles, namely, the

1675. LIFE OF SIR ISAAC NEWTON. 135

violet, will be most iiicurvated or refracted, and the red tlie
least ; and when these fall upon the refracting superficies of
the retina, they will there excite " the sensation of various
colours according to their bigness and mixture, the biggest with
the strongest colours reds and yellows, the least with the weakest
blues and violets, the middle with green, and a confusion of all
with white ; much after the manner that in the sense of hear-
ing, nature makes use of aerial vibrations of several bignesses
to generate sounds of divers tones." Pursuing this idea, " the
analogy of nature," he conjectures, " that colour may possibly
be distinguished into its principal degrees, red, orange, yellow,
green, blue, indigo, and deep violet, on the same ground that
sound within an eighth is graduated into tones," In order to
test this speculation by experiment, he forms a distinct spectrum,
and, " because his own eyes are not very critical in distinguisli-
ing colour," he employs a friend to whom he has not commu-
nicated his thoughts, to measure the lengths of the different
coloured spaces. The differences between the measures thus
obtained, he says, " were but little, especially towards the red
end, and taking means between these differences, the length of
the image (reckoned not by the distance of the verges of the
semicircular ends, but by the distance of the centres of those
semicircles, or length of the strait sides as it ought to be) was
divided in about the same proportion that a string is between
the end and the middle to sound the tones in the eighth.^'

Ingenious as this speculation is, it is contradicted by all the
recent discoveries respecting the prismatic spectrum, of which
we have given an account in a preceding chapter. It is not
even true in the spectnim which Newton himself observed.
There are not seve7i colours in any spectrum, and even if we
divide it into such a number of parts, the divisions have no
resemblance to those of a musical string.

From the explanation of colours produced by refraction,
Newton proceeds to explain those produced by reflexion, namely,
the colours of thin plates described by Hooke in his Micrographia.

136 LIFE OF SIR ISAAC NEWTON. CHAP. VII.

Ill order to do this, he supposes that the ethereal vibrations
excited by a ray move faster than the ray itself, and so " over-
take and outrun it, one after another." When light, therefore,
is incident upon a thin transparent* plate, the waves, excited by
its passage through the first surface, overtaking it one after
another, till it arrive at the second surface, will cause it to be
there reflected or refracted according as the condensed or the
expanded part of the wave overtakes it there. If the plate be
so thin that the condensed part of the first wave overtakes the
ray at the second surface, it must be reflected there ; if double
that thickness, so that the following rarified part of the wave,
that is, the space between that and the next wave, overtake it,
there it must be transmitted ; if triple the thickness, so that
the condensed part of the second wave overtake it, there it must
be reflected, and so where the plate i&five, seven, or nine times
tfiat thickness, it must be reflected by reason of the third,
fourth, or fifth wave overtaking it at the second surface ; but
when it w,four, six, or eight times that thickness, so that the
ray may be overtaken there, by the dilated interval of those
waves, it shall be transmitted, and so on ; the second surface
l)eing made able or unable to reflect according as it is condensed
or expanded by the waves.

In this way he explains the coloured rings produced by
pressing a convex lens against a plain glass ; and he concludes
this portion of his discourse, namely, his " Hypothesis," by
applying it to certain phenomena of Inflexion or Diff'raction, as
observed by Grimaldi.

It was after the reading of this portion of his discourse that
Hooke said, " that the main of it was contained in his Micro-
graphia, which Mr. Newton had only carried farther in some
particulars," — a remark which led to the correspondence with
Oldenburg and Hooke, which we have given in the preceding
chapter.

In the remainder of his discourse, Newton gives an account
of his beautiful experiments on the colours of thin plates ; but

1664. LIFE OF SIR ISAAC NEWTON. 137

before we enter upon their consideration, we must notice the
previous observations of Boyle and Hooke, in order that we
may apportion to Hooke and to Newton the discoveries which
they actually made. In the details into which this will lead
us, we shall see two great minds striving for victory, — calling
forth all their powers to surmount the difficulties which beset
them in their path, — deviating fr^^m the rigorous process of
research which both of them recognised, and perhaps forgetting,
in the ardour of their pursuit, some of those courtesies which
are now deemed essential in intellectual warfare.

In his book on Colours,^ Mr. Boyle informs us, that divers,
if not all essential oils, as also spirit of wine, when shaken,
" have a good store of bubbles, which appear adorned with
various and lively colours." He mentions also, that bubbles of
soap and turpentine exhibit the same colours, which " vary
according to the incidence of the sight and the position of the
eye ;" and he had seen a glass-blower blow bubbles of glass,
which burst, and displayed " the varying colours of the rain-
bow, which were exceedingly vivid."

In the year 1664, Hooke published, in his Microgi'aphia,^
a very interesting chapter of tJie colours observable in Miiscovy
glass (mica), and other thin bodies, in which he has described
many new phenomena.

1. In several parts of plates of mica, he found white specks
or flaws diversely coloured with all the colours of the rainbow,
the colours being ranged in rings, encompassing, and having the
same form as the speck. The colours from the middle of the
spot were blue, pur-ple, scarlet, yellow, and green, the same
series of colours recurrins: nine or ten times.

1 Experiments and Observiitions touching Colours. Exp xix. p. 243. London, 1664.

2 " Micmiraphia, or some Physiological Descriptions of Minute Bodies made by
magnify ing-gla&ses, with Observations and Inquiries thereupon." In many of the copies
the date is 1667, but the title-page which hears this date was a trick of the printer, to
indicate a second edition, which was never printed. The imprimatur of the President
of the Royal Society is Nov. 23, ]664. See Ward's Life of Hocke, iu the Lives of tha
Gresham Professors, p. 190.

138 LIFE OF SIR ISAAC NEWTON. CHAP. VII.

2. By pressing together two pieces of plate-glass with his
forefingers and thumbs, he produced the same series of colours
as in mica, the colours changing with the thin plate of air
between the glasses. The same phenomena were produced by
placing different fluids between the plates, the colours being
more strong and vivid in proportion as the refractive power of
the fluids differed from that of the glass-plates.

3. If the plate of air or fluid is thickest in the middle like a
convex lens, or thinnest as in a concave lens, the colours will
also be produced, the order of colours in the first case being red,
yellow, green, blue, &c. ; and, in the second, quite contrary.

4. As the colours cease when the plates have a certain thick-
ness, so they cease also when the plate has a certain thinness,
the colours ending in a white and colourless ring.

5. When we cleave a plate of mica with a needle, we shall
come to one of such a thickness as to exhibit a uniform colour,
every different degree of thinness below this giving a different
colour.

6. When two or three or more of these coloured plates are
laid one upon another, they exhibit such compound colours " as
one would scarce imagine would be the result of such ingre-
dients." A faint yellow, for example, and a blue, may produce
a very deep purple.

7. The same coloured ]aminse may be obtained by blowing
glass very thin ; and also from bubbles of pitch, rosin, colophony,
turpentine, solutions of gums, or any glutinous liquor, such as
wort, wine, spirit of wine, oil of turpentine, glare of snails, soap-
water, &c.

8. The same colours are produced upon polished steel by
gradually tempering or softening it with a sufficient degree of
heat. They are also produced on brass, copper, silver, gold, tin,
but most conspicuously upon lead ; and the colours that cover
the surface of the metal are nothing else than a very thin vitrified
part of the heated metal.

9. The same colours are exhibited in animal bodies, as in

1664. LIFE OF SIE ISAAC NEWTON. 139

pearls, mother-of-pearl shells, oyster shells, and almost all other
kinds of stony shells. They are seen also in muscles and
tendons.

10. If we take any glutinous substance, and run it exceed-
ingly thin upon the surface of a smooth glass, or a polished
metalline body, the same colours are produced ; " and in general
wheresoever you meet with a transparent body thin enough,
that is terminated by reflecting bodies of differing refractions
from it, there will be a production of these pleasing and lovely
colours."

Such is a brief account of Hooke's elaborate inquiry into the
colours of thin plates. We shall now consider the theory which
he invented to explain them. He considers light as produced
by "a very short vibrating motion propagated every way through
a homogeneous medium by direct or straight lines extended
every way like rays from the centre of a sphere, and with equal
velocity, so that the pulse or vibration of the luminous body
will generate a sphere which will continually increase, and grow
bigger, just after the same manner (though indefinitely swifter)
as the waves on the surface of the water do swell into bigger
circles about a point of it w^here, by the sinking of a stone, the
motion was begun ; — whence it necessarily follows, that all the
parts of these spheres, undulated through a homogeneous medium,
cut the rays at right angles." Our author then proceeds to
explain how refraction and reflexion take place at the confines
of media, in vfhich the " fluid undulating substance" (or ether)
has different densities.

In applying this theory to the explanation of the colours of
thin plates, he considers it " most evident that the reflexion
from the under or farther side of the body, is the principal cause
of the production of these colours." Supposing a ray " to fall
obliquely on the thin plate, part thereof is reflected back by the
first superfices," but, as the body is transparent, another part of
the ray is refracted by the first surface, reflected by the second,
and refracted again by the first surface, so that after two refrac-

1 40 LIFE OF SIR ISAAC NEWTON. CHAP. VII.

tioiis and one reflexion, there is propagated a kind of fainter ray,
whose pulse, by reason of the time spent in passing and repass-
ing between the two surfaces, comes behind the former reflected
pulse, so that hereby (the surfaces being so near together that
the eye cannot discriminate them from one) this confused or
duplicated pulse, whose strongest part precedes, and whose
weakest follows, does produce on the retina the sensation of a
yellow. If the two reflecting surfaces be yet farther removed
asunder, then will the weaker pulse be so far behind, that it
may be coincident with the second, third, fourth, fifth, &c., as
the plate grows thicker ; " so that if there be a thin transparent
body that, from the greatest thinness requisite to produce colours,
does, in the manner of a wedge, by degrees grow to the greatest
thickness that a plate can be of to exhibit a colour by the re-
flexion of light from such a body, there shall be generated sucli
a consecution of colours, whose order, from the thin end towards
the thick, shall be yellow, red, purple, bhie, green, and these so
often repeated, as the weaker pulse does lose pace with its
primary or first pulse, and is coincident with a second, third,
fourth, &c., pulse behind the first. And this, as it is coincident,
or follows from the first hypothesis I took of colours, so upon
experiment have I found it in multitudes of instances that seem
to prove it."

Dr. Thomas Young has quoted nearly the whole of these
passages as such an approximation to the true explanation of the
colours of thin plates, that if he had not satisfied himself respect-
ing the phenomena of this class of colours, these passages would
have led him earlier to a similar opinion. The doctrine of inter-
ference is distinctly stated in them, and had Hooke adopted
Newton's views of the diff'erent refrangibility of light, and applied
them to his own theory of the coincidence of pulses, he would
have left his rival behind in this branch of discovery.

Relying on the correctness of his views respecting the colours
produced by reflexion, Hooke very ingeniously applied the same
principle to the colours produced by refraction; and his objection

I(j75. LIFE OF SIR ISAAC NEWTON. 141

to Newton's doctrine always was, that it was contrary to his
theory. It is very obvious that hypotheses, however much
they were abjured by the experimental philosophers of that
day, were not only invented but admired ; and Newton was
thus driven to propose a hypothesis to satisfy his friends, he
himself declaring that he neither believed it, nor wished them
to believe it.

When this hypothesis was read, Hooke, as we have already
seen, stated " that the main of it was contained in his Micro-
graphia, which Mr. Newton had only carried farther in some
particulars." The reader will, we think, be able to judge, from
our abstract of Hooke's theory and observations, of the truth of
this remark. We think it substantially true, and do not hesitate
to say, that Newton has not done justice to H(5oke. Excepting
once, in reference to the inflexion of light, Hooke's name is never
mentioned. The results of his experiments are made use of, and
his theory partly adopted and altered, without any acknowledg-
ment of the one, or notice of the other. In his vindication, read
on the 21st December 1675, Newton admits that he made use
of some of Hooke's observations ; that he adopted the idea of
a vibrating ether ; and he thanks him for his explanation of
opacity, and for his notice of the colours of plated bodies. In
his interesting letter to Hooke, which we have given in the
preceding chapter, he goes much farther, acknowledging that
Hooke had added much several ways to Descartes' theory, espe-
cially in considering the colours of thin plates, and giving him
the credit of two important discoveries (which we do not find
in the Micrographici), namely, the dilatation of the coloured
rings by the obliquation of the eye, and the apparition of a black
spot at the contact of two convex glasses, and at the top of a
water bubble. In thus justifying the criticism of Hooke, and
throwing' some blame on Newton, we revert with pleasure to the
noble amends which he made in his private letter, when there
was no " intermeddling friend" to pervert the native generosity
of his character.

142 LIFE OF SIR ISAAC NEWTON. CHAP. VII.

We have hitherto considered only that part of Newton's dis-
course which contained his hypothesis, and its application to
refraction, reflexion, transparency, and opacity. The remaining
portions of it were read at the Royal Society on the 20 th
January, the 3d and the 10th February 1675-6, and contain
all the optical discoveries of Newton.

The portion which was read on the 20th January, contains
fifteen observations. In tlie first three of these he describes
the arcs and circles of colours, which are exhibited by pressing
together the imperfectly flat surfaces of two prisms. The place
where they touched was absolutely transparent, appearing like
a black spot " when looked upon," and " when looked through"
it seemed like a hole in the thin plate of air between the prisms.
The arcs and rings were generally of many colours, and about
eight or nine in number. By turning the prisms about their
common axis, the rings became black and white, and were
sometimes about thirty in number. In order to see them dis-
tinctly, and without any other colour, it was necessary to hold
the eye at a considerable distance from them, and also to view
them through a slit or oblong hole narrower than the pupil of
the eye.

In order to observe the order of the colours more correctly,
and obtain measures of the rings at different thicknesses of the
plate of air between the glasses, Newton took two object-glasses,
the one a plano-convex for a fourteen feet telescope, and the
other a large double convex for one of fifty feet, and having
laid upon this the other with its plane side downwards, he
pressed them slowly together, and observed the foUoMdng orders
of colours, next to the pellucid or dark central spot.

Order 1st, — Dark spot, violet, blue, white, yellow, and red.
Order 2d, — Violet, blue, green, yellow, and red.
Order 3d, — Purple, blue, green, yellow, and red.
Order 4 th, — Green and red.

The succeeding orders became more and more imperfect, "till

1675-76, LIFE OF SIR ISAAC NEWTOJf. 143

after three or four more revolutions they ended in perfect
whiteness."^

When his eye was placed perpendicularly over the glasses, he
found the diameter of the first six rings, at the most luminous
" part of their orbits," to be, when squared in arithmetical
progression of the odd numbers, 1, 3, 5, 7, 9, 11, and the
diameter of the dark rings between the more luminous ones,
when squared, to be in arithmetical progression of the even
numbers, 2, 4, 6, 8, 10, 12. When the rings were viewed
obliquely, they became bigger, as Hooke had observed, con-
tinually swelling as the eye was removed farther from their
axis.

" By measuring the diameter of the same ring at several
obliquities of the eye, partly by other means, as also by making
use of the two prisms for very great obliquities," Newton found
its diameter, and consequently the thickness of the air at its
perimeter, to be " proportional to the secant of an angle whose
sine is a certain mean proportional between the sines of inci-
dence and refraction. And that mean proportional is the first
of 106 arithmetical mean proportionals between the sines of
incidence and refraction counted from the lesser sine, that is,
from the sine of refraction when the refraction is made out of
air into water, otherwise from the sine of incidence."''^ That
is, the angle to whose secant the thickness of the air is propor-
tional, is one whose sine is to the sine of the real angle of inci-
dence in the constant ratio of

106 + ^

107
m being the index of refraction of the glass.

In repeating the experiment with the light of a monochro-
matic lamp, and measuring the angles with great care, and at

1 The reader will observe that the orders here given, and their colours, differ somewhat
from those published nearly thirty years afterwards in his " Optics."
* Opiics, Book ii. Part i. Obs. 7, 18.

144 ' LIFE OF SIR ISAAC NEWTON. CHAP. VII.

incidences so great as 85° 21', MM. Provostayes and Desaiiis
obtained the following results. At an incidence of 85° 21'
the diameter of the seventh black ring in niillionths of a
millimetre, was

By observation, . . . 4753

By Newton's Formula, . 4011

According to the doctrine of interference, the thickness of the
plate of air should be proportional to the secant of the angle of
incidence, which, in the present case, would give 47*55 for the
diameter of the seventh ring, a coincidence with the experiment
so remarkable, as to leave no doubt of the truth of the theory.^

The difference between Newton's experiment and the result
of theory, is so great as to call forth the remark from Sir John
Herschel,^ that " it might be drawn into an argument against
the theory, were we sure that the law of refraction at extreme
incidences, and with very thin laminae, does not vary sensibly
from that of the proportional sines." The important results
obtauied by MM. Provostayes and Desains will teach us rather
to doubt the accuracy of an unconfirmed experiment, and care-
fully to repeat it, than to explain it by calling in question a
well established law.

By various modes of observation, Newton found the following
relations between the diameter of the rings and the thickness of
the plate of air : —

1 10, IOt's, lOJ, lOi 111. 12^, 14. 15i, ItiJ, 19i. 22f, 29, 35.

ickness of the )

plate of air, } 10, 10t\. 10§, lU, 13, 15^, 20, 23J, 28^, 37, 52i. 84, 122J.

Diameter of the

ring
Thickness of the

Our author next proceeded to examine the effects of homo-
geneous coloured light, and was thus led to more important
results. In place of eight or nine rings which he saw in the
open air, he now saw more than twenty. In red light the rings

1 Cotnptes Ri'tuliis, &c. &c., torn. xxv. p. 498. 1850

2 Treatise on Light, Art. 670.

I(i75-7(i. LIFE OF SIR ISAAC NEWTON. 145

were much larger than in hlue and violet. The thickness of
the plate of air at which any red ring was produced, was to
that at which the same violet ring was produced/ as nine to
fourteen. The rings were not of various colours, as before,
when white light was used, but of the prismatic colour which
was employed, and each ring was separated from the other by
a dark ring or space. Upon placing a white paper behind the
rings, Newton observed rings painted upon it of the same
colour with those which were reflected, and of the same size
as their intermediate dark space. Hence he concluded that
the light which fell on the dark spaces was transmitted through
the glasses without any change of colour, and that the aerial
interval of the glasses according to its various thickness is dis-
posed in some places to reflect^ and in others to transmit^ the
light of any colour^ and in the same place to reflect one colour
where it transmits another.

From the examination of the colours of thin plates of air,
Newton proceeded to that of the colours of thin plates of water,
as exhibited in the soap-bubble. Havhig covered the soap-
bubble with a glass shade, he saw its colours emerge in a
regular order, like so many concentric rings encompassing the
top of it. As the bubble grew thinner by the continual sub-
sidence of the water, the rings dilated slowly and overspread
the whole of it, descending to the bottom, where they vanished
successively. When the colours had all emerged from the top,
there arose in the centre of the rings a small round black spot,
like that in the centre of the rings formerly described, dilating
it to more than half an inch in breadth till the bubble burst.

Upon examining the rings between the object-glasses, New-
ton found that when they were only eight or nine in number,
more than forty could be seen by viewing them through a
prism ; and even when the plate of air seemed all over uni-
formly white, multitudes of rings were disclosed by the prism.
The same result was obtained with thin plates of water, mica,
and glass.

VOL. L K

146 LIFE OF Sm ISAAC NEWT0J5. CHAP. VII.

By means of these interesting observations, Newton proceeds
to show how the system of coloured rings exhibited by white
light, are produced by the superposition of the rings belonging
to each separate colour in the spectrum, and he constructs a
diagram, explaining a method of finding the colours of wdiich
the rings are composed at any distance from their centre. He
then concludes this part of his discourse with a table showing,
in miilionths of an inch, the different thicknesses of plates of
air, water, and glass, when they exhibit the different colours in
the seven rings or orders of colours. The thicknesses, for ex-
ample, of air, watevj and glass, at which no light is reflected,
or at which the black of the first ring is produced, are 2, l^,
IJ miilionths of an inch respectively, and the thicknesses at
the margin of the seventh ring are 84, 63, and 541 miilionths
of an inch. This Table, which is known by the name of
Newton s Scale of Colours, is of great value in all optical
researches, and is constantly referred to by modern writers on
Optics.

This celebrated discourse is concluded by nine propositions,
showing how the phenomena of thin transparent plates stand
related to the colours of all natural bodies, and how the size of
the component parts of such bodies may be conjectured by
their colours, — a subject which will be discussed in another
chapter.

Such is a brief account of Newton's discoveries respecting
the colours of thin plates, and of the hj^othesis of ethereal
vibrations, by which he proposed to explain them. The experi-
ments from which they were deduced were all made previous
to 1675 ; and it does not appear that, during the remaining
fifty-two years of his life, he made any other communications
on optical subjects to the Koyal Society. In the preface to his
Treatise on Optics, dated 1704, he tells us that "^^ar^ of the
ensuing discourse about light was written at the desire of some
gentlemen of the Royal Society in the year 1675, and then
sent to their secretaiy and read at their meetings ; and tli^ rest

l(i75-76. LIFE OF SIR ISAAC NEAVTON. 147

was added about twelve years after, to complete the Theory,
except the third book and the last proposition of the second,
which were since put together out of scattered papers." These
additions to the discourse, which were made in 1687, are no
doubt his ampler discussion of the theory of the colours of
natural bodies, and his theory of fits of easy re^exion and easy
transmission, by which he explains the colours of thin plates ;
and what was since put together out of scattered papers, was
the first part of the third book on the in4exion of light, and
the fourth part of the second book on the colours of thick plates.
An explanation, therefore, of the theory of fits, will form an
appropriate conclusion of our account of Newton's discoveries
respecting the colours of thin plates.

In the propositions of his Optics, where he explains this
theory, Newton does not attempt to assign any cause by which
these fits are produced. He does not inquire whether the kind
of action or disposition in which they originate " consist in a
circulating or vibrating motion of the ray or of the medium, or
something else ;" but he says, that those who require a hypo-
thesis, " which, whether it be true or false, he does not con-
sider, may for the present adopt the one previously explained,
in which the rays of light, by impinging on any refracting or
reflecting surface, excite vibrations in the refracting or reflect-
ing medium or substance," and that the ray is refracted or
i'eflected according as it is in that part of the vibration which
conspires with or impedes its motion.^ A popular idea may be
formed of these fits of reflexion and transmission, by supposing
that each particle of light, after its emission from a luminous
body, revolves round an axis perpendicular to the direction of
its motion, and presenting alternately to a refracting surface,
which it approaches, an attractive and a repulsive pole, in
virtue of which it will be refracted if the attractive pole is

1 It is curious that Newton here makes no mention of an ethereal medium as that in
which the vibrations are executed, as he does in his Hypothesis, formerly described.
See p. 118.

148

LIFE OF SIR ISAAC NEWTON.

CHAP, vir.

nearest the refracting surface, and reflected if the repulsive pole
is nearest that surface.

In order to explain this more clearly, let s be a ray of light
which falls upon a trans-
parent surface mn, and
is transmitted by that
surface. It is obvious
that it must have been
nearer its fit of transmis-
sion than its fit of re-
flexion wlien it met the
surface mn at t ; but
whether it was exactly
in its fit of transmission,
or a little way from it,
the theory supposes that
it is put by the action
of the surface into the
same state as if it had
begun its fit of transmis-
sion at T. Let us now
suppose that its fit of
reflexion takes place at
R, and that these fits
recur at t', r', t", r", &c., so that if there was a second trans-
parent surface at t' or t", the ray would be transmitted ; and
if there was a second transparent surface at r', r", it would be
reflected. The spaces tt', t't", are called the intervals of
the fits of transmission, and the spaces rr', r'r", the intervals
of the fits of reflexion. Now, as the spaces tt' rr' are equal
for light of the same colour, it is obvious that the ray r will
be transmitted, if the thickness of the body is tt', tt", &c.,
that is tt', 2 tt', 3 tt', or any multiple whatever of tt', the
interval of a fit of easy transmission ; and as tt' is equal to
rr', the ray R will be reflected when the thickness of the body

Fig. 14.

1(575-76.

LIFE OF SIR ISAAC NEWTO?f.

149

is 1 tt', 1 J tt', 21 tt', 31 tt', &c. If the body mn, there-
fore, were a plate with parallel surfaces, and if the eye were
placed above it so as to receive the rays reflected perpendi-
cularly, it would in every case see the first surface mn by the
portion of light uniformly reflected from that surface ; but if
the thickness of the body were tt', 2 tt', 3 tt', 4 tt', or
1000 tt', the eye would receive no rays from the second sur-
face, because they would be all transmitted ; and, in like
manner, if the thickness were I tt', IJ tt', 2 J tt', or
1000 J tt', the eye would receive all the light reflected from
the second surface, because it would be all reflected. When
this reflected light meets the first surface mn, on its way back
from the second surface, it will be all transmitted, because it is
then in its fit of transmission. At intermediate thicknesses,
such as J tt', a portion only of the light will be reflected from
the second surface, increasing as the thickness increased from
tt' to IJ tt', and diminishing again as the thickness increased
from IJ tt' to 2 tt'.

Let us now suppose that the plate whose surface is mn has

Fig. 15.

its thickness varying like a wedge mnp. Fig. 15, and that the
eye is placed above it to receive the light which it reflects.

150 LIFE OF SIR ISAAC NEWTON. CHAP. ^'11.

The interval of the fits being tt', rr', as before, it is evident
that, near the point n, the light that falls upon the second
surface tF, will be transmitted, because it is in a fit of trans-
mission, but at the thickness tr the light will be reflected from
the second surface at r, because it is then in a fit of reflexion,
and again transmitted in returning through the first surface
MN. In like manner, the light will be transmitted at t' and
t'\ and reflected at r and r\ so that the observer will see a
series of dark and luminous bands, the middle of the dark
ones being at t, t', t", and of the luminous ones at r, r, r" .

Let us now suppose that the figure is adapted to red light ;
then since the length of a fit is greatest in red^ least in violet ^
and of an intermediate size in yellow light, it is obvious that
in yellow light there will be a set of dark and luminous bands
less than those in the figure, and in violet light another set
less than in the yellow. When, therefore, the light incident
on the plate is white, all these bands will be superimposed, and
form the coloured bands already described. When the thin
plate is wedge-shaped, the bands will be parallel. When it
has the form of a concave lens, like air or vacuity between two
object-glasses, the bands will be circular, with the lowest tints
in the centre. When it has the form of a convex lens, like the
plates of air in mica, the bands will also be circular, with the
lowest tints at the margin ; and when the thin plate has differ-
ent thicknesses like a film of blown glass, the bands will have no
regular shape, the same thickness giving always the same colour.

The preceding doctrine of fits has always been regarded as
an ingenious explanation of the colours of thin plates. It is
not given by its author as a theory or a hypothesis, but simply
as an expression of the facts which he has observed ; and yet
it has to a certain extent the character of a hypothesis, in so
far as it assumes that the second surface of the plate does not
in every part of it reflect light like the first, whereas in the
theory of interference, certain portions thus reflected are des-
troyed before they reach the eye of the observer.

l<i75-7<5. LIFE OF SIR ISAAC NEWTON. 151

With the exception of tlie interesting observations of MM.
Provostayes and Desains already referred to, no discovery of
any great importance has been made on the subject of thin
plates since the time of Newton. We have had occasion to
observe a number of curious phenomena in the thin plates of
decomposed glass when acting upon light in a state of combina-
tion. The colours which they reflect and transmit are not
deducible from any theory of light, and have an intimate
(connexion with the absorption of light by coloured media. ^

Among natural phenomena illustrative of the colours of thin
plates, we have found none more remarkable than one exhibited
l)y the fracture of a large crystal of quartz of a smoky colour,
and about two and a quarter inches in diameter. The surface
of fracture, in place of being a face of cleavage, or irregularly
conchoidal, as we have sometimes seen it, was filamentous like
a surface of velvet, and consisted of short fibres so small as to
be incapable of reflecting light. Their size could not have
been greater than the third of the millionth part of an inch, or
one-fourth of the thinnest part of the soap-bubble when it ex-
hibits the black spot where it bursts.'-^

Although Newton did not communicate his observations on
the colours of thick plates to the Royal Society in his discourse
on light and colours, but " put them together out of scattered
papers" some time before the publication of his Optics,^ yet
this is the proper place for bringing them under the notice of
the reader.

The colours of thick plates arise from a quantity of light
scattered in all directions from the little inequalities or imper-
fections which exist in the surface of a glass mirror either
silvered or unsilvered. In order to observe them, a sunbeam is

1 " Oa the Connexion between the Phenomena of the Absorption of Light and the
Colours of Thin Plates."— Pft«. Trans. 1837, p. 245.

2 Edinburgh Journal of Science, vol. i. p. 108. June 1824.

3 These observations, thirteen in number, entitled, " Observations concerning the He-
fUctions and Colours of (hick transparent jjolished Plates, form tb.e fourth part of tho
Second Book of Optics.

lo2 LIFE OF SIR ISAAC NEWTON. CHAP. VII.

admitted through a small hole about a third of an inch in dia-
meter into a dark room. This beam is received perpendicularly
on a concavo-convex glass mirror, a quarter of an inch thick,
and having each surface ground to a sphere six feet in radius.
When the sunbeam passes through a small hole in the middle
of a sheet of white paper placed in the centre of the mirror's
(•oncavity, the whole is surrounded with four or five coloured
rings. The rings resembled those seen by transmission through
two object-glasses, but were larger and fainter in their colours.
When mirrors of different thicknesses were used, the diameters
of the rings were reciprocally as the square roots of the thick-
nesses ; and in homogeneous light they were largest in the
red, and smallest in the violet rays, like those formed by thin
plates.

These and other phenomena described by Newton, he ex-
plains by taking into consideration the fits of easy reflexion
and transmission of the faint scattered light already mentioned.
On the undulatory theory they are explained by the interference
of the portions of light scattered at the first surface by the rays
in passing and repassing through it.

The Duke de Chaulnes^ observed similar rings when the
surface of the mirror was covered with fine gauze, or with a
thin film of milk dried upon it, and Sir William Herschel^
noticed analogous colours when hair-powder was scattered in
the air before a metallic mirror, on which a beam of light was
incident.

When we look through two plates of parallel glass of exactly
the same thickness, at a circular disc of light 1° or 2° in dia-
meter, no coloured bands will be seen when the light is incident
perpendicularly, and when the plates are parallel. But if we
incline them slightly to one another, we shall see, beside the
direct image of the luminous body which is crossed with no
fringes, a series of lateral images formed by successive reflexions
between the surfaces of the plates, which are crossed with

1 MM. Acad. Par. 1105. 2 Phil. Trans. 1807.

U;75-76. LIFE OF SIR ISAAC NEWTON. 153

fifteen or sixteen highly coloured bands parallel to the common
section of the surfaces of the plates. The breadth of these
bands is inversely as the inclination of the plates, and at a
given inclination their magnitudes are inversely as the thickness
of the plates employed.

These brilliant bands, which we have described minutely in
a separate memoir, ^ are explicable by the doctrine of fits of
easy reflexion and transmission. They have been explained
also on the undulatory hypothesis by Dr. Thomas Young,^ and
in greater detail by Sir John Herschel.^

Another species of coloured fringes, produced by the reflexion
of a pencil of light between the lenses of a double or a triple
achromatic object-glass, is equally explicable by Newton's
theory of fits, and by the doctrine of interference. Owing to
the curvature of the surfaces which produce them, the forms of
the isochromatic lines, or the lines of equal tint, are various
and beautiful.*

1 Edinburgh Transactions, 1815, vol. \u. p. 435.

2 Art. Chromatics in Encyclopaedia Britannica.

3 Treatise on Light, § 688-695.

* Edinburgh Transactions, 1832, vol. xii.

154 LIFE OF SIR ISAAC NEWTON. CHAP. VIII.

CHAPTER VIIL

Influence of Colour in the Material World — Newton's Theory of the Colours of Natural
Bodies — Coloured Bodies reflect only Light of their own Colour, absorbing all the
other parts of White Light — The Colours of Natural Bodies are those of Thin Plates
— The Transparent Parts reflecting one Colour and transmitting another — Arrange-
ment of the Colours exhibited in Natural Bodies into Seven Classes — Coloured Juices
and Solutions, Oxidated Films, Metals, &c. &c. — Newton's Theory applicable only to
one Class of Colours — Objections to it stated — M. Jamin's Researches on the Colours
of Metals — The Cause of Colours must be in the Constitution of Bodies — Examples of
the effect of Heat upon Rubies and Nitrous Gas — Effoct of Sudden Cooling — On
Phosphorus — Effect of Mechanical Action on Iodide of Mercury — Indication of a New
Theory — And of the Cause of the Absorption of Definite Rays — Illustration of these
Tiews in a remarkable Tourmaline.

Had the objects of nature been rendered visible only by
white light, and exercised upon it the same action in refracting
and reflecting it to the human eye, all the combinations in the
material world, and all the various forms of life, would have
displayed no other tint than that which they exhibit in a
pencil sketch, a China-ink drawing, or a photographic picture.
The magnificent foliage of the vegetable world might have
filled the eye with its picturesque and lovely forms, and given
protection to its fruit and its flowers, but we should not have
rejoiced in the verdure of its youth, nor mourned over the
yellow of its age. The sober mantle of twilight would have
replaced the golden vesture of the rising and the setting sun.
The stars would have twinkled colourless in a gi'ey sky, and
the rainbow would have dwindled into a naiTow arch of dusky
light. The diamond, the ruby, and the sapphire might have
displayed to science the nice geometiy of their forms, and
yielded to the arts their adamantine virtues ; but they would

I
1

l(>75-7(x LIFE OF SIR ISAAC NEWTON. \55

have ceased to sparkle in the chaplet of beauty, or adorn the
diadem of princes. The human face divine might have ex-
pressed all the qualities of the mind, and beamed with all the
affections of the heart ; but the purple light of love would not
have risen on the cheek of beauty, nor the hectic flush have
heralded its decay. Life would have breathed and perished in
its pale marble ; and nature would have sprung and decayed in
its russet brown. The material world, however, has been other-
wise framed, and those exquisite models of organic and inor-
ganic life, into which the great sculptor has chiselled the furni-
ture of his terrestrial temple, have been enhanced by that
ethereal beauty which the play of light and colour can alone
impart.

Many attempts were made previous to the time of Newton,
to explain the colours of natural bodies ; but they all neces-
sarily failed, while philosophers were ignorant of the true
nature of colours themselves. In his earliest communications
to the Royal Society, Newton had clearly indicated his views
respecting the colours of natural bodies ; and after showing
" that they appear of divers colours, according as they are dis-
posed to reflect most copiously the rays endued by these
colours," he proceeds, in the last part of his " Discourse," read
to the Royal Society on the 10th February 1675-6, to con-
sider " the constitution of bodies on which their colours de-
pend." This curious subject continued to occupy the attention
of Newton, and he enters upon it more fully in two different
parts of his Optics, where " by the discovered properties of
light he explains the permanent colours of natural bodies,"^
and points out the " analogy between such colours, and the
colours of thin transparent plates."^

After showing that all bodies, whatever were their coloure,
exhibited these colours best in white light, or in light which
contained their peculiar colour, he proves by experiment, that
when coloured bodies are illuminated with homogeneous red

I Optics, Book i. Part ii. Prop. 10. 2 Optics, Book ii. Part iii.

156 LIFE OF SIR ISAAC NEWTON. CHAP. VIII.

light, they appear red, with homogeneous blue light, blue, 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 green light in greater abundance
than any other. When the leaf was placed in homogeneous
red light, it no longer appeared green, because there were no
green rays in the red ; but it reflected red light in a small
degree, because there were some red rays in the compound
green, which it had the property of reflecting. If the leaf had
originally reflected a pure homogeneous green, unmixed with
red, and reflected no white light (as all leaves do) from its
outer surface, it would have appeared quite black, in pure ho-
mogeneous red light, as this light does not contain a single ray
which the leaf is capable of reflecting. Hence it follows that
the colours of natural bodies are owing to the property which
they possess of stopping or absorbing certain rays of white
light, while they reflect or transmit to the eye the rest of the
rays of which white light is composed. The green leaf, for
example, stops or absorbs the red, blue, and violet rays of the
white light which falls upon it, and reflects and transmits only
those which compose its peculiar green.

To this extent the views of Newton are demonstrable, and
have been universally adopted ; but when he attempts to deter-
mine the manner in which the colour of any body is insulated
from the other colours which fall upon it, and in which these
other colours are stopped or lost, or, in other words, the physi-
cal constitution of natural bodies by which these processes are
effected, he enters the region of hypothesis and fails in bringing
conviction to the mind. His theory, however, is grand and
imposing, but standing as it does, and as we shall presently show,
on a perishable basis, it must soon be swept away in the pro-
gress of optical discovery.

The following are the principles on which this theory is
founded.

l«7o-7<i. LIFE OF SIR ISAAC NEWTON. 157

1 . Bodies that have the highest refractive powers, reflect the
greatest quantity of light from their surfaces, and at the con-
fines of equally refracting media there is no reflexion.

2. The least parts of almost all natural bodies are in some
measure transparent.

3. Between the jmrts of opaque and coloured bodies, are
many spaces or pores, either empty or filled with media of other
densities.

4. The parts of bodies and their interstices or pores must
not be less than of some definite bigness, to render them co-
loured.

5. The transparent parts of bodies, according to their several
sizes, reflect rays of one colour, and transmit those of another,
on the same grounds that thin plates do reflect or transmit
these rays.

6. The parts of bodies on which their colours depend, are
denser than the medium which pervades their interstices.

7. The bigness of the component parts of natural bodies may
be conjectured by their colours.

In illustration of the ^fth, or leading proposition of the theory,
Newton remarks, " that if a thinned or plated body, which
being of an even thickness, appears all over of one uniform
colour, should be slit into threads or broken into fragments of
the same thickness with the plate, he sees no reason why every
thread or fragment should not keep its colour, and by conse-
quence why a heap of those threads or fragments should not
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 colours."

In order to prove this, Newton proceeds to describe various
kinds of colours, to which he considers the theory specially
applicable ; but before we follow him in this investigation, we
must endeavour to classify all the varieties of colours which are
exhibited in the natural world.

158 LIFE OF SIR ISAAC NEWTON. CHAP. VIII.

Colours may be arranged into seven classes, in each of which
the colour has a different origin.

1. Transparent coloured fluids, such as the juices obtained
from the coloured parts of plants, and coloured solutions, whether
natural or artificial. Transparent coloured solids, such as
coloured minerals, glasses, powders, and vegetable tissues.

2. Oxidated films on metals — colours of precious and hydro-
phanous opal — of Labrador felspar — of the feathers of birds —
of the wings, &c., of insects — of the scales of fishes — of the
tapetum of animals — of the intermd films of mother-of-pearl
and various shells — and of decomposed glass.

3. Superficial colours of mother-of-pearl, striated and grooved
surfaces, which can be communicated by pressure to other
surfaces.

4. Opalescences, or colours dispersed from the particles of
diff'erent solid and fluid and gaseous bodies, some of which are
coloured, and others colourless. These colours appear in ice, in
water, in the atmosphere — in fluorspar and several glasses — in
solutions of sulphate of quinine, &c., and in the juices of plants
and several oils.

5. At the surfaces of media of different dispersive powers,
and in which the index of refraction is the same in each me-
dium for certain rays, but different for all the rest.

6. The colours produced by heat, and during combustion.

7. The colours of metals.

The colours referred to in the Jlrst of these classes are repre-
sented by red and yellow wines — by the coloured fluids shown
in the windows of the apothecary — by the green leaves of plants
— by the ruby, the cairngorm, the topaz, and the sapphire — and
by the powders of cinnabar, red lead, ultramarine, sulphur, &c.

In all these bodies Newton supposes that the colour peculiar
to each, namely, that which passes through its substance, is the
tint reflected from the minute particles of which it is composed,
the opposite or complementary tint, which is transmitted by the
particles being lost within the body by a multitude of internal

l()75-7t). LIFE OF SIR ISAAC NEWTON. 159

reflexions. In the ruby, for example, the particles are supposed
to have such a size as to appear red by reflexion, and the green
light which would be seen by transmission through a single
particle, is supposed to be lost by repeated reflexions within the
body composed of such particles. If we now examine the ruhy,
or any other coloured solid or fluid, we shall find that neither
red nor green light is reflected from any of its external surfaces,
or any of its internal parts. The red light which characterizes
the body is seen only by transmission through its substance.
If we now analyze the red light by the prism, we shall find that
it has not the composition of any of the red rings in Newton's
scale of colours.

In the case of the riihy, which we have purposely selected j
we are able to apply another test, and one which Newton him-
self authorizes, when he remarks that changes of colour may be
produced by the swelling or shrinking of the tinging corpuscles.
In subjecting the halas ruby to a high degree of heat, which
must have had the effect of swelling the tinging corpuscles, I
found that it became green, which, as the cooling advanced,
gradually faded into brown, the ruby resuming its original
brilliant red when it had returned to its former temperature.
Berzelius 'observed an analogous fact in the spinelle of Ceylon
and Aker, which became brown by heat, then black, and opaque
as the heat increased. Upon returning to its former tempera-
ture, it passed through a fine chrome green before it recovered
its red colour. Hence it is obvious that these colours and
changes of transparency, which have no relation to those of
thin plates, could not have arisen from the gradual swelling and
subsequent shrinking of tinging corpuscles.

A still more striking proof of the want of analogy between
the colours of natural bodies and those of thin plates, may be
obtained from the prismatic analysis of certain colours in which
Newton himself believed that analogy to exist. A green of the
third order of colours is, as he observes, " constituted princi-
pally of original green, but not without a mixture of some blue

160 LIFE OF SIR ISAAC NEWTON. CHAP. VIII.

and yellcnv,'^ and contains not a single ray of orange, red, indigo,
or violet. He considers the green of all vegetables, to be a
green of the third order, not only because this green is the
purest and most intense in colour, but because when vegetables
wither, some of them turn to a greenish yellow, and others to a
more perfect yelloiv or orange, or perhaps to red, passing first
through all these intermediate colours. " Now," he adds, " the
green is without doubt one of the same orders with those colours
into which it changeth, because the changes are gradual, and those
colours, though usually not very full, yet are often too full and
lively to be of the fourth order." These changes from green
to red, he considers as " effected by the exhaling of the mois-
ture which may leave the tinging corpuscles more dense, and
something augmented by the accretion of the oily and earthy
part of that moisture."

In order to put these opinions to the test of direct experi-
ment, we examined the brilliant green juice extracted by alcohol
from the leaves of twenty different plants, and also the same
juice when taken from the leaves in their yellow, orange, and
red state, and found that their composition had not the least
resemblance to that of the colours of any order whatever, and
least of all to those of the greens of the third order. The
spectrum obtained from a sunbeam passing through these juices
is one of singular beauty, divided by dark spaces into several
coloured bands of unequal breadths, and possessing all the
colours which ought not to exist in the green of the third
order. When the green fluid thas analyzed has stood for three
or four days it loses its bright green colour, and becomes of an
olive green, which grows more and more of a brownish yelloiv,
till it becomes almost colourless, a series of changes which have
no relation whatever to the effects that might be expected to
arise from an increase or decrease in the density or size of the
tinging corpuscles.

In some plants the green leaf decays in a different manner
from that described by Newton. In place of becoming yellow^

1^75-76. LIFE OF SIR ISAAC NEWTON. 161

the green leaves of the privet become of a deep hlach violet,
when they wither ; a colour which has no resemblance what-
ever to any of the colours of thin plates. The fluid obtained
from these violet leaves was of a deep red colour^ — much deeper
than that of the darkest port wine. It divided the red space
of the spectrum into two red bands, absorbed the violet and
blue spaces generally, and obliterated the middle of the green
space. Its action was so different from that of the green juice,
that the two tints had no resemblance to those of adjacent
colours of the same order. ^

The pale blue of the sky is regarded by Newton as a blue of
the first order, produced by the minute particles of " vapours
which have not arrived at that grossness which is requisite to
reflect other colours ;" and while he considers the whiteness of
froth, paper, linen, &c., as that which arises " from a mixture
of the colours of several orders," that is, from the action of
particles of a much greater size than those of vapours which
produce the blue of the first order. Now, it is obvious that
froth, when seen under a clear blue sky, must have the colour
of the sky itself, as it is nothing more than an accumulation
of images of the sky reflected from the innumerable aqueous
vesicles which compose it. The colour of froth, wherever it is
placed, must be the average tint of all the diff'erently coloured
rays which fall upon it and are reflected to the eye.

The colours referred to in the second class are undoubtedly
analogous to those of thin plates. Newton has himself men-
tioned the colours of the feathers of some birds as those of
thin plates, and the fine colours of the diamond and other
beetles obviously have the same origin. The splendid colours
of the tapetum, or membrane behind the retina of animals,
afford an interesting example of this class of colours. Even
when the membrane has been taken out, it exhibits the most
beautiful colours by reflexion, but it becomes absolutely black

1 A full account of these experiments, with coloured drawings of the spectra, will be
found in the Edinburgh Transactions, 1833, toI. xii, pp. 538-545.

VOL. I. L

162 LIFE OF SIR ISAAC NEWTON. CHAP. VIII.

wlien dry. The colours, however, may be revived by moisture,
and, after remaining in the dry state for upwards of twenty
years, we have succeeded in restoring the colours by steeping
the membrane in warm water. The black passes into a bright
hlue^ the blue into green, and the green into greenish yellow.

In placmg the internal colours of mother-of-pearl under this
class, we must carefully distinguish them from the external
colours communicable to wax. By reducing the mother-of-pearl
to exceedingly thin plates, we are able to exhibit the action of
the colorific films which they enclose, and which, like those of
thin plates, give one colour by reflexion, and its complementary
colour by transmission. ^

The splendid colours exhibited by decomposed glass, both in
the light which it reflects and transmits, belong also to colours
of the second class ; and though they are clearly those of thin
plates, yet they exhibit peculiarities when produced by a great
number of films, which place them in a certain interesting re-
lation with the colours of the first class. ^

The colours of Labrador felspar, and of precious and hydro-
phanous opal, which we have shown to be produced by thin
plates and minute pores and tubes, belong also to the second
class of colours.^

The superficial colours which we have placed in the third
class, have obviously no relation whatever to the colours of thin
plates. They are spectra produced by interference, and, had
he been acquainted with them, they would have been re-
garded by Newton himself as inexplicable by his theory."*

The very remarkable colours produced by internal dispersion,
and which have recently excited so much interest from the
discoveries of Professor Stokes, form a fourth class, which has

1 See Phil. Trans. 1814, p. 397 ; and 1836, pp. 55, 56.

2 See Layard's Discoveries in the Ruins of Nineveh, 1853, pp. 674-676 ; and Phil.
Trans. 1837, p. 249.

3 See Edinhimih Transactions, 1829, Tol. xi. p. 322 ; and Reports of the British Asso-
ciation, 1844, p. 9.

i See Phil. Trans. 1814, p. 397 ; and 1829, p. 301.

1675-76. LIFE OF SIR ISAAC NEWTON. 163

not been identified with those of thin plates. Tlie light thus
dispersed must be reflected, in cases of ordinary opalescence,
from the faces of minute pores in solids, or from particles of
different densities disseminated through sohds or suspended in
fluids. The beautiful colours exhibited by fluor spar, by solu-
tions of the sulphate of quinine, and various other solids and
fluids, are emanations of a phosphoric nature, generated by
certain rays in the solar spectrum, and have therefore no analogy
with the colours of thin plates. These emanations have all
colours, — red in the alcoholic juices of leaves, violet^ blue, pink,
and ivhitish in fluor spar, sky-blue in sulphate of quinine, bright
green in alcoholic solutions of the colchicum autumnale, and in
various glasses and oils, and violet in an alcoholic solution of
guiacum.^

In i\\& fifth class we have placed a new species of colours
which we discovered many years ago, and which we believe have
never been studied, or even alluded to by any other person. In
the year 1814, when investigating the law of polarization for
light reflected at the separating surface of difi'erent media, we
had occasion to enclose oil of cassia between two flint-glass
prisms, and were surprised to observe that the colour of the
reflected light was blue. The cause of this we had some
difficulty in discovering. The refractive power of oil of cassia
exceeds greatly that of flint-glass for the mean rays of the
spectrum, while the action of the two bodies on the less re-
frangible rays is nearly the same. Hence the red rays must
be in a great measure transmitted, while there will be reflected
a small portion of the orange, a greater portion of the yellow,
and a much greater proportion of the blue and violet, so that
the colour of the pencil, formed by reflexion, must necessarily
be blue, mixed with some of the less refrangible rays.

By employing difi'erent kinds of glass, and difierent oils, we

1 See Edinburgh TVantactions, 1833, vol. xii. p. 542; and 1846, vol. xvi. p. Ill;
Reports of the British Association, 1838, pp. 10-12 ; Phil. Trans. 1845, p. 143; and
1852, p. 463.

164 LIFE OF SIR ISAAC NEWTON. CHAP. VIII.

obtained various analogous results, in which rays of different
colours were extinguished from the reflected pencil according to
the part of the spectrum where an equilibrium had been esta-
blished between the refractive powers of the media in contact.
When the refractive indices were equal in the blue rays, the
colour of the reflected pencil was yellow. As the indices of
refraction are the same for all obliquities of incidence,^ the tint
of the reflected pencil, though it must vary in intensity, can
never vary in colour ; and as that colour is abstracted from the
white incident light, its complementary tint must appear, how-
ever faintly, in the transmitted pencil. Hence it follows as a
general result, that as all reflecting surfaces are the separating
surfaces of two media, the pencils which they reflect and trans-
mit must necessarily have a diff'erent tint from the incident
pencil, excepting in the extreme case, and one not known to
exist, where the two bodies in contact have the same refractive
power, or the same differences of refractive power for every ray
of the spectrum.

Hitherto we have supposed the irrationality of the coloured
spaces to be simple, but it may be compound, and there may
be two, three, or more points in the spectrum of two adjacent
media where the indices of refraction are the same, or have
equal diff'erences, while in other points they are not the same,
or have their diff'erences unequal. In these cases the reflected
and transmitted tints will be compound ; but as such colours
have not been observed, it would be out of place to make any
farther reference to such a supposition. It may be sufficient to
remark, that even if we never discover spectra of such a char-
acter, they may exist in the refractions at the separating sur-
faces of the tinging corpuscles of Newton, and the media which
fill their interstices.

In the sixth class of colours may be ranked those produced

1 In- his Memoir on Diffraction, Fresnel has thrown out the idea that, at great inci-
dences, and with very thin laminae, the law of refraction may not follow the proportion-
ality of the sines.

1675-76.

LIFE OF SIR ISAAC NEWTON.

165

by heat in metals and other substances, the colours of different
bodies in combustion, and those exhibited in the deflagration of
metals. There is no reason to believe that any of these colours
have the slightest analogy with those of thin plates, and their
nature and origin remain to be investigated.

The colours of metals, which form the seventh class in our
enumeration, have been referred by Newton to those of thin
plates, but without any plausible reason. The polarization of
light by metallic bodies required to be investigated before the
problem of their colour could be solved, and we owe its solution
to the recent and beautiful researches of M. Jamin. As it would
be foreign to the character of the present work to give an
account of the process by which M. Jamin obtained his results,
we must content ourselves with presenting them in the following
Table :—

coronas aitbe onb refiexion.

Copper, . .

Orange, very red,

69»

56'

0-113

Brass, .

Yellow,

103

0112

Bell metal, .

Orange, yellow, .

0065

Speculum metal, .

Orange, very red.

0-027

Zinc,

Blue, ....

. 180

021

Silver, .

Orange, yellow, .

0-013

j Steel, .

White, . . .

)10UE8 AFTBE TEN BBFLEXIONS.

—

• Copper,

Red, middle.

42°

29'

0-812

Brass, .

Orange, very red.

0-349

Bell metal.

Red, ....

0-767

Speculum metal, .

Red, orange.

0-292

Zinc, . . .

Blue, indigo,

267

0.188

Silver, .

Orange, yellow, .

. 84

0-124

Steel, . . .

White, . . .

—

The numbers in the column marked d are the distances of
the tint of the metal from the red end of the spectrum, whose
whole length is 360° ; and those under the letter c are the
intensities of the tints, that of the incident white light being
I'OOO.

After a careful study of these dififerent classes of colours.

166 ' LIFE OF SIE ISAAC NEWTON. CHAP. VIII.

philosophers will have no hesitation in concluding that Newton's
theory of the colours of natural bodies has only a limited appli-
cation, and that instead of any general theory such as he
contemplated, we must look for a separate explanation of the
different classes of phenomena. The first class of our enumera-
tion, which comprehends the largest number of coloured bodies,
is the one which presents the greatest difficulty to philosophers ;
and to it the Newtonian hypothesis is certainly inapplicable.
Within the solids, fluids, and gases of this class, certain rays of
the intromitted pencil are absorbed or lost, while others are
transmitted, or, what is the same thing, the coloured body has
different degrees of transparency for different rays, being opaque
for different portions of the spectrum at different thicknesses ;
whereas, in colourless bodies, the rays are absorbed in equal
proportions, so that the transmitted beam emerges colourless.
The colour of a body, therefore, is not produced by particles
having the same colour as itself, but it is the colour v/hich
arises from the mixture of all the transmitted rays, and these
rays proceed from every part of the spectrum, though in different
proportions. Hence we must look for the cause of the colour
in the constitution of the body itself, that is, in the manner in
which its atoms are combined, and not in the size or nature of
the atoms themselves.

In support and in illustration of this opinion, we may mention
a few remarkable examples, in which the colour is changed by
a change in the condition of its particles. The most remarkable
of these is nitrous gas. This body is almost transparent in small
thicknesses, and at low temperatures. By heating it, its colour
becomes in succession straw yellow, orange, red, and even abso-
lutely hlack.'^ When phosphorus, which in its ordinary state
is of a pale yellow colour, is melted and thrown into cold water,
it becomes hlach, and recovers its original colour when again
melted. It is therefore obvious, that in both these cases the
blackness could not be produced by any diminution in the size

1 See Edinburgh Transactions, Tol. xii. p. 523.

1675-76. LIFE OF SIR ISAAC NEWTON. 167

of the particles. A similar change of colour is produced by
simple mechanical pressure on the crystals of iodide of mercury^
which change their colour by simply pricking them with a sharp
point.

The various phenomena of colour in crystallized bodies, and
the influence of the continued action of light upon coloured sub-
stances, indicate the existence of different causes of colour ; and
the influence of structure, as one of these causes, is finely shown
in the relation of the colours of dichroitic crystals to their axes
of double refraction or crystallization.

The great diversity in the constitution of coloured bodies is
peculiarly shown in the diversity of their action on the difi'erent
rays of the spectrum ; and it is therefore probable that the cause
of their difference of colour may be found in the diversity of
action exercised upon light by their particles or elementary
atoms. In describing the colours of the ffth class, we have
already mentioned an experiment with flint glass and oil of
cassia, and its indication of a new theoiy of the colours of natural
bodies of the first class. In Fraunhofer's spectrum, the principal
black lines which it contains are represented by the letters a, b,
c, D, E, F, G, H, I ; — Ai being nearly the whole of its length.
If a, h, c, d, e, /, g, h, i, represent the same lines in a spectrum
of equal length formed by any fluid or solid different from that
which produces the spectrum a i, then though ai he equal to ai,
it frequently happens, and we venture to say, always happens,
that a 6 is not equal to ab, nor cf to cf, while ac maybe equal
to AC, and dh to dh. The equal spectra may coincide in par-
ticular points, that is, individual lines in the one, indicating
particular colours, may coincide with individual lines marking
the same colours in the other spectrum; and yet other lines may
not coincide, indicating different colours. When a ray of white
light, therefore, is incident on the separating surface of the two
media which give these two spectra, a very large portion, or
rather the whole of the colours, indicated by the coincident
lines, will be transmitted, while a very small portion of the

168 LIFE OF SIR ISAAC NEWTON. CHAP. VIII.

colours indicated by the non-coincident lines will be reflected,
the greatest quantity of the colours being reflected where the
non-coincidence is greatest, and the greatest quantity being
transmitted at the points of coincidence. Where there are many
separating surfaces, and many elements in the body, the spectrum
obtained by the prismatic analysis of the transmitted light will
be cut up by obscure portions exactly as it is found to be in all
coloured media.

When the constitution of any coloured body is altered by heat
or pressure, the refractive and dispersive powers of its elements
are changed, and the resulting colour altered, according to the
ratio in which the refracting forces are changed in the elementary
molecules. Changes of this kind are finely exhibited in the
growth of certain coloured crystals. In the tourmaline, for
example, we have sometimes a red nucleus which absorbs one
of the doubly refracted pencils, namely, the green one, and
transmits only the red. When this nucleus was completed,
some change had taken place in the circumstances under which
the crystallization was proceeding, and the molecules, though
still combining as tourmaline, combine in such a manner as to
produce no colour — no difference in the tint of the pencils — and
no absorption of one of them. At a subsequent stage, the
structure which produces the red colour again appears and dis-
appears, forming in succession coloured and colourless laminae
round the original nucleus !

Another example of great interest is afforded by certain spe-
cimens of fluor spar, in which the colours of the fourth class
are produced.^ The structure which produces a white phosphor-
escence, is succeeded by one which produces a coloured phos-
phorescence, and this again by a structure which produces no
phosphorescence at all. The changes of structure to which these
different effects are owing, arise, in all probability, from a change
in the arrangement of the atoms in the molecular groups of
which the body is composed.

1 See Edinburgh Tramactioiu, vol. xtL p. 112.

1672. LIFE OF SIR ISAAC NEWTON. 169

CHAPTER IX.

Newton's Discoveries on the Inflexion of Light— Previous Researches of Hooke— New-
ton's Animadversions on them offensive to Hooke — Newton's Theory of Inflexion as
described by Grimaldi, having made no experiments of his own — Discoveries of
Grimaldi, which anticipate those of Hooke— Hooke suggests the Doctrine of Inter-
ference — Newton's Experiments on Inflexion — His Views upon the Subject unsettled
— Modern Researches — Dr. Young discovers the Law of Interference — Discoveries of
Fresnel and Arago — Fraunhofer's Experiments — Diffraction by Grooved Surfaces —
Diffraction by Transparent Lines— Phenomena of Negative Diffraction— Experiments
and Discoveries of Lord Brougham— Explanation of Diffraction by the Undulatory
Theory.

Among the optical discoveries of Newton, those which he
made on the inflexion of light hold a high place. They were
first published in his Treatise on Optics in 1704, but we have
not been able to ascertain at what period they were made. In
the preface to this work, Sir Isaac informs us, that the third
book, which contains his experiments on inflexion, "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 we were then inter-
rupted, and cannot now think of taking these things into
consideration."

The earliest notice of the inflexion of light by English philo-
sophers was taken by Dr. Hooke in a discourse read to the
Royal Society on the 27th November 1672, "containing diverse
optical trials made by himself, which seemed to discover some
new properties of light, and to exhibit several phenomena in

170 LIFE OF SIR ISAAC NEWTON. CHAP. IX.

his opinion not ascribable to reflection or refraction, or any-
other till then known properties of light." The Society desired
him to pursue these experiments, and to register some account
of them, in order "to preserve his discoveries from being
usurped."

After an interval of more than two years, he communicated
to the Society a second discourse " on the nature and properties
of light, in which were contamed several new properties of
light, not observed that he knew of by optical writers." These
properties were, —

" 1. That there is an inflexion of light differing both from
refraction and reflexion, and seeming to depend upon the un-
equal density of the constituent parts of the ray, whereby the
light is dispersed from the place of condensation, and rarefied,
or gradually diverged into a quadrant.

" 2. That this deflexion is made towards the superficies of
the opaque body perpendicularly.

" 3. That in this deflexion of the rays, those parts of
diverged radiation that are deflected by the greatest angle from
the strait or direct radiations are faintest ; those that are
deflected by the least are the strongest.

" 4. That rays cutting each other in one common foramen,
do not make the angles ad verticem equal.

" 5. That colours may be made without refraction.

*' 6. That the true bigness of the sun's diameter cannot be
taken with common sights.

" 7. That the same rays of light falling upon the same point
of the object will turn into all sorts of colours, only by the
various inclination of the object.

" 8. That colours begin to appear when two pulses of light
are blended so very well and near together, that the sense takes
them for one."^

These observations of Hooke on the Inflexion of Light, were

1 See Birch's Hist. Royal Society, voL iil pp 63, 194, and Hooke' a Posthumous Works,

pp. 186-190.

1672-75. LIFE OF SIR ISAAC NEWTON. 171

referred to, not very courteously, by Sir Isaac Newton, at the
close of the celebrated Discourse on Colours, of which we have
already given an account. After treating of the colours of
natural bodies, he says, " that there is another strange pheno-
menon of colours which may deserve to be taken notice of.
Mr. Hooke," he adds, " you may remember, was speaking of
an odd straying of light, caused in its passage near the edge of
a razor, knife, or other opaque body, in a dark room ; the rays
which pass very near the edge being thereby made to stray at
all angles into the shadow of the knife. To this Sir William
Petty, then President, returned a very pertinent query, —
Whether that straying was in curve lines ? and that made me
(having heard Mr. Hooke, some days before, compare it to the
straying of sound into the quiescent medium) say, that I took
it to be only a new kind of refraction, caused perhaps by the
external ether's beginning to grow rarer a little before it came
at the opaque body, than it was in free spaces, the denser
ether without the body, and the rarer within it, being termi-
nated not in a mathematical superficies, but passing into one
another through all intermediate degrees of density ; whence
the rays that pass so near the body, as to come within that
compass where the outward ether begins to grow rarer, must
be refracted by the uneven denseness thereof, and bended in-
wards towards the rarer medium of the body. To this Mr.
Hooke was then pleased to answer, that though it should be
but a new kind of refraction, yet it was a new one. What to
make of this unexpected reply I knew not, — having no other
thoughts but that a new kind of refraction might be as noble
an invention as any thing else about light ; but it made me
afterwards, I know not upon what occasion, happen to say,
among some who were present to what passed before, that I
thought I had seen the experiment before in some Italian author.
And the author is Honoratus Faber, in his dialogue De Lumine,
who had it from Grimaldi, whom I mention because I am to
describe something further out of him."

172 LIFE OF SIR ISAAC NEWTON. CHAP. IX.

This passage, which must have been very offensive to Hooke,
may be fairly adduced as affording an additional apology for
his statement that Newton had, in his Discourse, only carried
farther, in some particulars, what was contained in his Muyro-
gvaphia. We have no doubt that Hooke discovered the
inflexion of lights without knowing anything of the previous
experiments of Grimaldi. Hooke was right in calling his
discovery a new property of light, and Newton was wrong in
calling it " 07ily a new kind of refraction," — thus stripping it
of much of its value, and placing it in the same category with
his own discoveries. Hooke felt the bitterness of the remark,
and with more temper than might have been expected, replied,
*' that though it should be hut a new hind of refraction^ yet it
was a new one ;'"' thus taking to himself the credit of making
a new discovery even when reduced in importance by another
designation. Newton confesses that he knew not what to
make of this unexpected reply. The reply was a proper one,
and might have been expected ; but though Newton felt its
full significance, he had not the readiness to make the explana-
tion which it required, and which he subsequently gave. He
had no thoughts, he afterwards said, of undervaluing the dis-
covery of a property of light by calling it "a new kind of
refraction ; " yet he did not give this explanation till he had
ascertained that the new property had been previously discovered
by Grimaldi ; and though he now gave its true value to the
new discovery, he but embittered the admission when he an-
nounced to the Society, that the discovery belonged to an
Italian philosopher. On a former occasion, Newton had un-
necessarily claimed for Descartes some of Hooke's theoretical
opinions ; and when a similar claim was made for Grimaldi,
Hooke could not but feel the unkindness of his rival Nearly
two centuries have elapsed since these controversies raged ; and
it is not without its moral in intellectual strife, nor yet with-
out, its consolation to the humbler cultivators of science, that
while Newton's Theory of the Inflexion of Light is maintained

1675. LIFE OF SIR ISAAC NEWTON. 173

by nobody, the Theory of Hooke, imperfect as it is, is adopted
by the greater number of modern philosophers.

It is obvious from these details, that Newton had at this
time made no important experiments on the Inflexion of Light.
" He propounded his theory with diffidence," as he had " not
made sufficient observation about it." It is equally obvious
that he had not seen the work of Grimaldi,^ which he quoted
from Honoratus Faber, although a copy of the work had been
three years in the possession of the Koyal Society, or at least
of their secretary, Mr. Oldenburg, who published an analysis of
it in the Philosophical Transactions for January 22, 1671-72.
The analysis, indeed, is a very imperfect one, in so far as it
refers to the diffraction of light, and could scarcely have led
Hooke to his discovery, even if he had perused it with atten-
tion. " The author," says the reviewer, " explains how many
ways light is propagated or diff'used, viz., not only directly, and
by refraction and reflexion, but also by diffraction ; which last,
according to him, is done when the parts of light, separated by
a manifold dissection, do in the same medium proceed in dif-
ferent ways," — a definition of diffraction which Newton could
scarcely have comprehended, and which, if he had, he would
not have accepted.

That Newton had not seen Grimaldi's work in 1675, is
avowed by himself ; and there is every reason to believe that
he had not even seen it in 1704, when he published his Optics.
If he had seen it, and was aware of the discoveries which it
contains, he has not only done great injustice to the Italian
philosopher, but neglected the opportunity which it aff'orded
him of anticipating the discoveries of his successors. In the
third book of his Optics, he gives to Grimaldi the credit merely
of having observed that the shadows of all bodies, placed in
light let into a dark room through a small hole, were larger
than they ought to be, and that these shadows had three

1 Physico-Mathesis de Lumine, Cokribiis, et Iride, aliisque annexis. Bononiae,
166.5. 4to.

174 LIFE OF SIR ISAAC NEWTON. CHAP. IX.

parallel fringes of coloured light adjacent to them, whereas
the Italian philosopher had penetrated more deeply into the
subject, and obtained, as we shall now see, very important
results.

Having admitted a ray of light through a small hole into a
dark room, Grimaldi observed that it was diffused in the form
of a cone, and that all bodies placed in this light had their
shadows larger than they should have been had the light passed
by their edges in straight lines. Upon a closer examination of
these shadows, he discovered that they were surrounded by
three coloured fringes, growing narrower as they receded from
the shadow. When the sun's light was strong, he perceived
similar coloured fringes within the shadow of narrow bodies like
a needle. These fringes were sometimes only two in number,
and sometimes four, their number increasing and their size
diminishing with the thickness of the body, and also, in the
same shadow, when it was received on a sheet of paper at a
greater distance from the body. From these new and valuable
facts Grimaldi concluded that light is bent from its rectilineal
direction in passing by the edges of bodies. By admitting the
sun's rays through two small holes, so near each other that the
two cones of light which they produced did not penetrate each
other till they had reached to a considerable distance from the
two holes, Grimaldi discovered the remarkable fact, that in
consequence of the mutual interference of the two cones of light,
the spot which was illuminated by both the pencils of light
was more obscure than when it was illuminated by either of
them singly, or, what is the same thing, " that a body actually
illuminated may become more obscure by adding a light to
that which it already receives." Grimaldi discovered also the
beautiful phenomenon of the crested, or curved fringes exhibited
within the shadow of the rectangular termination of bodies.

Although Hooke was anticipated by Grimaldi in the greater
number of his observations, yet he is clearly entitled to share
with the Italian philosopher in the discovery of the doctrine of

1675. LIFE OF SIR ISAAC NEWTON. ' 175

the interference of light, though it was left to Dr. Thomas
Young to complete the discovery.

Such was the state of the subject of Inflexion when Newton
directed to it his powers of acute and accurate observation.
His attention, however, was turned only to the enlargement of
the shadow of inflecting bodies, and to the three fringes adjacent
to it. He was therefore led to take exact measures of the
shadow of a human hair, and of the breadth of the fringes at
different distances behind it, and to repeat these observations
with light of diflerent colours. In this way he was led to two
new and remarkable results.

1. That these breadths were not proportional to the distances
at which they were measured ; and,

2. That the fringes made in homogeneous red light were red^
and the largest ; that those made in violet light were violet^ and
the smallest ; and that those made in green light were green^
and of an intermediate size, the rays which formed the red
fringe passing by the hak at a greater distance than those
which formed the violet.

When Newton made the preceding observations, he intended
to repeat most of them with more care, and to make " some
new ones, to determine the manner how the rays of light are
bent in their passage by bodies ;" but having been then inter-
rupted, he could not think of resuming the inquiry.

It is very difficult to ascertain his real views on the subject
of inflexion. In his Discourse, read in 1675, he ascribes it to
the variable density of the ether within and without the inflect-
ing body, thus regarding it as a new species of refraction ; and
in his letter to Robert Boyle in 1679, he takes the same view
of the subject, and considers the several colours of the fringes
as produced " by that refraction." Pursuing the same idea, he
asserts in the Scholium to the 96th Prop, of the first book of
the Principia, that the rays of light, in passing near bodies, are
bent round them as if by attraction ; that the rays which pass
nearest them are most bent, as if they were most attracted ;

176 LIFE OF SIR ISAAC NEWTON. CHAP. IX.

that those which pass at a greater distance are less bent ; and
that those which pass at still greater distances, are bent in an
opposite direction.

In this remarkable passage, Newton introduces, for the first
time, the idea of a force bending the rays ; or of an inflecting
force bending the rays inwards, accompanied with a deflecting
force bending them outwards. This opinion, however, he sub-
sequently abandoned ; for in the third book of his Optics, he
refers all the phenomena to a force which " bends the rays not
towards, but from the shadow ;" and he distinctly asserts,
" that light is never known to follow crooked passages, nor to
bend into the shadoiv."

These erroneous opinions, now wholly exploded, arose from
Newton's having never observed the internal fringes, or those
seen within the shadow. Grimaldi had described them minutely
in his work, and, as they have been seen by every philosopher,
it is not easy to explain how they should have escaped the
notice of two such careful observers as Hooke and Newton.
Without this cardinal fact our author stumbled in his path,
and was misled into the erroneous propositions that bodies act
upon light at a distance ; — that this action bends in rays with
a force diminishing with the distance ; — and that rays which
differ in refrangibility differ also in flexibility. Nor was he
nearer the truth, when he conjectured in his third query that
the rays of light, in passing by the edges of bodies, may be
bent several times backwards and forwards with a motion like
that of an eel, and that the three fringes of coloured light may
arise from three such bendings.

A subject which had thus baffled the sagacity of Newton,
was not likely to unfold its mysteries to ordinary observers.
The experiments of Grimaldi and Newton were repeated by
various philosophers in various lands. Observations better
made, and measures more accurately taken, were continually
accumulating. A Pelion of inferences was heaped upon an
Ossa of facts, but no Baconian conjurer could elicit from them

1801-18. LIFE OF SIR ISAAC NEWTON. 177

the vital spark. The cardinal facts were still wanting, and a
century passed away before a single experiment dissipated the
inflexion theories of a graduated ether, of refracting atmo-
spheres, and molecular actions. This humble experiment,
which neither merits nor claims any particular notice, was, we
believe, first made by ourselves in 1798, and afterwards, ex-
tended in 1812 and 1813. We found that ice, cork, metals,
and diamond, the lightest and the heaviest bodies, the least
refractive and the most refractive substances, produced exactly
the same fringes ; and that no change in the phenomena of
inflexion was produced when a fibre of an opaque body was
placed in fluids of precisely the same or of greater refractive
power. Hence it followed that the light which passed by the
edges of bodies was not inflected by any refracting agent, or by
any action whatever of the bodies themselves.

It is to Dr. Thomas Young, however, that we owe the master
fact which enabled philosophers to unveil the mysteries of
diffraction, and to account for a great variety of hitherto un-
explained phenomena. In studying the internal fringes, and
the crested ones discovered by Grimaldi, he found that, by in-
tercepting the rays which passed by one side of the diffracting
body, the internal and the crested fringes completely disappeared ;
and hence he concluded that the fringes were produced by the
joint action, or by the interference, of the two portions of light
which passed on each side of the diff'racting body.

Having thus discovered the cause of the internal fringes,
Dr. Young directed his attention to the external ones. He
considered them as produced by the interference of the direct
rays, or " those which have pursued their course without inter-
ruption," with those which are reflected from the margin of the
diffracting body ; and as the fringes are on this supposition
formed by light " turned away from the substance near which
it passes," he has characterized the phenomenon as one of de-
'^ected light.

M. Fresnel, to whose fine researches we owe the best ex-

VOL. L M

178 LIFE or SIR ISAAC NEWTON. CHAP. IX.

periments on diffraction, and the most perfect theory of it,
followed Dr. Young in ascribing the external fringes to the
influence of light reflected from the edge of the diffracting
body, — an opinion which we never could reconcile with the
palpable fact, that the fringes had always the same character,
whatever was the reflecting power, or the shape of the edge of
the body. Fresnel, influenced no doubt by the same considera-
tion, suggested a diSerent origin for the rays which interfere
with the direct ones, namely, that the rays which pass at a
sensible distance from the diff'racting body deviate from their
primitive direction towards the shadow, and thus interfere -with
the direct rays that pass near the body. In comparing these
two hypotheses, and assuming with Dr. Young that half an
undulation was lost by the reflected rays, he found that the
real place of the fringe, on the hypothesis of a reflection, would
be xVo^^^ ^^ ^ millimetre diff'erent from what it really was.

In conducting his experiments on difl'raction, Fresnel adopted
a new and accurate method of observing and measuring the
fringes. In place of using a small hole, he employed a convex
lens of short focal length, which collected the solar rays into
a focus, from which they again diverged, as if they had pro-
ceeded from a small aperture.^ When bodies were placed
in this divergent light, he examined the fringes adjacent to
their shadows by means of an eye-glass furnished with a micro-
meter, instead of receiving them upon a white surface ; and he
was thus able to measure their breadths even to the one hundred
or two hundredth part of a millimetre. In this way he traced
the external fringes to their origin, and with a lens of short
focus he perceived the third fringe at a distance of less than
the one-hundredth part of a millimetre from the edge of the
inflecting body.

By measuring the angular inflection of homogeneous red
light, when the radiant point was placed at different distances

J A concave lens is preferable to a convex one, for reasons which will presently be
seen ; and we recommend that it should be achromatic.

1801-18. LIFE OF SIE ISAAC NEWTON. 179

in front of the diJEfracting body, and also when the radiant
point remained fixed at different distances of the fringes behind
the inflecting body, he was led to two important discoveries — :

1. That the angular inflexion diminishes with the distance
of the inflecting body from the radiant point ; and,

2. That when the radiant point remains fixed, the successive
positions of the same fringe are not in a straight line, but form
a curve whose concavity is turned towards the diffracting
body,^ the curves being hyperbolas, having for their common
foci the radiant point and the edge of the diffracting body.^

The discovery of Dr. Young, that an opaque screen, on one
side of the inflecting body, extingiiished the interior fringes,
was extended by M. Arago, who found that the same effect is
produced by a transparent screen of sufficient thickness, and
that thin screens merely displace the fringes, and transfer them
from the side where they were formed. When such a screen
is placed on each side of the diffracting body, the effect is
equal to the difference of the transferences which each screen
would have produced separately. As the amount of this trans-
ference may be computed theoretically from the thickness and
refractive power of the screen, MM. Arago and Fresnel em-
ployed this method for measuring, with great exactness, the
refractive power of gases.

The late M. Fraunhofer of Munich made a series of experi-
ments on the diffraction of light on a large scale, and obtained
many interesting results. The experiments were made with a
telescope, which enabled him to obtain accurate measures of the
fringes or rings produced by apertures of various forms ; and he
has published beautiful drawings of the spectra, and groups of
spectra produced by a great number of diffracted rays, — by
small apertures variously arranged, and by wire-gratings either
acting singly, or crossed at right angles.

1 This result had been previously obtained by Sir Isaac Newton.

2 The hyperbolic form of the fringes had been previously discovered by Dr. Young.—
Led,, vol. i. p. 287.

180 LIFE OF SIR ISAAC NEWTON. CHAP. IX.

We have had occasion to study some of the same phenomena,
when produced by lines cut upon polished steel with a diamond.
The grooved surfaces which we employed were executed for us
by the late Sir John Barton, and contained groups of lines
varying from 500 to 10,000 in an inch. When divergent
light was reflected from these surfaces, the central image formed
by ordinary reflexion from the original surface of the steel-plate
was, in general, white, as observed in every case by Fraunhofer
and others, and the other spectra had their usual character.
But when the bright spaces in the plate, or those between the
grooves had a certain relation to the width of the groove, or the
part of the steel that was excavated by the diamond point, a
series of new and remarkable phenomena were produced. The
light reflected from the original surface of the steel forming the
central image was no longer white, but coloured, the colour
varying with the angle of incidence at which the steel-plate
received the divergent beam. In some of the groups of lines,
the colour varied slightly from 0° to 90° of incidence. In
others, it passed through the first order of colours ; and in
others, where the original steel surface was nearly removed, it
passed through three or more orders of tints. The light which
is obliterated from the central image, at any angle of incidence,
or the complementary colour of the tint at that angle, is ob-
literated also from all the coloured spectra at less angles of
incidence, the angle diminishing with the distance of the spec-
trum from the central one, and being less in each spectrum for
tlie less refrangible rays.

If we cover the surface of the grooved steel with a fluid so
as to reduce the refractive power of its surface, we develop
more orders of colours on the ivhite or central image, and con-
sequently on all the spectra, higher tints being produced at a
given incidence. But what is very remarkable, when the central
image is perfectly white, and when the spectra are complete
without any obliteration of their tints, the application of fluids
to the grooved surface develops colours on the central or whit€

1829. LIFE OF SIR ISAAC NEWTON, 181

image, and a corresponding obliteration of tints in the coloured
spectra.^

In the experiments hitherto made on diffraction, the lines
employed have been opaque, such as wires, hairs, or fibres of
glass, which act upon light as if they were opaque. A series of
beautifid phenomena are produced when we employ transparent
lines drawn upon glass with solutions of gums of different
kinds, and different degrees of strength. A section of these
transparent lines varies with the nature and density of the
solution, though it is generally thicker at its edges. The con-
sequence of this is, that the light which passes through the
transparent line not only interferes with that which passes on
each sido of it, but also with part of the light which has its
direction changed by the refraction of its curvilineal edges.
Hence it follows, that a series of new interferences takes place,
and we accordingly have a splendid display of coloured fringes
infinitely surpassing in variety and brilliancy of colour the ordi-
nary phenomena of diffraction. ^

In all the experiments on inflexion and diffraction made by
Newton and Fresnel, the fringes were viewed either on paper,
or in the focus of a lens when the rays had actually interfered
and produced the coloured fringes. The fringes thus seen may
be called positive, because they are formed in space and out of
the eye, on the retina of which they are afterwards delineated ;
but there is another form of these fringes, which I have exa-
mined, and which may be called negative, because they are not
brought to a positive focus in space, or do not interfere till
they reach the retina. In order to see these fringes, place the
lens behind the diffracting body, so as to see the jjositive fringes,
and then move it forward till these fringes disappear. The
diffracting edge will now be in the anterior focus of the lens.

1 See the Phil. Trans. 1829, pp. 301-317.

- These effects are so beautiful, that we have recommended the use of a diffracting
apparatus for suggesting patterns for ribands. — See Rexwrts of British Association, 1838,
vol. vii. p. 12 ; Treatise on Optics, Edit. 1853, p. 117.

182 LIFE OF SIR ISAAC NEWTON. CHAP. IX.

If we advance tlie lens towards the diffracting body, the negative
fringes will appear, and will increase in size till the lens touches
the body, when they will have the same magnitude as the
positive fringes have when the lens is placed behind the body,
at the distance of twice its focal length.

If we wish to see the fringes larger, we must use a lens
with a longer focus ; and when it is placed in contact with the
diffracting body, the fringes will in every case be the same as
the positive ones seen by the same lens placed behind the body
twice its focal length. If the diffracting body is included in a
fluid lens, or even placed in front of tlie lens, the negative
fringes will be seen. In producing the negative fringes, the
interfering rays are those which virtually radiate from the
anterior focus of the lens, and which being refracted into
parallel directions, enter the eye, and interfere on the retina ;
and in consequence of their not interfering till they enter the
eye, they are much more distinct than the positive fringes.^

The most recent experiments on the inflexion of light have
been made by Lord Brougham, who had investigated the sub-
ject so early a.s 1796, and given an account of his experiments
in two interesting papers printed in the Philosophical Transac-
tions. ^ These investigations were published before Dr. Young
discovered the key to this class of phenomena, and before Fresnel
had explained them on the principles of the undulatory theory.
In his early papers. Lord Brougham considered the phenomena
as produced by inflecting and deflecting forces emanating from
the diffracting body, and acting, as Newton supposed, upon the
passing rays ; but in his recent researches he has used these
terms merely for the purpose of making the narrative shorter
and more distinct, and has avoided all arguments and sugges-
tions relating to the two rival theories.

The recent investigations of Lord Brougham were carried on
under the clear sky of Provence, and with an excellent set of

1 See Reports of British Association, vol. Tii. p. 12. 1838.

2 Phil. Trans. 1796, p. 227 ; and 1797, p. 852.

1850. LIFE OF SIR ISAAC NEWTON. 183

instruments constructed by M, Soleil of Paris. It would be
impossible, without diagrams, to make them intelligible to the
general reader, but some idea may be formed of the originality
and importance of his discoveries from the two following pro-
positions, which relate to a new property of the inflected and
deflected rays : —

1. " The rays of light, when inflected by bodies near which
they pass, are thrown into a condition or state which disposes
them to be on one of their sides more easily deflected than
before their first flexion, and disposes them on the other side to
be less easily deflected ; and when deflected by bodies, they are
thrown into a condition or state which disposes them on one
side to be more easily inflected, and on the other side to b^less
easily inflected than they v/ere before the first flexion.

2. " The rays disposed on one side by the first flexion are
polarized ^ on that side by the second flexion ; and the rays
polarized on the other side by the first flexion, are depolarized
and disposed on that side by the second flexion."'^ In con-
tinuing his researches. Lord Brougham was led to conclude that
the rays of light difler in deflexibility and inflexibility, the
least refrangible being the most flexible ; the law of different
flexibility having this peculiarity, that the fringes or images
by flexion are not rectilineal but curvilineal from the extreme
violet to the extreme red.

Whatever opinion we may form of the undulatory theory in
its physical aspect, the explanation which it afl'ords of a vast
variety of optical phenomena, entitles it to the highest con-
sideration. With the exception of Lord Brougham's discoveries,
and the peculiar colours on the central image formed by
grooved surfaces, to which we have already referred, the undu-
latory theory gives a satisfactory explanation of the leading phe-
nomena of diff'raction, while the Newtonian or atomical hypothesis
has not even ventured to suggest a probable explanation.

1 Lord Brougham uses the term polarization " merely because the effect of the first
edge resembles polarization, and without giving any opinion as to its identity."

2 Phil. Trans. 1850 ,pp. 235-260.

184 LIFE OF SIR ISAAC NEWTON. CHAP. X.

CHAPTER X.

Miscellaneous Optical Researches of Newton— His Experiments on the Absolute Refrac-
tive Powers of Bodies— More recent Experiments — His Conjecture respecting the
Inflammability of the Diamond confirmed by more direct Experiments — His Errone-
ous Law of Double Refraction — His Observations on the Polarity of Double Refracted
Pencils — Discveries on Double Refraction in the present Century — His Experiments
on the eye of a Sheep — Results of them— His three Letters on Briggs's New Theory of
Vision — His Theory of the Semi-Decussation of the Optic Nerves — Partly anticipated
by Rohault — Opinions of later writers on Vision, of Reid, Brown, Wollaston, Twin-
ing, and Alison, dlscus^sed — The true laws of Sensation and Vision — Newton's Observa-
tions on the Impression of Strong Light upon the Retina — More recent Observations
—His Reflecting Sextant — His Reflecting Microscope — His Reflecting Prism for
Reflecting Telescopes — His Method of Varying the Magnifying Power of Newtonian
Telescopes — Newton's Treatise on Optics — His Lectiones Opticge.

Although the discoveries described in the preceding chap-
ters are those on which Newton's reputation in optics chiefly
rests, yet it is necessary to notice some of his less elaborate
researches, which, though of inferior importance in the science
of light, have either exercised an influence over the progress of
discovery, or have been associated with the history of other
branches of knowledge.

In the second book of his Optics,^ Newton proves, with
much fulness of detail, that " the cause of reflexion is not the
impinging of light on the solid or impervious parts of bodies, as
is commonly believed ;" and that " bodies reflect and refract
light by one and the same power variously exercised in various
circumstances." He then proceeds to show, that " if light be
swifter in bodies than in vacuo, in the proportion of the sines
which measure the refraction of the bodies, the forces of the bodies
to reflect and refract light are very nearly proportional to the

1 Part iii. Prop. viii. ix. &c.

1704. LIFE OF SIR ISAAC NEWTON. 185

densities of the same bodies, excepting that unctuous and sul-
phureous bodies refract more than others of the same density^
This remarkable exception led our author to point out the con-
nexion between the refractive powers and the chemical composi-
tion of bodies. Having obtained measures of the refractive
powers and densities, or specific gravities of twenty-two sub-
stances varying in density between air and diamond^ and
having computed their refracting forces, and compared them
with their densities, he calculated their refractive powers in
respect of their density. From this comparison he found that
topaz^ selenite, rock-crystaly Iceland spar, common glass, glass of
antimony, and air, have their refractive powers almost in the
same proportion as their densities, " excepting that the refrac-
tion of that strange substance, Iceland spar, is a little bigger
than the rest." — " Again," he adds, " the refraction of camphor,
olive oil, lintseed oil, spirit of turpentine, and amber, which are
fat sulphureous unctuous bodies, and diamond, which probably
is an unctuous substance coagulated, have their refractive
powers in proportion to one another as their densities, without
any considerable variation. But the refractive powers of these
imctuous substances are two or three times greater in respect
of their densities than the refractive powers of the former
substances are in respect of theirs. Water has a refractive
power in a middle degree between these two sorts of substances
.... salts of vitriol between those of earthy substances and
water, and spirit of wine between water and oily substances."
The foUowuio' are a few of the numbers in Newton's Table :

Refractive Power.

Pseudo topaz,! .

3,979

Rain water.

7,845

Air, .

5,208

Spirit of wine, .

10,121

Rock crystal, .

5,450

Oil of olives, .

12,607

Iceland crystal,

6,536

Amber, .

13,654

Rock salt,

6,477

Diamond,

14,556

To the results in this table we have added the following,,
computed chiefly from observations of our own, and interesting

1 Probably Sulphate qfBarptes.

186

LIFE OF SIR ISAAC NEWTON.

CHAP. X.

as being, mth the exception of three in italics^ below the lowest
and above the highest in Newton's Table : —

Refractive Power.

Tabasheer,

9T6

Realgar artificial.

16,666

Cryolite, .

2,742

Ambergris,

. IT.OOO

Fluor spar,

3,426

Sulphur, .

. 22,000

Sulphate of Barytes,

3,829

Phosphorus, .

. 28,857

Greenockite, .

12,861

Hydrogen,

. 29,964

Octohedrile, .

18,816

Hydrogen,

. 31,862

Diamond,

13,964

The enormous refractive powers possessed by the last six
bodies in the preceding table, when taken in connexion with
those given by Newton, exhibit in a striking degree the con-
nexion between a high degree of inflammability and a great
refracting force. The conjecture of Newton that the diamond
"is an unctuous substance coagulated," has been generally re-
garded as a proof of singular sagacity, and as an anticipation
of the results of chemical analysis ; but it is certainly not
entitled to such praise. Its solitary/ position among the oils
and inflammable bodies led to the conjecture ; but had he
known the refractive index and specific gravities of greenockite
and octohedrite, he would have drawn the same conclusion re-
specting them, and been mistaken. The real inference respect-
ing the composition of the diamond, which Newton's Table
authorizes, is not that it should consist of carbon, but of
siJphur. " So then," says he, " by the foregoing table, all
bodies seem to have their refractive powers proportional to
their densities (or very nearly), excepting so far as they partake
more or less of sulphureous oily particles, and thereby have
their refractive power made greater or less. Whence it seems
rational to attribute the refractive power of all bodies chiefly,
if not wholly, to the sulphureous particles with which they
abound. For it is probable that all bodies abound more or less
with sulphurs. And as light congregated by a burning glass
acts most upon sulphureous bodies, to turn them into tire and

1689, LIFE OF SIR ISAAC NEWTON, 187

flame ; so since all action is mutual, sulphurs ought to act most
upon light r^

That diamond is a soft substance coagulated^ has been
rendered probable by experiments of a more direct nature. We
have shown by the examination of a great number of diamonds
in polarized light, that the little cavities which many of them
contain, have been pressed outward by an elastic force emanat-
ing from some gas or fluid with which they had been filled.
Several such cavities we found in the Koh-i-noor diamond, and
in the two smaller ones which accompanied it ; and in a speci-
men in the British Museum, we found a yellow crystal of
diamond that had crystallized upon the cleavage surface of
another which was colourless, having been expelled from an
adjacent cavity, in which it had existed in a fluid state. 2

Among the more interesting optical researches of Newton,
we rank his observations on the double refraction and polariza-
tion of light. On the 12th of June 1689, when Huygens
was in England, during the presidency of Sir Robert Southwell,
he attended a meeting of the Royal Society, at which Newton
was present. Huygens informed the Society that he was about
to publish a treatise concerning the cause of gravity, and an-
other about refraction, giving, among other things, the reasons
of the doubly refracting Iceland crystal. " Mr. Newton, con-
sidering a piece of the Iceland crystal, did observe that of the
two species wherewith things do appear through that body, the
one suffered no refraction when the visual ray came parallel
to the oblique sides of the parallelopiped ; the other, as is
usual in all other transparent bodies, suff"ered more when the
beam came perpendicular to the planes through which the
object appeared."^ It is remarkable that this observation of
Newton, which had been made long before by Bartholinus, as

1 Optics, Book ii. Part iiL Prop. x.

2 See Transactions oj the Geological Society, 2d Series, vol. iil. p. 455 ; and North
British Review, vol. xviii. p. 227.

8 Journal Booh of the Royal Society.

188 LIFE OF SIR ISAAC NEWTON. CHAP. X.

Huygens knew at the time, and as the Royal Society ought to
have known,^ should not have been claimed for that author.

In the admirable Treatise on Light, to which Huygens re-
ferred at the Royal Society, and which was published in 1690,
he has shown that the observation of Bartholinus, adopted by
Newton, is erroneous,2 and has explained the law of tmusual
refraction^ as exhibited in one of the two pencils formed by the
double refraction of Iceland or calcareous spar. This law he
deduced from the principles of the undulatory theory, and he
confirmed it by direct experiment. Viewing it probably as a
theoretical result, Newton seems to have regarded it as incor-
rect, and though he has given Huygens the credit of describing
the phenomena more exactly than Bartholinus, who first dis-
covered and described the remarkable property of this spar, yet
without assigning any reason, or even referring to the law of
Huygens, he substitutes another in its place. The observations
of Newton were first published in his Optics m 1704,^ fourteen
years after the appearance of Huygens's work. The law of
unusual refraction, adopted by Newton, is not given as the result
of theory. It is stated as an undoubted truth, and no experi-
ments whatever are referred to as having been made either by
himself or others. " One of these refractions," he says, " is
performed by the usual rule of optics, the sine of incidence out
of air into this crystal being to the sine of refraction as five to
three. The other refraction, which may be called the unusual^
refraction, is 'performed hy the following riiUy This rule was
first sh(jwn to be erroneous by the Abb^ Hauy,^ and it has been
rejected by all succeeding philosophers.6

In his observations on the successive disappearance and re-

1 It was published in the 'PUl. Trans. 1671, p. 2039.

2 TraiU de la Lumiere, chap. v. p. 67 ; and Maseres' Scripiores Optica, p. 234.

3 Query 25th and 26th at the end of the work.

* The term unusual, and the ratio of the sines, viz., 5 to 3, were given by Bartholinus
in the abstract of his Paper in the Phil. Traits. No, 67, Jan. 1670-1, pp. 20, 39.

5 TraM de Mineralogk, torn. i. p. 159, Note.

6 Hauy's Elements of Nat. Phil, by Gregory, vol. 11. p. 337.

1704-1810. LIFE OP SIR ISAAC NEWTON. 189

appearance of two of the four images which are formed when
a luminous object is viewed through two rhombs of Iceland
spar, one of which is made to revolve upon the other, Newton
has been more successful, though he has omitted to give to
Huygens the credit of having discovered these curious pheno-
mena. He considers " every ray of light as having four sides
or quarters, two of which are originally endued with the pro-
perty on which the unusual refraction depends, and the other
two opposite sides not endued with that property ;" and he
adds, that " it remains to be inquired whether there are not
more properties of light by which the sides of the rays differ,
and are distinguished from one another."

In animadverting on Huygens' s theory of two vibrating media
within the Iceland crystal, he asserts that the unusual refrac-
tion depends " not on new modifications, but on the original
and unchangeable dispositions of the rays," which, he says,
" had Huygens known, he would have found it difficult to ex-
plain how these dispositions, which he supposed to be impressed
on the rays by the first crystal, could be in them before their
incidence on that crystal ; and in general, how all rays emitted
by shining bodies can have these dispositions in them from the
beginning. To me, at least," he adds, " this seems inexplic-
able, if light be nothing else than pression or motion propagated
through ether."

After Newton wrote these imperfect observations, more than
a century elapsed before the double refraction and polarization
of light in Iceland spar and other bodies were reduced to regular
laws. In 1810, Mains announced to the Academy of Sciences,
the remarkable discovery that a ray of light reflected at a par-
ticular angle was polarized like one of the pencils formed by
Iceland spar, that is, exhibited the same properties in its four
sides or quarters which are exhibited in one of the pencils of
Iceland spar ; and the result of this fine discovery has been the
establishment of a new branch of Physical Optics, which pos-
sesses the highest interest, not only from the beauty of its laws

190 LIFE OP SIR ISAAC NEWTON. CHAP. X.

and the splendour of its phenomena, but from the new power
with which it arms the philosopher in detecting organic or inor-
ganic structures, which defy the scrutiny of the eye and the
microscope.

Although Sir Isaac Newton has not published any of his
opinions or experiments on Vision, or on the structure and
functions of the eye, yet we fortunately possess some fragments
of his researches, which are both valuable and interesting.
Among these is a manuscript in his own handwriting, which we
found among the family papers, containing some accurate obser-
vations and experiments on the form and dimensions of the eye
of a sheep, and accompanied with an outline drawing, on a large
scale, of a section of the eye.^ The following are the most
interesting results contained in this manuscript.

In the first part of it, which is written in Latin, he makes
the outer surface of the cornea part of a prolate spheroid, the
major axis coinciding with the optical axis, or that of the eye,
and having to the transverse axis the ratio of 1350 to 972.

He places the focus for parallel rays of the first surface of
the cornea at a point behind the eye, and as far beyond the
sclerotic coat as one-seventh of the diameter of the eye-ball,
which he makes an oblate spheroid, having its vertical axis
1025, and its horizontal one 975, the anterior portion of the
spheroid coinciding nearly with the front of the iris.

He represents the crystalline lens as having a great degree
of convexity, differing not much from a sphere,^ and he remarks
tliat the anterior superficies of the crystalline is more full than
tlie posterior surface, which is certainly not the case, and is not
so represented in the diagram.

The second part of the manuscript, which contains minute
measurements of every part of the eye, is written in English,
and concludes with an expression of regret, that " he was pre-
vented by an accident from taking the distance of the crystal-
line humour from the horny tunic (the sclerotic coat), which I

1 See Appendix, No. III.

1682. LIFE OF SIR ISAAC NEWTON. 191

would gladly have done to have had the conformity of all the
parts one to another, in one and the same eye." The elliptical
form of the cornea was detected not many years ago by M.
Chossat of Geneva, who, of course, could not know that he had
been anticipated by Newton.

We have not been able to ascertain at what time these obser-
vations were made, but it appears from the correspondence of
Newton with Dr. W. Briggs, published by Mr. Edleston,^ that
in 1682 his attention was called to the subject of binocular
vision, in consequence of Dr. Briggs having communicated to
the Royal Society on the 15th March, a paper entitled, " A
New Theory of Vision."^ Briggs, who was a contemporary of
Newton's at Cambridge, and a Fellow of Corpus Christi Col-
lege, seems to have sent him a copy of his paper, and to have
solicited his opinion of it. The theory which he proposes
evinces neither sagacity nor genius. Setting out on the erro-
neous principle which has so long disfigured the physiology of
the senses, and which has not yet been exploded, that sensation
is performed only in the brain, he seeks for an explanation of
single vision with two eyes, and of other visual phenomena in
" the rise of the optic nerve, the position of its fibres, and the
manner of their insertion into the eye." He describes the
optic nerves as arising " from two gibbous protuberances," ^ in
such a manner that those fibres that are in the zenith or apex
of the thalami have the greatest tension, while those in the
imdir, or opposite part, have the least tension by reason of a
less flexure. Every fibre that passes into the upper part of the
right eye from the upper part of one thalamus, has a correspond-
ing one passing from the upper part of the other thalamus into
the upper part of the left eye, and the same thing takes place
with the lower fibres. The fibres which thus correspond in site

1 Correspondence, &c. pp. 264-273. From the Originals in the British Museum, Add.
MSS. 4237, fol. 32 and 34.

2 Hooke's Collections, March 1682, No. 6, p. 167.

3 The Thalami Nervorum Opticorum.

192 LIFE OF sm ISAAC NEWTON. CHAP. X.

con-espond also in tension, " so that when any impression from
an object without moves both fibres^ it causes not a double sen-
sation any more than unisons in two viols struck together cause
a double sound.'' This theory may be called the theory of corre-
sponding fibres, and is doubtless the parent of one more modem
though equally inadmissible — the theory of corresj)onding points.

In his first letter to Briggs, Newton tells him that he has
" perused his veiy ingenious theory of vision, in which (to be
free with you as a friend should be) there seems to be some
things more solid and satisfactory, others more disputable, but
yet plausibly suggested, and well deserving the consideration of
the ingenious. The more satisfactory I take to be your assert-
ing that we see with both eyes at once, — ^your speculation about
the musculas obliqnus infenor,^ — ^your assigning every fibre in
the optic nerve of one eye to have its correspondent in that of
the other, both which make all things appear to both eyes, in
one and the same place, and your solving hereby the duplicity
of the object in distorted eyes, and confuting the childish opinion
about the splitting the optic cone. The more disputable seems
your notion about every pair of fellow fibres being unisons to
one another, discords to the rest, and this consonance making
the object seen with two eyes appear but one, for the same
reason that unison sounds seem but one sound." Newton here
terminates his letter to " his honoured friend. Dr. Briggs," with
the observation that he had intended to state his objections
" against- this notion," but that he thought it better " to reserve
it for discourse at their next meeting."

Briggs, probably anxious for an earlier discussion than one
living at Cambridge could concede, seems to have requested
him to make his objections in writing. Newton accordingly
addressed to his honoured friend a long letter of nearly seven
printed pages,^ a letter of very great interest, and Utterly sub-

1 Briggs considers this muscle necessary to prevent squinting, by "keeping the eye
cve7i and in sight." — Hooka's Coll., March 1682, p. 170.

2 Dated Trin. Coll. Cambridge, September 12, 1682. Appendix, No. IV.

1682. LIFE OF SIR ISAAC NEWTON. 193

versive of the theory of his correspondent. In the commence-
ment and conclusion of this letter, which is of a slightly-
personal nature, we see finely displayed the modesty and pecu-
liar character of its author. " Though I am of all men," he
begins, " grown the most shy of setting pen to paper about
anything that may lead into disputes, yet your friendship over-
comes me so far, that I shall set down my suspicions about
your theory, yet on this condition, that if I can write but plain
enough to make you understand me, I may leave all to your
use without pressing it further on. For I design not to
confute or convince you, but only to present and submit my
thoughts to your consideration and judgment."

After showing that the hending of the nerves in the thalami
is no proof of a difference of tension, he states, that when the
ear hears two sounds in unison, it does not hear them as one
sound, unless they come from nearly the same spot ; and for
the same reason a similar tension of the optic fibres will not
make the object appear one to two eyes.

He then proceeds to show that the singleness of the picture
arises from the coincidence of the two pictures, and therefore
that the cause of single vision must be sought for in the cause
that produces the coincidence. " But you will say," he adds,
" how is this coincidence made 1 I answer, what if I know
not ? Perhaps in the sensorium after some such way as the
Cartesians would have believed,^ or by some other way. Per-
haps by the mixing of the marrow of the nerves in their junc-
ture before they enter the brain, the fibres on the right side of
each eye going to the right side of the head, those on the left
side to the left. "2

In support of his theory, Briggs maintained that " it was

1 Descartes himself distinctly states that we see objects single with two eyes in exactly
the same way as we feel objects single with two hands, forgetting that we see them
double by the displacement of the coincident images, and never feel them double by the
two hands. See Descartes' Dioptrice, cap, 6, 1)e Visione, Art. X. The experiment of
feeling a pea double bettveen two fingers, is not hostile to this observation.

2 This is precisely the theory of Rohault, see p. 200.

VOL. I. N

194 LIFE OF SIR ISAAC NEWTON. CHAr. X.

not to be imagined that the nerves decussate one another, or
are blended together," at the place where they approach each
other before they set off to the right and left eye ; and he
adduces the case of many fishes, where the nerves are joined
only by simple contact, " and in the cJutmeleon not at all (as is
said)," admitting, at the same time, that in whitings^ and per-
haps some other fishes, they do decussate.

To this Sir Isaac replies : " If you say that in the chameleon
and fishes the nerves only touch one another without mixture,
and sometimes do not so much as touch ; 'tis true, but makes
altogether against you. Fishes look one way with one eye, the
other way with the other ; to the right hand with this, to the
left hand with that, twisting their eyes severally this way or
that as they please. And in those animals which do not look
the same way^with both eyes, what wonder if the nerves do not
join ? To make them join would have been to no purpose ;
and nature does nothing in vain. But then, whilst in these
animals, where 'tis not necessary, they are not joined, in all
others which look the same way with both eyes, so far as I can
yet learn, they are joined. Consider, therefore, for what reason
they are joined in the one and not in the other. For God, in
the frame of animals, hath done nothing without reason."

The last objection of Sir Isaac to the new theory is un-
answerable. Admitting that consonance unites objects seen
with the fibres of two eyes, "much more," says he, "will it
unite those seen with those (consonant fibres) of the same eye,
and yet we find it much otherwise."

" You have now seen," he says in conclusion, " the sum of
what I think of worth objecting, set down in a tumultuary
way, as I could get time from my Stourbridge Fair friends.
If I have anywhere expressed myself in a more peremptory way
than becomes the weakness of the argument, — pray, look on
that as done not in earnestness, but for the mode of discoursing.
Whether anything be so material as that it may prove any way
useful to you, I cannot tell ; but pray, accept of it as written

1682. LIFE OF SIR ISAAC NEWTON. 195

for that end. For having laid ])hilosophical speculations aside,
nothing but the gratification of a friend would easily invite me
to so large a scribble about things of this nature."^

Notwithstanding the force of these objections, Dr. Briggs
continued to press his theory on public notice, and in May

1683, he published in Hooke's Philosophical Collections addi-
tional explanations of it, and a reply to seven different objections
that had been sent him " by Mr. Newton, our worthy Professor
of Mathematics at Cambridge, and other friends." It would
be out of place to make any observations on this defence of his
theory. We hear no more of it for two years ; but it appears
that Newton had requested Briggs to print a Latin version of
it, and we accordingly find that it was published in London in
1685, with a curious letter of Newton's prefixed. This letter^
must have been solicited by Briggs, in order to call the atten-
tion of philosophers to his book ; and we confess that we feel
great difiiculty in appreciating the motives that could have
induced its author to express the opinions which it contains.

In this letter,^ written in Latin, Sir Isaac speaks of Briggs's
two treatises* as advancing at once two sciences of great name.
Anatomy and Optics. He compliments him on having diligently
inquired into the mysteries of an organ so skilfully constructed,
and he expresses the great delight which he had formerly re-
ceived from the skill and dexterity with which he had dissected
it. He tells him that he had so elegantly developed the muscles
of the eye-ball, and expounded the other parts, that we could
not only understand, but see the uses and functions of each,

1 This letter contains, as will be seen In the Appendix, No. IV., a paragraph respecting
the opinions of a Mr. Sheldralce, who, as Mr. Edleston informs us, was a Fellow of Corpus
Christi College, and seven years senior to Newton. Mr. Sheldrake states that vision is
more distinct when the eye is directed to the object, than when the object is above or
helow the optic axes. I do not recollect that this curious fact has been stated by any
previous writer on vision.

2 See Appendix, No. V.

3 Dated Cambridge, May 1685.

* The one the Theory of Vision, and the other his OiMhalmographia. Cantab. 1676.
and Lond. 1687.

196 LIFE OF SIK ISAAC NEWTON. CHAP. X.

and that this showed that nothing inaccurate could be expected
from his scalpel. He then speaks of his excellent anatomical
tract, in which he shows the value of accurate observation by
" a most ingenious theory." After describing Briggs's theory
in a few lines, and mentioning the analogy between unisons in
music and in optics, he says that nature is simple — that a great
variety of effects may be produced by the same mode of opera-
tion, and that this was probable in the causes of the cognate
senses. But notwithstanding all this general praise, which is
certainly not merited, Newton does not adopt the theory. For
though he vnay suspect that there is another analogy between
these senses, than that contained in the theory, he must willingly
confess that that of Briggs is very ingeniously excogitated. He
then remarks that he does not think the second dissertation
useless in which he dilutes the objections made against the
theory. " Go on, then," he adds, " illustrious sir, as you are
doing, and advance these sciences by your very great inventions,
and teach the world that those difficulties in investigating
physical causes which usually yield with difficulty to vulgar
attempts, may be so easily overcome fby talent."

While Newton was writing this letter, there is reason to
believe that he had himself conceived another theory of single
vision with two eyes, proceeding on the supposition that Briggs
was wrong in his Anatomy as well as in his Optics. This, we
think, is indicated by the " other analogy " of the senses of
sight and hearing which he then suspected, and to which he
was no doubt led by his correspondence with Briggs. It is
evident, that in September 1682, the date of his second letter,
he had laid aside philosophical speculations, and that he un-
willingly wrote his opinion "about things of that nature ;" and
it is equally obvious, from his supposition about the mixing of
the marrow of the nerves in their juncture before they enter
the brain, that if the idea of the semi-decussation of the fibres
had been then in his view, he had not at that time given it
any serious consideration.

1682. LIFE OF SIR ISAAC NEWTON. ] 97

That he had studied this subject with peculiar care, is mani-
fest from the 15th Query of his Optics,^ where he has given a
brief abstract of his theory of corresponding points, or of the semi-
decussation of the optic nerves, but particularly from an elaborate
paper on the subject which was never published in his lifetime,
but was found in MS. among the papers of William Jones, Esq.,
known as the celebrated Macclesfield Collection of scientific
correspondence. A copy of this paper was given to Joseph
Harris, who inserted it in his Treatise of Optics,'^ but from the
manner in which he has garbled it, we cannot discover whether
or not he has published the whole of the manuscript.^

The theory of Newton, as published in his Optics, and as
more fully developed in the MS. in question, will be understood
from the annexed diagram given by himself. Let p, q represent
the two eyes, tveg, yxeh the optic nerves, crossing at what
has been called the sella turcica, gh, and passing between il
or MK towards the brain. Newton observes, that if the nerve
be cut crosswise anywhere between tg or yh, the section will

1 See Appendix, No. VI. 2 gee Appendix, No. VII.

3 Although it is evident, from a careful perusal of the 15th Query, that it contains the
same doctrine of the scmi-decussation of the optic nerves which is given in the MS., yet
it has been misunderstood by Dr. Reid, who obviously had not seen the copy of it in
Harris's Optics. " Sir Isaac Newton," says Dr. Reid {Inquiry, cap. vi. sect 13), " who
was too judicious a philosopher and too accurate an observer to have offered even a con-
jecture which did not tally with the facts which had fallen under his observation, pro-
poses a query with respect to the cause of it (namely, the relation and sympathy between
corresponding points of the two retinae)." — Optics, Query 15. Dr. Reid seems not to
have detected the doctrine of semi-decussation in the Query, and to have believed that
individual nerves, not half-nerves, from the two sides of both eyes, united before they
reached the brain, and there produced a joint and single impression; and Dr. Alison
has either taken up Dr. Reid's opinion, or misunderstood the Query, and also the theory
of semi-decusi^ation. " It is well-known," he says, " that an explanation (of single vision
by means of double images) was proposed by Newton, fully considered by Reid, and
since supported by Wollaston (often called the theory of Wollaston, but quite incor-
rectly) , proceeding on the supposition of a scmi-decussation of the human optic nerves at
their commissure, whereby the fibres from the riyht half of the retina go to the right optic
lobe in the brain, and vice versa." This is the theory of Rohault, and not of Newton
and Wollaston, in which the half-fibres, from the right half of the retina of each eye,
unite into one fibre at their commissure gh in Fig. 12, and then go to the right optic
lobe.

198

LIFE OF SIR ISAAC NEWTON.

CHAP. X.

" appear full of spots or pimples, which are a little prominent,
especially if the nerve be pressed or warmed at a candle ; that
these shoot into the very eye, and may be seen withinside
where the retina grows to the nerve ; and that they continue
to the very juncture efgh. But at the juncture they end on
a sudden into a more tender white pap, like the anterior part

Fig. 16.

of the brain, and so the nerve continues after the juncture into
the brain, filled \^ith a white tender pap, in which can be seen
no distinction of parts as betwixt the said juncture and the
eye."

" Now I conceive," says he, " that every point in the retina
of one eye hath its correspondent point in the other, frQm which
two very slender pipes, filled with a most limpid liquor, do
without any interruption, or any other unevenuess or irregu-

1682. LIFE OF SIR ISAAC NEWTON. 199

larity in their process, go along the optic nerves to the juncture
EFGH, where they meet either betv/ixt gf or fh, and ^ there
unite into one pipe as big as both of them ; and so continue
in one passing either betwixt IL or mk into the brain, where
they are terminated perhaps at the next meeting of the nerves
between the cerebrum and cerebellum, in the same order that
their extremities were situated in the retinas. And so there
are a vast multitude of these slender pipes which flow from the
brain, the one-half through the right-side nerve il, till they
come at the juncture gf, where they are each divided into two
branches, the one passing by g and t to the right side of the
right eye ab, the other half shooting through the space ef, and
so passing by x to the right side of the left eye a/3. And, in
like manner, the other half shooting through the left -side nerve
MK, divide themselves at fh, and their branches passing by e v
to the right eye, and by hy to the left, compose that half of
the retinii in both eyes which is towards the left side CD
and 78."

From this theory of the sevni-deciissation of the optic nerves,
ISTewton draws the following conclusions : —

" Hence it appears," says he, —

" 1 . Why the two images of both eyes make but one image,
abed, in the brain.

" 2. Why, when one eye is distorted, objects appear double,
for if the image of any object be made upon a in the one eye,
and p in the other, that object shall have two images in the
brain at a and b. Therefore, the pictures of any objects ought
to be made upon the corresponding points of the two retinas ;
if upon A in the right eye, then upon a in the left ; if upon b,
then also upon /?. And so shall the motions concur after they
have passed the juncture gh, and make one image at a or b
more vivid than one eye alone coidd do.

" 3. Why, though one thing may appear in two places by
distorting the eyes, yet two things cannot appear in one place.
If the picture of one thing fall upon a, and of another upon a.

200 LIFE OF SIR ISAAC NEWTON. CHAP. X.

they may both proceed to p, but no farther. They cannot both
be carried on the same pipe p a into the brain ; that which is
strongest, or most helped by phantasy, will there prevail, and
blot out the other.

" 4. Why, if one of the branches of the nerve beyond the
juncture, as at g f or f H should be cut, that half of both eyes
towards the wounded nerve would be blind, the other half re-
maining."^

This ingenious theory, decidedly superior to that of Briggs,
was to a considerable extent anticipated by M. Rohault, in his
Traite de Physique, published in 1671, more than ten years
before Newton's attention was called to the subject. Rohault
gives the very same figure as the preceding one, with this differ-
ence, that the nerves neither cross nor split into two at g h.
He supposes that the two optic nerves have their corresponding
or sympathetic fibres, which unite in one point in the brain ;
and he thus explains single vision with two eyes, their duplicity
by distortion, and the impossibility of two things appearing in
one place. 2

During the 120 years that have elapsed since the publication
of Newton's Optics, we hear nothing more of the Theory of
Vision in the 1 5th Query, and in the manuscript above referred
to, till the year 1824, when Dr. WoUaston published in the
Philosophical Traiisactions of that year, a paper On Semi-decus-
sation of the Optic Nerves, in which he reproduces the very
theory of Newton, in order to account for the curious disease
of hemiopsy, or amaurosis dimidiata,^ in which the patient sees
with each eye only half of an object, being blind to the other

1 Sir Isaac draws other four conclusions from his theory, but they will find a fitter
place in the Appendix, No. VII.

2 A Latin translation of Rohault's work was published in 1 708, by Dr. Clarke, " with
annotations chiefly from the philosophy of Newton, and yet no notice is taken of New-
ton's Theory, as contwned in his 15th Query, although Dr. Clarke had translated the
Optics into Latin. He adds a note stating that the conjecture respecting the fibres of
the optic nerve had not yet been confirmed by dissection. Part I. cap. 31, p. 225, nok.

^ The suffusio dimidians of other authors.

1682. LIFE OF SIR ISAAC NEWTON. 201

half. This sympathy between the two eyes may certainly arise
from structure, and depend upon " connexion of nervous fibres,"
and if it does, is very well explained either by the hypothesis
of Rohault or of Newton ; but we cannot attach any value to
the invention of structural hypotheses when the phenomena
may be explained by that habitual sympathy of double organs
with which we are so well acquainted. This observation is still
more applicable to the remark of Wollaston, that by his theory
" we clearly gain a step in the solution, if not a full explana-
tion of the long agitated question of single vision with two
eyes," because this great fact in vision can be perfectly ex-
plained, as we shall presently see, without any hypothesis
whatever.

But not only is this theory of semi-decussation uncalled for,
it is contradicted by numerous facts. It has been examined
with great ability by Mr. Twining, of the Indian Medical
Service,^ who concludes " from anatomical observations respect-
ing the structure of the optic nerves and thalami, and the
effects of disease on those parts, that no decussation or semi-
decussation of the optic nerves exists in the human subject. No
anatomist, indeed, has pretended to say that there is any trace
of semi-decussation ; and it has been proved that the decussa-
tion or crossing at gh, Fig. 16, is only partial, the inner
bundles decussating, while the outer bundles remain on the side
on which they previously lay."^

There is no branch of physical science upon which such un-
sound views have prevailed as in that which relates to the
optical functions of the eye ; and in studying the speculations
of modern metaphysicians and physiologists, we feel as if we
were grappling with the chimeras of Aristotle or Descartes.
"While Dr. Reid maintains that objects appear single when
their images are formed upon corresponding points of the retina,

1 See Transactions of the Medical and Physical Society of Calcutta, vol. ii. p. 151 ; or
Edinburgh Journal of Science, July 1828, vol. ix. p. 143.

2 Wagner's Handworterbuch der Physiologic, vol. iii. part ii. p. 297.

202 LIFE OF SIE ISAAC NEWTON. CHAP. X.

and double in all other circumstances, he gives no explanation
whatever of single vision : he merely attaches the name of cor-
responding points to those upon which the image falls when it
is seen single ! And when Dr. Brown tells us that it is from
association alone we see objects single and erect, by means of
double and inverted pictures, he merely asserts his ignorance of
the cause ; and his assertion is contrary to the most notorious
facts and to all experience, as Dr. Reid has shown..^ Nor
does Dr. Alison, one of the latest writers on the subject,
bring us a single step nearer the truth. After controverting
the views of Brown and Reid, he apprehends that he has esta-
blished the following two facts, the one explaining single, and
the other erect vision :^ —

1. That images formed on corresponding points of the retinae
of the human eyes, and on those only, naturally affect our
minds in the same manner as a single image formed on the
retina of one eye ; and,

2. That impressions made on different points of the retina

1 If by the sense of touch we could make the two images appear one, then we should
also ?ee an object single when it is doubled by looking either at a nearer or a more dis-
tant object, or when it is made 100 by a multiplying glass ; but if a man were to live
1000 years, he would still see the two or the hundred images, though he knew there was
only one object. In order to illustrate his opinion, Dr. Brown says that the two English
words he. conquered, excite the same idea as the one Latin word vicit. In reply to this
Dr. Whewell says, " that to make this pretended illustration of any value, it ought to be
true that when a person has thoroughly learned the Latin language, he can no longer
distinguish any separate meaning in he and in conquered.'' With this assertion we can-
not concur. The two words he conquered, undoubtedly convey the same meaning as
vicit. If we unite the two words thus, heconquered or conqu^eredhe, we cannot doubt
that the word Ae is as truly included in the termination it of vicit, as he is in the single
word heconquered, unless it is alleged that vicit may also mean she conquered.

Dr. Brown's real mistake consists in not taking two exactlii similar words, as vicit,
vicit, like what he considers as the two exactly similar images. The two words pro-
nounced in succession convey certainly only one idea, but the mind recognised the same
in succession or its duplicity, just as it would do the two similar and united images, if
one of them were slipped from its superposition on the other by pressing aside one of the
eye-balls.

Dr. Brown's views are affected with another error, namely, in the assumption that the
pictures in each eye are exactly similar.

2 Edinbu)-gh Transactions, vol. xiii. p. 479.

LIFE OF SIR ISAAC NEWTON. 203

of the eye, are naturally followed by inferences as to tlie rela-
tive position of the objects producing these impressions, exactly
opposite to those which follow impressions made on different
points of the surface of the body.^

We are unable to controvert these two palpable facts. They
are truisms which explain nothing ; and if Nature had been so
perverse as to produce three pictures in place of one from two
eyes, and had turned round an erect picture 90° in place of
180°, which it does in inverting it, that is, had represented a
man upon the retina lying horizontally in place of vertically
and inverted, the explanation of Dr. Alison would have been,
that in the first case it was natural, and that in the other it
was naturally, and exactly half opp)Osite to other impressions
on the surface of the body. 2

From these speculations we venture to solicit the attention of
the reader to the true explanation of single and erect vision, and
of all the other normal visual phenomena with which we are
acquainted, an explanation which has been overlooked by our
most distinguished optical writers.

1. The retina^ is the seat of visual sensation and of vision ;
and there is a law of visual sensation as well as a law of vision,
which can be determined only by experiment.

2. In order to determine the law of visual sensation, or the
mental information given by the action of a physical point of

1 There is no opposition between the impressions on the concave retina and on a con-
cave surface of the body. If we hold up the hand vertically, and bend it into a con-
cavity, an impression made on the npTper part of the concavity, will be felt as coming
from below, and an impression on the lower part of the concavity will be felt as coming
from above, exactly as in the case of the concave retina.

2 We have not noticed the additional explanation adopted by Dr. Alison, " that im-
pressions on the upper part of the retina are impressions on the lower''/p&ri of the optic
lobes, i.e., of the scnsorinm ;" because he has not told us what requires as much explana-
tion as inverted vision, namely, why the lower part of the sensorium makes the object
seem lower ! Is the sensorium a plane, or a convexity, or a concavity ? If it is a con-
cavity, a physical impression on the lower part ivill correspond to the top of the object,
and an impression on the upper part with the bottom of it

3 I omit all consideration of the question, whether the choroid coat or retina is the seat
of vision, or whether the foramen centrale is or is not an opening in the retina.

204 LIFE OF SIR ISAAC NEWTON. CHAP. X.

light upon the retina, let us make a hole of the smallest size,
that of the minimum visibile, for example, on a sheet of black
paper, and let a ray of the sun's light pass through it and fall
upon the eye. This cone of rays, with the pupil for its base,
will be refracted by the humours of the eye into a smaller cone,
the apex of which falls upon the retina. This apex, or point,
is the image of the hole in the paper, and is formed by a cone
of rays whose angle we may suppose to be 12°, so that the im-
pression is made by rays falling at all angles on the retina from
0° to 6° on each side of the perpendicular or axis of the cone.
If, while looking at the hole in the paper, we stop all the dif-
ferent rays in succession from 0° to 6°, we shall find that the
hole is seen by them all in one direction^ and that this direction
is the axis of the cone, and, as nearly as can be ascertained, the
real direction of the hole, or the axis of the incident cone of
rays. Hence it follows, that the impression of a ray of light
upon the retina, whatever be the angle of its incidence, gives
the sensation of having proceeded in a direction perpendicular
to the retina, a direction as will be afterwards seen coinciding
nearly with the real direction of the hole from which it issues.
This is the law of visible direction.

3. In order to determine the law of vision, look at the hole
in the paper with both eyes, and it will be found, by opening
and shutting each eye alternately, that a single image of the
hole is seen, and always in the same place, namely, at the point
where the optical axes of the two eyes meet, and consequently
at the distance from the eye where these axes meet. The single
image seen by both eyes is formed by the superposition or coin-
cidence of the two images. This is the law of visible distance,
and the law of single vision ; but the law of single vision is
true only for visible points. If we had the hundred eyes of
Argus in place of two, the hundred images of a point would
coincide in one at the point where the hundred images con-
verge.

4. The law of vision for visual objects is entirely different

LIFE OF SIR ISAAC NEWTON. 205

from that for points. A visual object cannot be seen single at
once. Let the object, for example, be a line ^i\i of an inch
long. The two images of it cannot be seen coincident by both
eyes. When the right hand extremities of the images are coin-
cident or single, the left hand extremities are not, and vice versa.
When the object is a lineal space or superficies^ only one point
of it is seen single and distinct, the two eyes converging theu*
optic axes on every point of it in succession, and thus obtain-
ing the idea of space. When the object is a solid^ such as a
cube, only one point of it is seen single and distinct, the two
eyes converging their optical axes to the near and remote parts
of it in succession, and thus obtaining an idea of the difter-
ent distances of its parts by the varying angle of the optic
axes. This law of vision for solids, includes the theory of the
stereoscope. ^

We have stated that the law of sensation gives a visible
direction, which is nearly coincident with the real direction of
objects. The celebrated D'Alembert maintained that the action
of light upon the retina is conformable to the laws of Mechanics,^
and therefore that the visible direction of an object should be a
line perpendicular to the curvature of the retina at the excited
point ; but he rejected this law as contrary to observation. By
using, however, more correct refractive powers for the humours
of the eye, and more accurate measures of its parts, we have
shown that the visible and true direction of points nearly coin-
cide. ^

By means of these laws all the phenomena of erect vision from
an inverted image, — of the single vision of points, — of the
vision of plane surfaces and solids, — and of the conversion of

1 See Edinburgh Transactions, vol. xv. p. 360 ; North British Review, vol. xvii. p.
165 ; and my Treatise on the Stereoscope.

2 When a ray falls obliquely upon the retina (of any other surface of sensation) its
action may be decomposed into two, the one lying in the surface of the membrane, and
acting laterally upon the papillae, and the other perpendicular, and acting in the direc-
tion of the axis of the papillae, and therefore passing to the brain.

3 See Edinburgh Transactions, vol. xv. pp. 350-353.

206 LIFE OF SIR ISAAC NEWTON. CHAP. X.

two plane pictures into solids or objects in relief, may be calcu-
lated with as much accuracy as we can compute the positions of
the heavenly bodies.

Among the minor optical labours of Sir Isaac Newton, we
must rank some curious observations on the action of strong
light upon his own eyes, which have been only recently published
by Lord King in his Life of Locke. In his work on Colours,
Mr. Boyle has described a curious case, in which a gentleman
" eminent for his profound skill in almost all kinds of philolo-
gical learning, had injured his eyes by looking tc«3 fixedly upon
the sun through a telescope, without any coloured glass to take
off from the dazzling splendour of the object. The excess of
light did so strongly affect liis eye, that ever since when he turns
it towards a window or any white object, he fancies he sees a
globe of light of about the bigness the sun then appeared to
him, to pass before his eyes ; and having inquired of him how
long he had been troubled with this indisposition, he replied,
that it was already nine or ten years since the accident that
occasioned it first befell him." ^ This remarkable case having
attracted the attention of Locke, he requested Sir Isaac to give
him his opinion on the subject. In his reply, dated Cambridge,
Jime 30, 1691, Sir Isaac sent him the following very interest-
ing 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 Hght 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 aj^pearance, I

1 Experiments and Considerations touching Colours, chap. ii. § 9, p. 19. Lond. 1664.

2 King's life of Locke, vol. i. pp. 404-408. Edit. 1830.

1691. LIFE OF SIR ISAAC NEWTON. 207

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 anything 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
lef% yet my fancy began to make an im2:)ression upon my left
eye^ as ivell as upon my right. For if I shut my right eye, or
jlooked upon a book or the clouds with my left eye, I could see
\tke spectrum of the sun almost as plain as with my right eye, if

did but intend my fancy a little while upon it ; for at first,

I shut my right eye, and looked with my left, the spectrum

|of the sun did not appear till I intended my ftmcy upon it ; but

I by repeating, this appeared every time more easily. And now,

jin 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

iw the sun before me, so that I durst neither write nor read ;
mt to recover the use of my eyes, shut myself up in my chamber

lade dark, for three days together, and used all means to divert

ly imagination from the sun. For if I thought upon him, I pre-
sently 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 me-
ditate upon the phenomena, even though I lay in bed at mid-

208 LIFE OP SIR ISAAC NEWTON. CHAP. X.

night 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 pro-
bably 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, or of its pro-
duction in that eye merely by fancy, is particularly important ;
and it deserves to be remarked as a singular coincidence, that
we had occasion to observe, and to describe the same phenomena
above forty years ago,^ and long before the observations of Sir
Isaac were communicated to the scientific world, ^pinus of
St. Petersburg observed the circles of colours described by
Newton, when produced by looking at the setting sun for
fifteen seconds. In the experiments alluded to, we looked at
the brilliant image of the sun formed by a concave speculum
of 30 inches focus with the right eye tied up, and upon turning
the left eye to a white ground, we observed six successions of
different colours with their complementary tints when the left
eye was shut. Upon uncovering the right eye, and turning it
to a white ground, we were surprised to observe the reverse
spectra, as if the impression had been conveyed from the left to
the right eye, as in Sir Isaac's case. A spectrum of a darkish

1 Art. Accidental Coloues, in the Edinburgh Encyclopaedia, vol. i. pp. 91, 92.

1700. LIFE OF SIR ISAAC NEWTOX. 209

hue floated before the left eye for many hours, and this was
succeeded by severe pains shooting through every part of the
head. A slight inflammation, affecting both eyes, continued
for several days, and it was not till several years had elapsed
that our eyes had recovered their former power.

Among the inventions of Sir Isaac Newton, we may enu-
merate his reflecting sextant 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

Fig. 17.

from having mislaid the manuscript, or from attaching no value
to the invention, he never submitted it to the Royal Society,
and it remained among his papers till after his death in 1742,
when it was read on the 28th October. The following is Sir
Isaac's own description of it, as copied from the original manu-
script :^ —

" In the annexed figure, pqrs denotes a plate of brass, accu-
rately divided in the limb dq into J degrees, J minutes, and
jV minutes by a diagonal scale ; and the ^ degrees, and J

1 See Phil. Trans. 1742-43, vol. xlii. p. 155.
O

210 LIFE OF SIR ISAAC NEWTON. CHAP. X.

miiiutes, and ^^ minutes, counted for degrees, minutes, and ^
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
I)late 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 other-
wise come through the telescope to the eye. c d is a moveable
index tumhig about the centre c, and, with its fiducial edge,
xshowing the degrees, minutes, and ^ minutes on the limb of the
brass plate p q ; 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.

" 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 tm'n 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 mil 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 de-
termined 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 obser-
vation may notwithstanding be made exactly, by noting when

1672. LIFE OF SIR ISAAC NEWTON. 211

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 as that
which Mr. Hadley produced in 1731 ;^ and which, under the
name of Hadley's Quadrant, has been of so great sendee in
navigation. But though the merit of this invention is thus
transferred to Newton, we must not omit to state, that the
germ of it, and something more, had been previously published
by Hooke. In giving an account of the inventions of members
of the Koyal Society, Sprot mentions " a new instrument for
taking angles by reflexion, by which means the eye at the same
time sees the two objects both as touching on the same point,
though distant almost to a semicircle, which is of gTcat use in
promoting exact observations at sea."^ Hooke was the member
who made this invention, and there is a drawing and description
of it in his Posthumous Works. ^ About the end of the year
1730, Thomas Godfrey of Philadelphia invented an instrument
similar to Hadley's ; and the Royal Society, having found that
Hadley's invention could be traced to the summer of 1730,
decided that Hadley and Godfrey were independent inventors.
The enlargement of this valuable instniment, so as to measure
an angle of 120°, was first proposed by Captain Campbell in
1757.4

On the 6th February 1672, Sir Isaac communicated to Mr.
Oldenburg his " design of a microscope by reflexion^ which

> Phil. Trans. 1731, p. 147.

- Sprot's nisi, of tlie Royal Society, p. 2i6. Lond. 1667.

3 Tlic Posthumous Works o/ Robert Hooke, M.D., p. 503, tab. xi. fig. 2. Lond. I70.T,
In the description given of it by Waller, his biographer, the invention is mentioned as
" an instrument for taking angles at one prospect, which he found described on a
loose paper."

* Grant's Hist, of Physical Astronomy, p, 487 ; and Nautical Map. vol. i. p. 351.

iil2 LIFE OF SIR ISAAC NEWTON. CHAP. X.

should have, instead of an object-glass, a reflecting piece of
metal, and which seemed as capable of improvement as tele-
scopes, and perhaps more so, because but one reflective piece of
metal is requisite in them." This microscope is shown in the
annexed diagram, copied from the original, where a b is the
object-metal, c d 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, Professor Potter, and Dr. Goring,^ who make
A B a portion of an ellipsoid, whose foci are o and f, and who
fix a small plain speculum between o and a b, in order to

Fig. 18.

reflect into the speculum the object which is placed on one side
at p, for the purpose of being illuminated. ^

In another letter to Mr. Oldenburg, dated July 11th in the
same year, he suggests an improvement of microscopes by re-
fraction, " which I do," he says, " more willingly, because Mr.
Hooke hath made such excellent use of that instrument ; and
I shall be glad to contribute any thing to your promotion of
these his ingenious endeavours, or add to his inventions of that
kind. The way is, by illuminating the object in a darkened
room with light of any convenient colour not too much com-
pounded ; for by that means the microscope will, with distinct-
ness, bear a deeper charge and larger aperture, especially if its
construction be such as I may hereafter describe."^ This happy

1 See Edinburgh Journal of Science, vol. Ti. p. 61 ; Enct/clopcedia Brit., Art. Micro-
scope, vol. XV. p. 41.

^ Newtoni Opera, torn. iv. p. 300.

3 Sir Isaac does not seem to have afterwards described this construction.

1672.

LIFE OF SIR ISAAC NEWTON.

213

idea we have some years ago succeeded in realizing, by illumi-
nating microscopic objects with the light of a monochromatic
lamp, which discharges a copious flame of pure yellow light of
definite refrangibility.^ Since the time of Newton, the micro-
scope has undergone the greatest improvement, — the single
microscopes made of diamond and the other precious stones, —
the microscopic doublets, and the magnificent compound micro-
scopes of Ross, Powell, and Nachet fitted up as polarizing
microscopes.

In order to remedy the evil of want of light in his reflecting
telescope, 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 a B c, Fig. 19. Its side a b 6 a he
supposes to perform the office of that
.metal, by reflecting towards the eye-
glass the light which comes from the
[concave speculum d f. Fig. 20, the
[light reflected from which he supposes
[to enter into this prism at its side
jc B 6 c, and lest any colours should
[be produced by the refraction of these
3lanes, it is requisite that the angles
[of the prism at a a and b 6 be pre-
cisely equal. This may be done most
• conveniently, by making them half right angles, and conse-
quently the third angle at c c a right one. The plane a b 6 c/
[will reflect all the light incident upon it, " especially if the
jprism be made of crystal ;" but in order to exclude unnecessary
[light, it w^ill be proper to cover it all over with some black
[substance, excepting two circular spaces of the planes a c and
B c, through which the useful light may pass. The length of
the prism should be such that its sides a c and b c may be

1 See Edinburgh Transactions, vol. ix. p. 433 ; and the Edinburgh Journal of Science,
July 1829, No. I. new series, p. 108.

LIFE OF SIR ISAAC NEWTON.

CHAP. X.

" ibur-square," and so much of the angles b and h as are super-
iiuous ought to be ground off, to give passage for as much light
as is possible from the object to the speculum.

Fig. 20.

One gTcat 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 tele-

E Vg^a^ F

Fig. 21.

scope varied at pleasure, by merely varying the distances of
the speculum, the prism, and the eye-glass. This will be under-
stood from Fv:/. 21, where ai represents the great concave

LIFK OF SIR ISAAC NEWTUN. 215

speculum, e f the eye-glass, and b c d the prism of
whose sides b a and b d are not flat, but spherically convex.
The rays which come from g, the focus of the great speculum
A I, will, by the refraction of the first side b d, be reduced to
parallelism, and after reflexion from the base c d, will be made
by the refraction of the next side b c to converge to the focus
H of the eye-glass e f. If we now bring the prism b c d
nearer the image at g, the point h ayHI recede from b d, and
the image formed there will be greater than that at g ; and if
we remove the prism bod from g, the point n will approach
to B c, and the image at h will be less than at g. The prism
BCD perforins 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. These different contrivances were .suggested by some
criticisms upon his reflecting telescope by M. Auzout ; and
Newton does not seem to have executed them, as he recom-
mends " that the first trials be made with prisms who^e sides
are all of them plane." ^ As more than one-half of the light
is lost by reflexion from the small mirror, we have proposed
to substitute for it an achromatic prism to refract the rays to
the side of the tube.^ An advantage would be gained by the
use of a plane speculum of silver, which reflects much more
light than speculum metal. The objection to reflecting prisms
arises from the imperfection of the glass, and the difficulty of
obtaining three perfectly flat surfaces, and two angles perfectly
equal. 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 e f ; and by bisecting the lenticular
])rism BCD, and giving the halves a slight inclination, we
siiould be able to separate and to close the two images or discs
which the two halves would produce, and thus form a double
image micrometer.

1 See Newtoni Opera, torn. iv. p. 276.
■^ Treafixc on Optica, edit, of 1853, p. 494.

216 LIFE OF SIE ISAAC NEWTON. CHAP. X.

Ill concluding our account of Newton's optical discoveries,
some notice of the principal work which contains them will
suitably terminate the present chapter. This work, entitled
Optichs, or a treatise on the Reflexions, RefractioTis, Inflexions,
and Colours of Light, was published in London, without a date,
on the 16th February 1704. Newton, from the President's
chair, presented it to the Royal Society. Dr. Halley was
desired to peruse it and make an abstract of it, and the thanks
of the Society were given to the author " for the book, and for
being pleased to publish it." In the second edition, with the
date of July 16, 1717, the date of April 1, 1704, is added
to the advertisement of the first edition, a step of w^hich, as
Mr. Edleston observes, "the dispute with Leibnitz had pro-
bably taught our philosopher the importance."^

In the advertisement to the first edition, we are informed
by the author, that " a part of the ensuing discourse about
light was written at the desire of some gentlemen of the Royal
Society in the year 1675, and then sent to their Secretary and
read at their meetings, and the rest Avas added about twelve
years after, to complete the theory, except the third book, and
the last proposition of the second, which were since put to
gether out of scattered papers. To avoid being engaged in
disputes about these matters, I have hitherto delayed the
printing, and should still have delayed it, had not the im-
portunity of friends prevailed upon me. If any other papers
writ on this subject are got out of my hands, they are imperfect,
and were perhaps wTitten before I had tried all the experiments
here set down, and fully satisfied myself about the laws of re-
fractions and compositions of colours. I have here published
what I think proper to come abroad, wishing that it may not
be translated into another language without my consent," In
the advertisement to the second edition, which appeared in
1717, he mentions that he could have added at the end of the

1 It is a curious fact, that " there is the same peculiarity about the preface to the
Principia."— Edleston's Correspondence. &c &c , pp. Iviii. and Ixxi.

1728. LIFE OF SIR ISAAC NEWTON. 217

third book some questions (namely the thirty-one celebrated
queries) ; " and," he adds, " to show that I do not take gravity
for an essential property of bodies, I have added one question
concerning its cause, choosing to propose it by way of a ques-
tion, because I am not yet satisfied about it for want of ex-
periments."

At the request of Newton, Dr. Samuel Clark prepared a
Latin edition of his Optics, which appeared in 1706, and he
was generously presented by Sir Isaac with £500, or £100 for
each of his five children, as a token of the approbation and
gratitude of the author. Demoivre is said to have secured and
taken charge of this translation, and to have spared neither
time nor trouble in the task. Newton met him every evening
at a coffee-house,^ and when they had finished their work, he
took Demoivre home with him to spend the evening in philo-
sophical conversation.^ Both the English and the Latin editions
have been frequently reprinted, both in England and on the
Continent, and perhaps there never was a work of profound
science more widely circulated.^

The only other optical work by Newton was his Lectiones
Opticce, a course of lectures on optics, which he read as Lu-
casian Professor in the public schools of the University of
Cambridge in the years 1669, 1670, and 1671. It was not
published till after his death ; — an English edition in 1728,
in octavo,^ and the Latin original in 1729 in quarto.

This valuable work is divided into two parts, and contains
many beautiful propositions, and interesting and instructive
experiments, which are not to be met with in any modern trea-
tise on optics.

In the first part, which is entitled, On the Refraction of the

1 " Probably Slaughters' CofiFee-house ia St. Martin's Lane.'— Edleston's Cwrcspond-
«nce, p. Ixxiv.

2 Eloge, by Fontenelle. — MAn. Acad. Par. 1727. Hist. p. 121.

3 The English edition was reprinted at London in 171T, 1721, and 1730, and the Latin
one at London in 1719, 1721, 1728, at Lausanne in 1740, and at Padua in 1773.

* Biographia Brit. Art. Newton, toI. vii. p. 779.

218 LIFE OF SIR ISAAC NEWTON. CHAP. X.

Rays of Lights he treats mfour sections : — 1. Of the different
refrangibility of the rays of light ; 2. Of the measure of refrac-
tions ; 3. Of the refractions of plane surfaces ; and 4. Of tlie
refractions of curved surfaces.

In the second part, which is entitled, On the Origin of Co-
lours, he treats in five sections : — 1. On the doctrine of colours,
and its proof by experiments with the prism ; 2. On the various
phenomena of colours, and on the phenomena of light thrown
upon a wall by the prism ; 3. On the phenomena of light
received in the eye from a prism ; 4. On the phenomena of
light transmitted through a refracting medium terminated by
parallel planes ; and, 5. On the phenomena of light transmitted
through media terminated spherically, and on the rainbow.^

The manuscript from which the Latin edition was printed,
was that which had been given by Newton himself to David
(xregory, Savilian Professor of Astronomy at Oxford ; but after
the edition had been printed, the editor learned that a more
perfect manuscript, containing several corrections and emenda-
tions in Newton's own handwriting, had been preserved in the
archives of the University of Cambridge. These emendations,
occupying five quarto pages, were therefore printed at the end
of the work, and we observe that Bishop Horsley has intro-
duced them into the text in the third volume of his edition of
Newton's works.

1 An analysis of the Lectiones Opticce has been given by the suihor of the Life of Xew-
ton in the General Dictionary, vol. ii. p. 779, note ; but it is by some mistake confined
to x\iQ first Part, as if there were no second Part. The same mistake is committed in the
Bioffraphia Britannica, vol. v. p. 3215, note, where it is obvious that the author knew
nothing of the second Part, as he calls the last portion of i\\Q first Part the " Last Section
of these Lectures."

LIFK OF SIR ISAAC NEWTON. 219

CHAPTER XL

Astronomical Discoveries of Newton— Oorabined Exertion necessiry for the Coiiipletion
of great Discoveries— Sketch of the History of Astronomy previous to the Time of New-
ton — Discoveries of Nicolas Copernicus, born 1473, died 1553 — He places the Sun in
the centre of the System— His Work on the Revolutions of the Heavenly Bodies, printed
at the expense of Cardinal Schonberg, and dedicated to Pope Paul iii. — TychoBrahe,
born 1546, died 1601 — His Observatory of Uraniburg — Is visited by James vi. — Is
persecuted by the Danish Minister — Retires to Germany — His Discoveries and Instru-
ments—The Tychonic System— John Keplt^r, born 1571, died 1631— His Speculation
on the Six Regular Solids — Discovers the EUipticity of Mars' Orbit — His Laws of the
Planetary Jlotions— His Ideas of Gravitation— His Religious Character- Galileo, bom
1564, died 1642 — The First to apply a Telescope to the Heavens— Discovers the Four
Satellites and Belts of Jupiter— His Researches in Mechanics — Is summoned before the
Inquisition for Heresy — Retracts his Opinions, but persistsin teaching the Doctrine of
the Earth's Motion — Is again summoned before the Inquisition — His Sentence to Im-
prisonment for Life — Becomes Blind — His scientific Character — Labours of Bouillaud,
and of Borelli — Suggestion of Dr. Hooke on Gravity — His Circular Pendulum — His
Experiments veith it — His Views respecting the Cause of the Planetary Motions.

From the optical researches of Newton, brilliant though they
he, we turn with fresh wonder to the contemplation of his astro-
nomical discoveries — those transcendent deductions of human
reason,*^ by which he has added to the scientific glory of his
country, achieved for 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
won by his single arm. The torch of many a preceding age
had cast its light into the labyrinths of the material universe,
and the grasp of many a powerful hand had thrown down the
most impregnable of its barriers. An alliance indeed of many
kindred spirits had been long struggling in the combat, and

220 LIFE OF SIR ISAAC NEWTON. CHAP. XI.

Newton was but the leader of the mighty phalanx — the director
of their combined genius — the general who won the victorj^,
and wears its laurels.

The history of science presents us with no example of an
individual mind throwing itself far in advance of its contempo-
raries. It is only in his career of crime and ambition that
reckless man takes the start of his species, and, uncurbed by
moral and religious ties, represses the claims of truth and jus-
tice, and founds an unholy empire upon the ruins of ancient and
venerable institutions. The achievements of intellectual power,
though frequently begun by one mind, and completed by an-
other, have ever been the results of united labour. Slow in their
growth, they gradually approximate to a more perfect condition :
The variety in the objects and phenomena of nature, summons
to research a variety of intellectual gifts : Observation collects
her materials, and patiently plies her humble avocation : Expe-
riment, with her quick eye and ready hand, develops new facts :
The lofty powers of analysis and combination generalize insu-
lated results, and establish physical laws ; and in the ordeal of
contending schools and rival incjuirers, truth is finally purified
from error. How difterent is it with those systems which the
imagination rears — those theories of wild import which are
directed against the liberties, the consciences, and the hopes of
man ! The fatal poison tree distils its virus in the spring as
well as in the summer and 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
juice elaborated by the light and heat of a summer and an
autumnal sun.

In the century which preceded the birth of Newton, the
science of astronomy advanced with the most rapid pace.
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.
Ancient astronomers, indeed, had cleared and paved the way for

1497. LIFE OF SIR ISAAC NEWTON. , 221

the onward march of their science. A century and a half
before Christ, Hipparchus, in his observatory at Rhodes, made
the first catalogue of the stars, and representing the motions of
the sun and moon by epicycles revolving upon circular orbits,
he compiled tables for calculating their places in the heavens.
Guided by the genius of Hipparchus, Claudius Ptolemy, a cen-
tury and a half after Christ, though he placed the earth in the
centre of the system, improved the theories of the sun, moon,
and planets — discovered the principal inequality in the moon's
orbit — gave a theory of astronomical refractions more complete
than that of any astronomer before Cassini, and bequeathed to
posterity the valuable legacy of his Almagest, and his Five Books
of Optics}

After centuries of darkness, Bagdad, the capital of Arabia,
became the focus of science. The ancient astronomy was pre-
served and cultivated, but though new and more accurate obser-
vations were made, the science lay prostrate amid the cumbrous
appendages of cycles and epicycles.

In the thirteenth century, the noble-minded Alphonso x.,
sovereign of Castile, published, at a great expense, new astro-
nomical tables, computed by the most distinguished professors in
the Moorish universities ; and, as if he had obtained a glimpse
of a simpler arrangement, he denounced the rude mechanism of
epicycles in language less reverent in its expression than in its
truth. Were the heavens thus constituted, he said, I could
have given the deity good advice had he consulted me at their
creation. Notwithstanding these obstructions. Astronomy ad-
vanced, though with faltering steps, unable to escape from
the trammels of authority, and free itself from those vulgar
prejudices which a false interpretation of Scripture had excited
against a belief in the motion of the earth.

In this almost stationary condition, however, the science of
the heavens was not suffered to remain. Nicolas Copernicus
arose — a philosopher fitted to develop the true system of the

1 See Art. Optics in Edin. Encyclopaedia, vol. xv. p. 462.

<•}'}•)

LIFE OF SIK ISAAC NEWTON. CHAP. XI.

universe, and a priest willing to give absolution for the sin of
placing the great luminary in the centre of the sj'stem. This
distinguished individual, a native of Thorn in Prussia, though
of Bohemian origin, was bom on the 19th January 1472. He
at first followed his father s profession of medicine, but finding
it uncongenial with his love of astronomy, he went to Bologna
to study that science under Dominic Mario. In this situation
he was less the disciple than the assistant and friend of Mario,
and we find that he had made observations on the moon at
that place in 1497. About the year 1500, he went to Rome,
where he taught mathematics publicly to a large assemblage
of youth, and of persons of distinction ; and in the month of
November of the same year, he observed an eclipse of the
moon, and made other observations which formed the basis of
his future researches. While thus occupied, the death of one
of the Canons of the Cathedral Church of Ermeland, at Frauen-
burg, enabled his imcle, who was Bishop of that See, to nomi-
nate him to the vacant office. In this secluded spot, — in the
residence of the Canons, situated on the brow of a hill, Coper-
nicus carried on his astronomical observations. Dming his
sojourn at Rome, the Bishop of Fossombrossa, who presided
over the council for reforming the calendar, had requested his
assistance in that important undertaking. Upon this congenial
task he entered with youthful zeal. He charged himself witli
the duty of determining the length of the year, and the other
elements which were required hj the council ; but the observa-
tions became irksome, and interfered with the completion of
those interesting views which had already dawned upon his
mind.

Convinced that the simplicity and harmony which appeared
in the other works of creation should characterize the arrange-
ments of the planetary system, he could not regard the hypo -
thesis of Ptolemy as a representation of nature. This opinion
was strengthened by actual observation. The variable appear-
ance of the superior planets, of Mars, for example, in opposition

1530. LIFE OF SIR ISAAC NEWTON. 223

and conjunction, — in the one case shining with the effulgeii(;e
of Jupiter, and in the other with the light of a secondary star,
was irreconcilable with the dogma that the planet moved round
the earth. That it moved round the sun was the conclusion
to which he was then led ; and the grand idea of the bright orb
of day being the centre of the planetary system burst upon his
mind, though perhaps with all the dimness of a dream — the first
phase of eveiy great discovery. In the opinions of the Egyptian
sages, — in those of Pythagoras, Philolaus, Aristarchus, and
Nicetas of Syracuse, he recognised his first conviction that the
earth was not the centre of the universe ; and in the works of
Martianus Capella, he found it to be the opinion of the Egyp-
tians that Mercuiy and Venus revolved about the sun during
his annual motion roimd the earth. Thus confirmed in his
views, the difficulties which had previously surrounded them
were gradually dispelled, and after thirty-six years of intense
study, in which the labours of the observer, and the calculations
of the mathematician, were combined with the sagacity of the
philosopher, he was permitted to develop the true system of
the heavens.

lu his eye the sun stood immovable in the centre of the
universe, while the earth revolved annually round him between
the orbits of Venus and Mars, producing by its rotation upon
its axis in twenty-four hours all the diurnal phenomena of the
celestial sphere — Mercury and Venus moving round the sun
within the earth's orbit, and all the rest of the planets without
it, while the moon revolved monthly round the earth during its
annual motion. In the system thus constituted, all the pheno-
mena of the celestial motions received an immediate explanation.
The alternation of day and night — the vicissitudes of the sea-
sons — the varying brightness of the planets — their stations and
retrogradations, and even the precession of the Equinoxes,
became the necessary results of the Copernican System.

The circulation of these great truths, and of the principles
on which they rest, became the leading object of Copernicus's.

224 LIFE OF SIR ISAAC NEWTON. CHAP. XI.

life. The Canon of Ermeland, however, saw the difficulties of
his position, and exhibited the most consummate prudence in
surmounting them. Aware of the prejudice and even of the
hostility with which his discoveries would be received, he
resolved neither to startle the one nor provoke the other. He
committed his opinions to the slow current of personal com-
munication. The points of opposition which they presented to
received doctrine were thus gradually worn down, and they
insinuated themselves into ecclesiastical minds by the very
reluctance of their author to bring them into notice. In 1536,
Cardinal Nicolas Schonberg, Bishop of Capua, i and Tidemann
Gyse, Bishop of Culm, exerted all their influence to induce
Copernicus to lay his system before the world ; but their
entreaties were in vain, and it was not published till 1539,
when an accidental circumstance contributed with other causes
to alter his resolution.^ Having heard of the system of Coper-
nicus, George Rheticus, Professor of Mathematics at Wirtem-
berg, resigned his chair, and repaired to Frauenburg to make
himself master of his discoveries. After studying and adopting
them, this zealous disciple prevailed upon Copernicus to permit
their publication ; and they seemed to have arranged a plan
for giving them to the world without alarming the vigilance of
the Church. Under the disguise of a student of mathematics,
Rheticus published in 1540 an account of the manuscript
volume of Copernicus. The pamphlet was received without
any expression of censure, and its author was thus encouraged
to reprint it at Basle with his own name. The success of these
publications, and the flattering manner in which the new astro-
nomy was received, combined with the solicitations and even
reproaches of his friends, overcame the scruples of Copernicus,
and induced him to place his manuscript in the hands of
Rheticus. It was accordingly printed at the expense of
Cardinal Schonberg, and was published at Nuremberg in 1543,

1 The Cardinal's letter is published in the work of Copernicus afterwards mentioned.

2 These facts are recorded by Copernicus himself in the preface to his work.

1543. LIFE OF SIR ISAAC NEV/TON. 225

under the title of " On the Revolutions of the Celestial Bodies.'"'^
Its illustrious author, however, did not live to peruse it. A
complete copy was handed to him on his dying day, and he
saw and touched it a few hours before he expired. ^ In an
introductory address " on the hypotheses of his work," Coperni-
cus propitiates such of his readers as may be alarmed at their
novelty, by assuring them that it is not necessary that astrono-
mical hypotheses be either true or probable, and that they
accomplish their object if they reconcile the calculus with
observation.^ With the same view he inscribed his preface to
the Holy Pontiff himself,* and boldly alludes to the hostility to
which his opinions will expose him. " I have preferred," says
he, " dedicating my lucubrations to your Holiness rather than
to any other person, because, in the very remote corner af the
world in which I live, you are so distinguished by your rank
and your love of learning and mathematics, that you will easily
repress the virulence of slander, notwithstanding the proverb
that there is no remedy against the wound of the sycophant."
And " should there be any babblers who, ignorant of all mathe-
matics, presume to judge of these things, on account of some
passage of Scripture wrested to their own purpose, and dare to
blame and cavil at my work, I will not scruple to hold their
judgment in contempt. .... Mathematics are written for
mathematicians, and I am much mistaken if such men will not
regard my labours as conducive to the prosperity of the ecclesi-
astical republic over which your Holiness presides." Thus
recommended to the sovereign authority of the Church, and
vindicated against the charge of being hostile to Scripture, the

1 Nicolai Copemici Torinensis De Revolutionibus orbium coelestium, Lib. vi. Fol. A
second edition in folio appeared at Basle in 1666, and a third edition in quarto was pub-
lished at Amsterdam in 1617, with notes, by Nicolas Muler, under the title of Astro-
nomia Instaurata, &c.

- Copernicus died in 1543, at the age of 70.

3 Neque eniin aecesse est, eas hypotlieses esse ^eras, irao ne verisimiles quidem, sed
sufficit hoc unum, si calculum observationibus congruentem exhibeant." — Ad Lectorem.

* Paul III., a member of the Farnese family, who held the Pontificate from 1534 to
1560. The year in which this preface was written is not known.

VOL. I. • P

LIFE OF SIR ISAAC NEWTON. CHAP. XI.

Copernican system met with no ecclesiastical opposition, and
gradually made its way in spite of the ignorance and prejudices
of the age.

Although the true solar system was thus established, yet
much remained to be done by the practical astronomer before
the motions of the planets could be subjected to mechanical
laws. Copernicus had not rejected the machineiy of epicycles ;
and the distances of the planets and the form of their orbits
were very imperfectly known. A skilful observer, therefore,
expert in mechanism, and girt for nocturnal labour, was now
required to prepare for Kepler distances and periods, and for
Newton the raw material of his philosophy.

The astronomer thus required appeared in the person of
Tycho Brahe, who was born at Knudstrup, in Scania, on the
14th December 1546, three years after the death of Coper-
nicus. When a student at Copenhagen, the great solar eclipse
of the 21st August 1560, arrested his attention, and having
found that all its phases had been accurately predicted, he
resolved to acquire the knowledge of a science so infallible in
its results. Though destined for the profession of the law, he
refused to enter upon its study ; and when urged to it by the
entreaties and reproaches of his friends, he escaped from their
importunities by travelling into Germany. During his visit to
Augsburg, he resided in the house of Peter Hainzell, the burgo-
master, whom he inspired with such a love of astronomy, that
he erected an excellent obseiTatory at his own expense, and
thus enabled his youthful instructor to commence that splendid
career of observation which has placed him in the first rank of
practical astronomers.

On his return to Copenhagen in 1570, he was welcomed by
the King and the nobility as an honour to the nation, and his
maternal uncle at Herritzvold, near his native place, offered
him a retreat from the gaieties of the capital, and every accom-
modation for pursuing his astronomical studies. Love and
alchemy, however, distracted his thoughts ; and he found the

159(». LIFE OF SIR ISAAC NEWTON. 227

peasant girl, whom he fancied, of easier attainment than the
jjhilosopher's stone. His noble relatives were deeply offended
with the marriage, and it required all the influence of the King
to allay the quarrel which it occasioned. In 1572 and 1573,
he had observed the remarkable star in Cassiopeia, which
rivalled Venus in her greatest brightness, and which, after
being the wonder of astronomers for sixteen months, disap-
peared in March 1574 ; but he refused, for a long time, to
publish his observations upon it, lest he should thus cast a stain
upon his nobility !

Fickle in purpose, and discontented with Denmark, Tycho
set out in search of a more suitable residence ; but when the
King heard of his plans, he resolved to detain him by acts of
kindness and liberality. He was therefore presented to the
canonry of Roschild, with an annual income of 2000 crowns,
and an additional pension of 1000 ; and the island of Huen
was offered to him as the site of an observatory, to be furnished
with instruments of his own choice. The generous offer was
instantly accepted. The celebrated observatory of Uraniburg
— the city of the Heavens — was completed at the expense of
£20,000, and from its hallowed towers Tycho continued for
twenty-one years to enrich astronomy with the most valuable
observations. From every kingdom in Europe admiring dis-
ciples repaired to this sanctuary of the sciences, to acquire a
knowledge of the heavens ; and kings and princes felt them-
selves honoured as the guests of the great astronomer.

Among the princes who visited Uraniburg, we are proud to
enumerate James vi. of Scotland. In 1590, during his visit
to Denmark to celebrate his marriage with the Princess Anne,
he spent eight days with Tycho, accompanied by his counsellors
and a large suite of nobility. He studied the construction and
use of the astronomical instruments ; he inspected the busts
and pictures in the Museum, and when he found among them
the portrait of his own distinguished preceptor, George Buchanan,
he could not refrain fx'om the strongest expressions of delight.

228 LIFE OF SIR ISAAC NEWTON. CHAP. XI.

Upon quitting Uraniburg, James not only presented Tyclio
with a magnificent donation, but afterwards gave him his Royal
license to publish his works in England.

The equanimity of Tycho was not disturbed by these marks
of respect and admiration ; but while they animated his zeal
and stimulated his labours, they were destined to be the instru-
ments of his ruin. By the death of Frederick ii. in 1588,
Tycho lost his most valued friend ; and though his son and
successor, Christian iv., visited Uraniburg, and seemed to take
an interest in astronomy, his wishes to foster it, if he did
cherish them, must have been overruled by the influence of his
counsellors. The parasites of royalty found themselves eclipsed
by the brightness of Tycho's reputation. They envied the
munificent provision which Frederick had made for him ; and
instigated by a physician who was jealous of his reputation, as
a successful practitioner of medicine, they succeeded in exciting
against Tycho the hostility of the Court. Walchendorp, the
President of the Council, was the tool of his enemies, and on
the ground of an exhausted treasury, and the inutility of the
studies of Tycho, he was deprived of his canonry, his pension,
and his Norwegian estate.

Thus stripped of his income, and degraded from his office,
Tycho, with his wife and family, sought for shelter in a foreign
land. His friend. Count Henry Rantzau, offered him the
hospitality of his Castle of Wandesberg, near Hamburg, and
having embarked his family and his instruments on board a
small vessel, the exiled patriarch left his ungrateful country
never to return. In the Castle of Wandesberg he enjoyed
the kindness and conversation of his accomplished host, by
whom he was introduced to the Emperor Rodolph, who, to a
love of science, added a passion for alchemy and astrology.
The reputation of Tycho having already reached the Imperial
ear, the recommendation of Rantzau was hardly necessary to
insure him his warmest friendship. On the invitation of the
Emperor, he repaired in 1599 to Prague, where he met with

1601. LIFE OP SIR ISAAC NEWTON. 229

the kindest reception. A pension of three thousand crowns
was immediately settled upon him, and a commodious obser-
vatory erected for his use. Here he renewed with delight
his interrupted labours, and rejoiced in the resting-place which
he had so unexpectedly found for his approaching infirmities.
These prospects of returning prosperity were enhanced by
the pleasure of receiving into his house two such pupils
as Kepler and Longomontanus ; but the fallacy of human
anticipations was here, as in so many other cases, strikingly
displayed. His toils and his disappointments had made severe
inroads upon his constitution. Though surrounded wdth affec-
tionate friends and admiring disciples, he was still an exile in
a foreign land. Though his country had been base in its in-
gratitude, it was yet the land which he loved — the scene of his
earliest affections — the theatre of his scientific glory. These
feelings constantly preyed upon his mind, and his unsettled
spirit w^as 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 him. He
implored his pupils to persevere in their scientific labours. He
conversed with Kepler on some of the profoundest questions
in astronomy, and with these secular occupations he mingled
frequent acts of piety and devotion. In this happy frame of
mind he expired without pain on the 24th October 1601, at
the age of fifty -five, the unquestionable victim of the councils
of Christian iv.

Among the great discoveries of Tycho, his improvements of
the lunar theory are perhaps the most important. He discovered
the inequality, called the variation, amounting to thirty-seven
minutes, and depending on the distance of the moon from the
sun. He discovered also the annual inequality of the moon
depending on the position of the earth in its orbit, and affecting
also the place of her apogee and node. He determined like-
wise the greatest and the least inclination of the moon's orbit.

230 LIFE OF SIR ISAAC NEWTON. CHAP. XT.

and he represented this variation by the motion of the pole of
the orbit in a small circle. Tycho had the merit, too, of being
the first to correct by the refraction of the atmosphere the
apparent places of the heavenly bodies ; but, what is very
unaccountable, he made the refraction which he found to be
34' in the horizon, to vanish at 45°, and he maintained tlmt
the light of the moon and stars was refracted differently by the
atmosphere! By his observations on the comet of 1577 he
proved that it was three times as distant as the moon, and
that since these bodies moved in all directions, the doctrine of
solid orbs could not be true. By means of large and accurately
divided instruments, some of which were altitude and azimuth
ones, having their divided circles six and nine feet in diameter,
and others mural quadrants, sextants, and armillary spheres, he
made a vast collection of observations, which led Kepler to the
discovery of his celebrated laws, and formed the basis of the
Rudolphine Tables. But the most laborious of his undertakings
was his catalogue of 777 stars, for the epoch of 1600, a.d.^ —
a catalogue afterwards enlarged by Kepler from Tycho's obser-
vations, and published in 1627.^ The skill of Tycho in
observing phenomena, surpassed his genius for discovering their
cause, and it was perhaps from a mistaken veneration for the
Scriptures, rather than from the vanity of giving his name to
a new system, that he rejected the Copernican hypothesis. In
the system which bears his name, the earth is stationary in the
centre of the universe, while the sun, with all the other planets
and comets revolving around him, performs his daily revolution
about the earth.

Notwithstanding the great accessions which astronomy had
received from Copernicus and Tycho, yet no progress had been
made in developing the general laws of the Solar System,
and scarcely an idea had been formed of the invisible power
by which the planets were retained in their orbits. The

1 Astronomice InstauraUe Progymnasmata. 1602.

2 Published at the end of the Rudolphine Tables.

1571-95. LIFE OF SIR ISAAC NEWTON. 231

materials, however, were prepared, and Kepler arose to lay
the foundations of a structure which Newton was destined to
complete.

John Kepler was born at the imperial city of Wiel, in Wir-
temberg, on the 21st December 1571. Although his early
education was neglected, he made considerable progress in his
studies at the preparatory school of Maulbronn, and when he
took his degree of Master of Arts at the University of Tubingen
in 1591, he held the second place at the examination. While
he was the mathematical pupil of Msestlin, he not only adopted
his views of the Copernican System, but wrote an essay on the
" Primary Motion," as produced by the earth's daily rotation.
When the astronomical chair at Gratz, in Styria, fell vacant
in 1594, Kepler accepted the appointment, although he knew
little of mathematics. His attention, however, was necessarily
turned to astronomy, and in 1595, when he enjoyed some pro-
fessional leisure, he directed the whole energy of his mind to
the number, the dimensions, and the motions of the orbits of
the planets. After various fruitless attempts to discover some
relation betv/een the distances and magnitude of the planets, by
assuming the existence of new i)lanets in the wider spaces, he
at last conceived the extraordinary idea that the distances of
the planets were regulated by the six regular geometrical solids.
" The Earth's orbit," says he, " is the sj^here, the measurer of
all. Round it describe a dodecahedron^ the circle including
this will be (the orbit of) Mars. Round Mars describe a
Mrahedron, the circle including this will be Jupiter. Describe
a cuhe round Jupiter, the circle including this will be Saturn.
Then inscribe in the (orbit of the) Earth an icosahedron, the
circle described in it will be Venus. Describe an octohedron
round Venus, the circle inscribed in it will be Mercury.'' This
singular law, rudely harmonizing with some of Copernicus's
measures, would have failed, for want of solids, in its applica-
tion to Uranus and Neptune ; but it took possession of Kepler's
mind, and he declared that he " would not barter the glory of

2S2 LIFE OF SIR ISAAC NEWTON. CHAP. XI.

its invention for the whole Electorate of Saxony."^ When
Galileo's opinion of this hypothesis was requested by Kepler,
he praised the ingenuity which it displayed ; but when a copy
of the Prodromus was presented to Tycho, he advised his
young friend " first to lay a solid foundation for his views by
actual observation, and by ascending from these to strive to
reach the cause of things ;" and there is reason to believe, that
by the magic of the whole Baconian philosophy thus compressed
by anticipation into a nutshell, Kepler abandoned for a while
his visionary speculations.

When driven by religious persecution from the states of
Styria, he accepted an invitation from Tycho to settle at Prague
as his assistant. Here he was introduced to the Emperor
Kodolph, and upon Tycho's death in 1601, he was appointed
mathematician to the Emperor, a situation which he held
during the successive reigns of IMatthias and Ferdinand.

After devoting much of his time to the subjects of refraction
and vision, and adding largely to our knowledge of both these
branches of Optics,^ he resumed his inquiries respecting the
orbits of the planets. Possessed of the numerous and valuable
observations of Tycho, he endeavoured to represent them by
the hypothesis of a uniform motion in circular orbits ; but in
examining the orbit of Mars, he found the deviations from a
circle too great to be owing to errors of observation. He
therefore compared the observations with various other curves,
and was led to the fine discovery that Mars revolved round the
sun in an elliptical orbit in one of the foci of which tlie su7f
himself was placed. By means of the same observations he
computed the dimensions of the planet's orbit, and by com-
paring the times in which Mars passed over diff'erent parts of
it, he found that they were to one another as the areas de-

1 These researches were published in his Prodromus Lisscrtationum Cosmographi
corum, &c. Tubingse, 1596, 4to.

2 Kepler was foiled in his attempt to find out the law of refraction, afterwards disco-
Tered by Snellius. His optical discoveries will be found in his Paralipomcna ad Vitcl-
fionem, Francof. 1604 ; and in his admirable Dioptrica, Franc. 1611.

1618. LIFE OF SIR ISAAC NEWTON. 233

scribed by the lines drawn from the centre of the planet to the
centre of the sun, or, in more technical language, that the
radius vector^ or line joining the sun and planet, describes
equal areas in equal times. These two brilliant discoveries,
the first ever made in physical astronomy, were extended to all
the other planets of the system, and were given to the world
in his Commentaries on the Motions of the Planet Mars.^

Thus successful in his researches, and overjoyed with the
result of them, Kepler renewed his attempts to discover the
mysterious relation which he believed to exist between the
mean distances of the planets from the sun. Distrusting his
original hypothesis of the geometrical solids, he compared the
planetary distances with the intervals of musical notes, but
though he was supported in this notion by the opinions of
Pythagoras, and even of Archimedes, his comparisons were
fruitless, and he was about to abandon an inquiry which
had more or less occupied his mind during seventeen years of
his life.

After Kepler had refused to accept the mathematical chair
at Bologna, which was offered to him in 1617, he seems to
have resumed his speculations " on the exquisite harmonies of
the celestial motions." On the 8th March 1618, he conceived
the idea of comparing the powers of the different numbers
which express the distances of the planets, with the powers of
the different numbers which express their periods round the
sun. He compared, for example, the squares and the cubes of
the distances with the same powers of the periodic times, and
he even made the comparison between the squares of the periodic
times and the cubes of the distances ; but having, in the hurry
and impatience of research, been led into an error of calculation,
he rejected the last of these relations, — the relation that was
true, — as having no existence in nature. Before a week, how-
ever, had elapsed, his mind reverted to the law which he had

1 Nova Astronomia sett Physica Celestis (radita Commentariis de Motibns Stdloe
Martis. Pragae, 1609, fol.

234 LIFE OF SIR ISAAC NEWTON. CHAP. XI.

rejected, and, upon repeating his calculations, and discovering
his en'or, he recognised with rapture the great truth of which
he had for seventeen years been in search, tliat the jyeriodic
times of any two 'planets in the system are to one anothei' as the
cubes of their distances from the sun. This great discovery was
published in 1619 in his " Harmony of the World," ^ which
was dedicated to James vi. of Scotland, and which is marked
with all the pecidiarities of the author. The passage which
describes the feelings under which he recognised the truth of
his third law, is too instructive to be omitted from his his-
tory : — " What sixteen years ago I urged as a thing to be
sought — that for which I joined Tycho Brahe — for which I
settled in Prague — for which I have devoted the ' best part of
my life to astronomical contemplations — at length I have brought
to light, and have recognised its truth beyond my most sanguine

expectations It is now eighteen months since I got the

first glimpse of light, three months since the dawn ; a very few
days since the unveiled sun, most admirable to gaze on, burst
out upon me ... . the die is cast — the book is written, to
be read either now or by posterity, I care not which. It may
well wait a century for a reader, as God has waited six thousand
years for an intei-preter of his works." ^

As the planes of the orbits of all the planets, as well as the
line of their apsides passed through the sun, Kepler could not
fail to suspect that some power resided in that luminary, by
which the motions of the planets 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 in favour of that of the simple
distances. In the Introduction to his Commentaries on Mars,
he distinctly recognises the mutual gravitation of matter, in the
tlescent of heavy bodies to the centre of the earth, as the centre
of a round body of the same nature with themselves. He

1 Harmonia Mundi, lib. v. Linzii, 1619, fol,

2 Ibid. p. 178.

1630. LIFE OF SIK ISAAC NEWTON. 235

inaiiitaiiied, that two stones situated beyond the influence of a
third body would approach like two magnets, and meet at a
point, each describing a space proportional to the mass of the
other. He maintained also, that the tides were occasioned by
the moon's attraction, and that the lunar inequalities were
owing to the joint action of the sun and earth. Our country-
man, Dr. Gilbert, in his celebrated book De Magnete, published
in 1600, had about the same time announced similar opinions
on gravitation. He compares the earth's action upon the moon
to that of a great loadstone ; and in his posthumous work which
appeared half a century afterwards, he maintains that the earth
and moon act upon each other like two magnets, the influence
of the earth being the greater on account of its superior mass.
But though these opinions were a step in celestial physics, yet
the identity of the gxavity which is exhibited on the earth's
surface by falling bodies, with that which guided the planets in
their orbits, was not revealed either to the English 'or the Ger-
man philosopher. It required more patience and thought than
either could command, and its discovery was reserved for the
exercise of higher powers.

The misery in which Kepler lived, stands in painful contrast
with his arduous labours as an author, and his noble services
to science. His small pension was ever in arrears, and when
he retired to Silesia to spend the remainder of his days in re-
tirement, his pecuniary difficulties became more embarrassing
than before. He was compelled to apply personally for his
arrears ; and, in consequence of the great fatigue which he
suffered in his long journey to Ratisbon on horseback, he was
seized with a fever which carried him off on the 30th Novem-
ber 1630, in the fifty-ninth year of his age. Thus perished
one of the noblest of his race, a victim of poverty, and a martyr
to science.

In a work which is to record the religious character of New-
ton, it would be unjust to withhold from Kepler the credit
which is due to his piety and faith. The harmony of the

236 LIFE OF SIR ISAAC NEWTON. CHAP. XI.

universe, wliich he strove to expound, excited in him not only
admiration, but love. He felt his own humility the farther
he penetrated into the mysteries of the universe, and sensible
of the incompetency of his unaided powers for such transcen-
dent researches, and recognising himself as but the instrument
of the Almighty in making known his wonders, he never entered
upon an inquiry without praying for assistance from above.
Nor was this frame of mind inconsistent with the tumultuous
delight with which he surveyed his discoveries. His was the
unpretending ovation of success, not the ostentatious triumph
of ambition ; and if a noble pride occasionally mingled with
his feelings, it was the pride of being the chosen messenger of
physical truth, not the vanity of being the favoured possessor
of superior genius. With such a frame of mind, Kepler was
necessarily a Christian. The afflictions with which he was
tried confirmed his faith and brightened his hopes. He bore
them in all their variety and severity with Christian patience ;
and though he knew that this world was to be the theatre of
his glory, yet he felt that his rest and his reward could be
found only in another.

It is a remarkable fact in the history of astronomy, that
three of its most distinguished cultivators were contemporaries.
Galileo was tlie contemporary of Tycho during thirty-seven
years, and of Kepler during the fifty-nine years of his life.
Galileo was born seven years before Kepler, and survived him
nearly the same time. We have not learned that the intel-
lectual triumvirate of the age enjoyed any opportunity for
mutual congratulation. What a privilege would it have bean
to have contrasted the aristocratic dignity of Tycho with the
reckless ease of Kepler, and the manly and impetuous mien of
the Italian sage !

While his two predecessors were laying deeply and surely
the foundations of physical astronomy, Galileo was preparing
himself for extending widely the limits of the Solar system, and
exploring the structure of the bodies that compose it. He was

lt)09. LIFE OF SIR ISAAC NEWTON. 237

born at Pisa on the 15th February 1564, and was descended
from the noble family of Bonajuti. Although he exhibited an
early passion for geometry, and had studied without a master
the writings of Euclid and Archimedes, yet even after he was
called to the mathematical chair at Pisa in the twenty-fifth
year of his age, he was more distinguished for his hostility to
the Aristotelian philosophy than for his progress in original
inquiry. In 1592 he was promoted to the same chair in
Padua, where he remained for eighteen years, adorning the
university by his talents, and diffusing around him a taste for
science. With the exception of some minor contrivances, Galileo
had made no discovery till he entered his forty-fifth year, an
age at which Newton had completed all his discoveries. In
1609, the memorable year in which Kepler published his
" New Astronomy," Galileo paid that visit to Venice during
which he heard of the telescope of Lippershey.^ The idea of
so extraordinary an instrument at once filled his mind, and
when he learned from Paris that it had an existence, he re-
solved instantly to realize it. The simple idea, indeed, was the
invention, and Galileo's knowledge of optics was sufficient to
satisfy him that a convex lens at one end of a tube, with a
concave one at the other, would bring objects nearer to his eye.
The lenses were placed in the tube, the astronomer looked into
the concaye lens, and saw the objects before it " pretty largo
and pretty near him." This little toy, which magnified only
three times lineally, and nine times superficially, he carried in
triumph to Venice, where the chief magistrate obtained it in
barter for the life possession of his professorship, and 480
florins as an increase of salary. The excitement produced on
this occasion at Venice was of the most extraordinary kind ;
and, on a subsequent occasion, when Sirturi^ had made one of
the instruments, the populace followed him with eager curiosity,
and at last took possession of the tube, till they had each

^ Professor Moll, Jownal of Royal Instihition, 1831, vol. i. p. 496.
2 Sirturus, Be Tekscopio. Francofurtae, 1618.

238 LIFE OF SIR ISAAC NEWTON. CHAP. XI.

witnessed its wondrous effects. Galileo lost no time in availing-
himself of his new power. He made another telescope wliicli
magnified about eight or nine times, and, sparing neither labour
nor expense, he finally constructed an instrument so excellent,
as " to show things almost a thousand times larger (in surface),
and above thirty times nearer to the eye."

There is, perhaps, no invention in science so extraordinary
in its nature, and so boundless in its influence, as that of the
telescope. To the uneducated man the power of bringing
distant objects near to the eye must seem almost miraculous ;
and to the philosopher even who 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 power was placed, was a preference to
which Galileo owed much of his reputation.

Before the telescope was directed to the heavens, it was im-
possible to distinguisli a planet from a star. Even with his
first instrument, Galileo saw that Jupiter had a round appear-
ance like the sun and moon ; but, on the 7th January 1610,
when he used a telescope of superior power, he saw three little
bright stars very near him, ttvo to the right, and one to the
left of his disc. Though ranged in a line parallel to the eclip-
tic, he regarded them as ordinary stars ; but having, on the
8th of January, accidentally^ directed his telescope to Jupiter,
he was surprised to see the three stars to the west of the planet,
and nearer one another than before, — a proof that they had a
motion of their own. This fact did not excite his notice ; and
it was only after observing various changes in their relative
position, and discovering a fourth on the 13th of January,
that he was enabled to announce the discovery of the four
satellites of Jupiter.^

In continuing his observations with the telescope, Galileo

1 " Nescio quo fato ductus."— Suferci/.? Nuncius, p. 20.

2 The satellites were observed by our celebrated countryman, Harriot, on the 17t'a
October 1610.— See Martyrs of Science, Life of Galileo, pp. 40, 41.

IHIO. LIFE OF SIR ISAAC NEWTON. ' 239

discovered that Venus had the same crescent phases as the
waxing and the waning moon ; — that the sun had spots on his
surface which proved that he revolved round his axis ; — that
Saturn was not round, but had handles attached to his disc; —
that the surface of the moon was covered with mountains and
valleys, and that parts of the margin of her disc occasionally
appeared and disappeared ; — that the milky way consisted of
numerous stars, which the unassisted eye was unable to per-
ceive ; and that the apparent size of the stars arose from
irradiation, or a spurious light, in consequence of which they
were not magnified by the telescope. These various discoveries
furnished new arguments in support of the hypothesis of Co-
pernicus ; and we may now consider it as established by incon-
trovertible evidence, which ignorance or fanaticism only could
resist, that the sun is placed in the centre of the System, in the
focus of the elliptical, or in the centre of the nearly circular, orbits
of the planets, and that by some power, yet to be discovered, he
guides them in their course, while the Earth and Jupiter
exercise a similar influence over the satellites which accompany
them.

But it is not merely from his astronomical discoveries, brilliant
as they are, that Galileo claims a high place in the history of
Newton's discoveries. His profound researches on mechanical
science — his determination of the law of acceleration in falling
bodies — and his researches respecting the resistance and cohesion
of solid bodies, the motion of projectiles, and the centre of
gravity of solids, have ranked him among the most distinguished
of our mechanical philosophers. The great step, however, which
he made in mechanics, was his discovery of the general laws of
motion uniformly accelerated, which may be regarded as the
basis of the theory of universal gravitation.^

The current of Galileo's life had hitherto flow^ed in a smooth
and undisturbed channel. His discoveries had placed him at

' See Edinhtirgh Encyclopcedia, Art. Mechanics, vol. xiii. p. 502, where we hare
given a copious abstract of the mechanical discoTcries of Galileo.

240 LIFE OF SIR ISAAC NEWTON. CHAP. XI.

the head of the great men of the age, and with an income
above his wants, he possessed both the means and the leisure
for prosecuting his studies. Anxious, however, to propagate
the great truths which he discovered, and by force of reason to
make proselytes of his enemies, he involved himself in disputes
which tried his temper and disturbed his peace. When argu-
ment failed to convince his opponents, he wielded against them
the powerful weapons of ridicule and sarcasm, and he thus
marshalled against himself and his opinions the Aristotelian
professors, the temporizing Jesuits, the political churchmen,
and that timid section of the community who tremble at inno-
vation, whether it be in religion or in science. The party of
Galileo who abetted him in his crusade against error, though
weak in numbers, were strong in position and in zeal. His
numerous pupils occupying the principal chairs in the Italian
universities, formed a devoted band who cherished his doctrines
iind idolized his genius. The enemies of religion followed the
intellectual banner, and many princes and nobles, who had
smarted under ecclesiastical jurisdiction, were willing to see it
shorn of its power.

While these two parties were standing on the defensive,
Galileo hoisted the first signal for war. In a letter to his
friend and pupil, the Abb^ Castelli, he proved that the Scrip-
tures were not intended to teach us science and philosophy, and
that the expressions in the Bible were as irreconcilable with
the Ptolemaic as with the Copemican system. In reply to this
letter, Caccini, a Dominican friar, attacked G-alileo from the
pulpit, and so violent was his language, that Maraffi, the general
of the Dominicans, expressed his regret that he should be im-
plicated " in the brutal conduct of thirty or forty thousand
monks." Encouraged by this apology, Galileo launched another
pamphlet, addressed to the Grand Duchess of Tuscany, in which
he supports his views by quotations from the Fathers, and by
the conduct of the Koman Pontiff himself, Paul iii., in accepting
the dedication of Copernicus's work. It was in vain to meet

I(il5. LIFE OF SIR ISAAC XEWTON. 241

such arguments by any other weapon than that of the civil
power. It was deemed necessary either to crush the heresy, or
retire from the contest ; and the Church party determined to
appeal to the Inquisition.

Various circumstances concurred to excite the suspicions of
Galileo, and, about the end of 1615, he set off for Kome,
where he was lodged in the palace of the Tuscan ambassador.
While Galileo was enjoying the hospitality of his friend, Caccinl
was preparing the evidence of his heresy, and in due time he
was charged by the Inquisition with maintaining the motion of
the earth and the stability of the sun, — with teaching and
publishing this heretical doctrine, and with attempting to recon-
cile it to Scripture. On the 25th February 1615, the Inquisi-
tion assembled to take these charges into consideration, and
having no doubt of their truth, they desired that Galileo should
be enjoined by Cardinal Bellarmine to renounce the obnoxious
doctrines, and to pledge himself that he would neither teach,
publish, nor defend them in future. In the event of his refusing
to obey this injunction, it was decreed that he should be thrown
into prison. Galileo acquiesced in the sentence, and on the
following day he renounced before the Cardinal his heretical
opinions, abandoning the doctrine of the earth's motion, and
pledging himself neither to defend nor teach it either in his
writings or his conversation.

Although Galileo had made a naiTOw escape from the grasp
of the Inquisition, he left Rome in 1616 with a suppressed
hostility against the Church ; and his resolution to propagate
the heresy seems to have been coeval with the vow by which
he renounced it. Although he affected to bow to the decisions
of theology, he never scrupled, either in his writings or in his
conversation, to denounce them with the severest invective.
The Lyncean Academy, ever hostile to the Church, encouraged
him in this unwise procedure, and it was doubtless at their
instigation that he took the daring step which brought him a
second time to the bar of the Inquisition. Forgetting the

VOL. I. Q

24:2 LIFE OF SIR ISAAC NEWTON. CHAP. XI.

pledges under which he lay, — the personal kindness of the
Pope, — and the pecuniary obligations which he owed him, \w,
resolved to compose a work in which the Copernican system
should be indirectly demonstrated. This work, entitled. The
System of the World of Galileo Galilei, &c., was completed in
1630, but was not published till 1632, owing to the difficulty
of obtaining a license to print it. It was dedicated to the
Grand Duke of Tuscany ; and while the decree of the Inquisition
was referred to in insulting and ironical language, the Ptolemaic
system, the doctrine of the Church, was assailed by arguments
which admitted of no reply. The Copernican doctrines, thus
eloquently maintained, were eagerly received and widely dis-
seminated, and the Church of Rome felt the shock thus given
to its intellectual supremacy. Pope Urban viii., though attached
to Galileo, and friendly to science, was driven into a position
from which he could not recede. The guardian of its faith, he
mounted the ramparts of the Church to defend the weakest of
its bastions, and, with the artillery of the Inquisition, he silenced
the batteries of its assailants. The Pope brought the obnoxious
work under the eye of the Inquisition, and Galileo, advanced
in years, and infirm in health, was summoned before its stern
tribunal. He arrived in Rome on the 14tli of February 1663,
and soon after his amval he was kindly ^dsited by Cardinal
Barberino, the Pope's nephew, and other friends of the Churcli,
who, though they felt the necessity of its interference, were yet
anxious that it should be done with the least injury to Galileo
and to science.

Early in April, when his examination in person took place,
he was provided with apartments in the house of the Fiscal of
tiie Inquisition ; and to make this nominal confinement as
agreeable as possible, his table was provided by the Tuscan
ambassador, and his servant \\'as allowed to sleep in an adjoin-
ing apartment. Even with these indulgences, however, Galileo
could not brook the degradation under which he lay. A return
of his complaint ruftled his temper, and made him impatient

1(533. LIFE OF SIR ISAAC NEWToN. 243

for hi.s release ; and tlie Cardinal Barberino having been made
acquainted with his feelings, liberated the philosopher on hi,s
own responsibility, and on the 30th of April, after ten days'
confinement, restored him to the hospitable roof of the Tuscan
ambassador.

It has been stated on authority which is considered unques-
tionable, that during his personal examination Galileo was put
to the torture, and that confessions were thus extorted which
he had been unwilling to make. He acknowledged that the
obnoxious dialogues were written by himself; — that he had
obtained a license to print them without informing the function-
ary who gave it — and that he had been prohibited from
l)ublishing such opinions ; and in order to excuse himself, he
alleged that he had forgotten the injunction under which he
lay not to teach, in any manner, the Copernican doctrines.
After duly considering the confessions and excuses of their
}»risoner, the Inquisition appointed the 2 2d of June as the day
on which their sentence Avas to be pronounced. In obedience to
the summons, Galileo repaired to the Holy Office on the morning
of the 21st. Clothed in a penitential dress, he was conducted,
on the 2 2d, to the convent of Minerva, where the Inquisition was
assembled, and where an elaborate sentence was pronounced,
which will ever be memorable in the history of science. In-
voking the name of our Saviour and of the Holy Virgin,
Galileo is declared to be a heretic, in consequence of believing
that the sun was the centre of the earth's orbit, and did not
move from east to west, and defending the opinion that the
earth moved and was not the centre of the world. He is
tlierefore charged with having incurred all the censures and
penalties enacted against such offences ; but from all these he
is to be absolved, provided that with a sincere heart, and faith
imfeigned, he abjures and curses the heresies he has maintained,
as well as every other heresy against the Catholic Church. In
order to prevent the recurrence of such crimes, it was also de-
creed that his work should be prohibited by a formal edict, —

244 lifp: of sir isaac xewton. chap. xi.

that he should be imprisoned during the pleasure of the Inqui-
sition, — and that during the next three years he should recite
weekly the seven penitential psalms. This sentence was sub-
scribed by seven cardinals, and on the same day Galileo signed
the abjuration which the sentence imposed.

Clothed in the sackcloth of a repentant criminal, Galileo, at
the age of seventy, fell upon his knees before the assembled
cardinals, and laying his right hand on the Holy Evangelists,
he invoked the Divine assistance, in abjuring and detesting and
vowing never again to teach the doctrine of the earth's motion
and of the sun's stability. He pledged himself never again to
propagate such heresies either in his conversation or in his
writings, and he vowed that he would observe all the penances
which had been inflicted upon him. What a mortifying picture
does this scene present to us of moral infinnity and intellectual
weakness ! If we brand with infamy the unholy zeal of the
inquisitorial conclave, what must we think when we behold
the venerable sage, whose grey 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 1 Had Galileo
added the courage of the martyr to the wisdom of the sage, —
had he carried the glance of his eye round the circle of his
judges, and with uplifted hands called upon the living God to
witness the truth and immutability of his opinions, he might
have disarmed the bigotry of his enemies, and science would
have achieved a memorable triumph.

The sentence of abjuration was publicly read at several uni-
versities. At Florence it was promulgated in the Church of
Santa Croce, and the friends and disciples of Galileo were sum-
moned to the ceremonial, in order to witness the degradation of
their master. But though the Church was thus anxious to
maintain its authority, Galileo was personally treated with con-
sideration, and even kindness. After remaining only four days
in the dungeons of the Inquisition, he was, at the request of the

1638. LIFE OF SIR ISAAC NEWTON. 245

Tuscan ambassador, allowed to reside with him in his palace,
and when his health began to suffer, he was permitted to leave
Kome and to reside with his friend Piccolomini, Archbishop of
Sienna, under whose hospitable roof he completed his investi-
gations respecting the resistance of solids. At the end of six
months he was allowed to return to Florence, and before the
close of the year he re-entered his house at Arcetri, where he
spent the remainder of his days.

Although still a prisoner, Galileo had the happiness of being
with his family and living under his own roof ; but like the
other " spots of azure in his cloudy sky," it was ordained to
he of short duration. It was now that he was justly charac-
terized by the poet as " the starry Galileo with his woes."
His favourite daughter Maria, who, along with her sister, had
joined the convent of St. Matthew, near Arcetri, hastened to
the filial duties which she had so long been prevented from dis-
charging. She assumed the task of reciting weekly the seven
penitential psalms which formed part of her father's sentence ;
but she had scarcely commenced her domestic toils when she
was seized with a dangerous illness, which in a few weeks
proved fatal. Galileo was laid prostrate by this heavy and un-
expected blow. He was inconsolable for the loss of his daugh-
ter, and disease in various forms shook tlje frail tenement which
philosophy had abandoned. Time, however, the only anodyne
of sorrow, produced its usual effects, and Galileo felt himself
able to travel to Florence for medical advice. The Pope re-
fused him permission, and he remained at Arcetri from 1634
to 1638, preparing for the press his "Dialogues on Motion,"
and corresponding with the Dutch government on his proposal
to find the longitude by the eclipses of Jupiter's satellites.
Galileo, whose eyes had been gradually failing him since 1636,
was struck with total blindness in 1638. "The noblest eye,"
as his friend Father Castelli expressed it, " was darkened — an
eye so privileged and gifted with such rare powers, that it may
truly be said to have seen more than the eyes of all that are

246 LIFE OF SIR ISAAC NEWTON. (^HAP. XI.

gone, and have opened the eyes of all that were to come." To
the want of sight was soon added the want of hearing, and in
consequence of the mental labour to which he had been sub-
jected, " his head," as he himself said, " became too busy for
his body ;" and hypochondriacal attacks, want of sleep, acute
rheumatism, and palpitation of the heart, broke down his con-
stitution. His last illness, after two months' continuance,
terminated fatally on the 8th January 1()42, when he was in
the 78th year of his age.

" The scientific character of Galileo," as we have elsewhere^
had occasion to remark, " and his method of investigating truth,
demand our warmest admiration. The number and ingenuity
of his inventions, the brilliant discoveries which he made in the
heavens, and the depth and beauty of his researches respecting
the laws of motion, have gained him the applause of every
succeeding age, and have placed him next to Newton in the lists
of original and inventive genius. To this high rank he was
doubtless elevated by the inductive processes which he followed
in all his inquiries. Under the sure guidance of observation and
experiment, he advanced to general laws ; and if Bacon had
never lived, the student of nature would have found in the
writings and labours of Galileo not only the boasted principles
of the Inductive philosophy, but also their practical application
to the highest efforts of invention and discovery."

Among the astronomers who preceded Newton in astronomical
inquiries, and contributed some ideas to the establishment of the
true system of the planets, we must place the names of Bouil-
laud,^ Borelli, Hooke, Huygens, Wren, and Halley. After
refuting the magnetic notions of Kepler, Bouillaud maintained
that the force of attraction must vary reciprocally as the square,
and not, as Kepler asserted, in the simple ratio of the distance ;

1 Life of Galileo, chap. \i. in the Martt/rs of Science.

■ Ismaelis BuUialdi Astronomia Philola tea. —Vsiris, 164.5, p. 23. Sir Isanc admitted
that BuUialdus hei'e gives the true " proportion on gravity." — Liter to Ilallnj, June -H,
1686, postscript.

1()42. LIFPJ OF SIR ISAAC NEWTON. 247

but Delambre does not allow him any credit in this respect, and
remarks that he has done nothing more for astronomy than to
introduce the word evection into its language.

The influence of gravity as a central force in the planetary
motions has been very distinctly described by Borelli, Professor
of Mathematics at Pisa, in his work on the theory of Jupiter's
Satellites.^ He considers the motions of the planets round the
sun, and of the satellites round their primaries, as produced by
some virtue residing in the central body. In speaking of the
motion of bodies in circular orbits, he compares the tendency of
the body to recede from the centre of motion to that of a stone
whirled in a sling. When this force of recession is equal to the
tendency of the body to the centre, a balance is effected between
these tendencies, and the body will continually revolve round
the centre, and at a determinate distance from it. Delambre
attaches no value to these speculations of Borelli. He has in
his opinion pointed out no physical cause,^ and has merely made
a series of reflections which every astronomer would necessarily
make who was studying the theory of the satellites. He gives
him the credit, however, of being one of the first who conjectured
that the comets described round the sun elliptical or parabolic
orbits.^

The speculations of our distinguished countryman, Dr. Hooke,
respecting the cause of the planetary motions, exceeded greatly

' Theoricce Mediccem-um Pkmdarvm ex causis physicis deducted. A Alphonso E(j-
rellio.— Florentiaa, 1666.

- Newton (in his posthumous work, De Systeniate Miindi, § 2, Opera, torn. iii. p. ISO,
and in his postscript in his letter to Halley, June 26, 1688, where he says " that Borelli
did something") and Huygens have attached greater value to the views of Borelli. The
last of these philosophers thus speaks of them ; — " Retert Plutarchus in libro suprarae-
luorato de Facie in Orbe Lunce, fuisse jam olim qui putaret ideo manere lunam in orbe
suo, quod vis recedendi a terra, ob motum circularem, inhiberetur pari vi gravitatis, qua
ad terram accedere conaretur. Idemque tBvo nostro, non de luna tantum sed et planetis
ceteris statuit Alphonsus Borellius, ut nempe primariis eorum gravitas esset solera versus ;
lunis vero ad Terram Jovem et Saturnum quos comitantur. Multoque diligentius, sub-
tiliusque idem nuper explicuit Isaacus Newtonus, et quomodo ex his causis nascantur
Planetarum orbes Elliptici, quos Keplerus excogitaverat; in quorum foco altero Sol
jionitur. Christiani Hugenii Cosmotheoros, lib. ii. ad f nan. Opera, torn. ii. p. 720.

" Angelo Fabroni, Lcttere inedite d'uomini ilhisM., torn. i. p. 173.

248 LIFE OF SIR ISAAC NEWTON. CHAP. XI.

in originality and value the crude views of Borelli, and form a
decided step in physical astronomy. On the 21st of March
1066, he communicated to the Royal Society an account of a
series of experiments to determine if bodies experienced any
change in their weight at different distances from the surface of
the earth " either upwards or downwards." Kepler had main-
tained that this force, namely, that of gravity, was a property
inherent in all celestial bodies, and Hooke proposed " to consider
whether this gravitating or attractive power be inherent in the
parts of the earth ; and, if so, whether it be maguetical, elec-
trical, or of some other nature distinct from either." The
experiments which he made with the instrument described in
this communication, were far from being satisfactory, and he
was therefore led to the ingenious idea of measuring the force
of gravity " by the motion of a swing clock," which would go
slower at the top of a hill than at the bottom. ^

About two months afterwards, namely, on the 2 2d May 1666,
Hooke communicated to the Society a paper " On the inflexion
of a direct motion into a curve by a supervening attractive
principle." 2 After maintaining that the celestial bodies moving
in circular and elliptical orbits " must have some other cause
beside the first impressed impulse to bend their motion into
these curves," he considers the only two causes which appear to
him capable of producing such an efffect. The first of these
causes, which he considers an improbable one, is that the ten-
dency to a centre is produced by a greater density of the ether
in approaching to the sun. " But the second cause," he adds, " of
inflecting a direct motion into a curve may be from an attractive
property of the body placed in the centre, whereby it continually
endeavoiu-s to attract or draw it to itself. For if such a principle
be supposed, all the phenomena of the planets seem possible to
be explained by the common principle of mechanic motions ; and
possibly the prosecuting this speculation, may give us a true
hypothesis of their motion; and from some few observations their

' Birch's Hist, of Royal Society, vol. ii. pp. 69-72. 2 Ibid. vol. ii. pp. PO-92.

1066. LIFE OF SIR ISAAC NEWTON. 249

motions may be so far brought to a certainty that we may be
able to calculate them to the greatest exactness and certainty
that can be desired." After describing the circular pendulum^
for illustrating these views, he adds that " by this hypothesis
the phenomena of the comets, as well as of the planets, may be
solved ; and the motions of the secondary as well as of the
primary planets. The motions also of the progression of the
apsides are very evident, but as for the motion of lil)ration or
latitude that cannot be so well made out by this way of pendu-
lum ; but by the motion of a wheel upon a point is most easy."
By means of the circular pendulum already mentioned, it
was found that " if the impetus of the endeavour hy the tangent
at the first setting out was stronger than the endeavour to the
centre, there was then generated an elliptical motion whose
longest diameter was parallel to the direct endeavour of the
body in the first point of impulse. But if that impetus was
weaker than the endeavour to the centre, there was generated
such an elliptical motion whose shorter diameter was parallel
to the direct endeavour of the body in the first point of im-
pulse." Another experiment was made by fastening a small
pendulous body by a shorter string on the lower part of the
wire which suspended the larger ball, " that it might freely
make a circular or elliptical motion round about the bigger,
Avhilst the bigger moved circularly or elliptically about another
centre." The object of this arrangement was to explain the
manner of the moon's motion about the earth ; but neither of
the balls moved in such perfect circles and ellipses as when
they were suspended singly. "A certain point, however,
which seemed to be the centre of gravity of the two bodies,
however pointed (considered as one), seemed to be regularly
moved in such a circle or ellipsis, the two balls having other
peculiar motions in small epicycles about the same point." ^

1 This pendulum consisted of a wire fastened to the roof of the room, with a large
wooden ball of lignum vitce at the end of it.— Waller's Life of IJooke, p. xii.
- Waller's Life of Ho- he, p. xii. ; and Birch's Hist., vol. ii. p. 92.

2o() LIFE OF Sm ISAAC NEAVTON. CHAP. XI.

At a later period of his life, Hooke re8umed the considera-
tion of the subject of the planetary motions, and, in a work
which appeared in 1674,^ he published some interesting ob-
servations on gravity, which we shall give in his own words. —
" I shall hereafter," he says, " explain a system of the world
differing in many particulars from any yet known, but answer-
ing in all things to the common rules of mechanical motions.
This depends upon three suppositions : First, Tliat all celestial
bodies whatsoever have an attraction or gravitating power to-
wards 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 in-
fluence 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, de-
flected, and sent into a motion describing a circle, ellipsis, or
some other more compound curve line. The third supposition
is, that these 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 motion which,
if fully prosecuted, as it ought to be, will mightily assist tlie
astronomers to reduce all the celestial motions to a certain rule,
which I doubt will never l^e done without it. He that under-
stands the nature of the circular pendulum, and of circular

1 An Attempt to prove the Motion of the Earth, from Ohsermfions made ?>// Robert
ITooke, 4to. See Phil. Trans. No. 101, p. 12.

IH79. LIFE OF SIR ISAAC NEWTON. 251

motion, will easily imderstand the whole of this principle, and
will know where to find directions in nature for the true stat-
ing thereof. This I only hint at present to such as have
al)ility 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 T would first complete, and therefore cannot so
well attend it. But this I durst 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." ^

In this remarkable passage, the doctrine of universal gravi-
tation, and the general law of the planetary motions, are clearly
laid down. The diminution of gravity as the square of the
distance, is alone wanting to complete the basis of the New-
tonian philosophy ; but even this desideratum was in the course
of a few years supplied by Dr. Hooke. In a letter which he
addressed to Newton in 1679, relative to the curve described
by a projectile influenced by the Earth's daily motion, he
asserted, that if the force of gravity decreased as the square of
the distance, the curve described by a projectile would be an
ellipse, whose focus was the centre of the earth. But however
great be the merit which we may assign to Hooke' s experimen-
tal results and sagacious views, they cannot be regarded either
as anticipating the discoveries of Newton, or diminishing his
fame. Newton had made the same discoveries by independent
researches, and there is no reason to believe that he derived
any ideas from his contemporaries.

1 In quoting this passage, which Delainbre admits to be very curious, we think he
scarcely does justice to Hooke, when he says that what it contains is found expressly in
Kepler. It is quite true that Kepler mentioned as probable the law of the squares of
the distances, but be afterwards, as Delambre admits, rejected it for that of the simple
distances. Hooke, on the contrary, announces it as a truth. — See Astronoinie du ISinc
Sarle, pp. 9, 10. Clairaut has justly remarked, that the example of Hooke and Kepler
shows how great is the difference between a truth conjectured or asserted, and a truth
demonstrated.

2/52 LIFE OF SIR ISAAC NEWTON. CHAP. Xll.

CHAPTER XII.

The First Idea of Gravity occurs to Newton in 1665 — His first Speculations upon it — He
abandons the subject from having employed an erroneous measure of the Earth ;«
Radius — He resumes the subject in consequence of a discussion with Dr. Hooke. but
lays it aside, being occupied with his Optical Experiments — By ado[iting Picard's
Measure of the Earth he discovers the Law of Gravity, and the cause of the Planetary
Motions — Dr. Halley goes to Cambridge, and urges him to publish his Treatise on
Motion — The germ of the Principia which was composed in 1685 and 1686 — Corre-
spondence with Flamsteed — Manuscript of Principia sent to the Royal Society —
Halley undertakes to publish it at his own expense — Dispute with Hooke, who claims
the, discovery of the Law of Gravity — The Principia published in 1687 — The New
Edition of it by Cotes begun in 1709, and published in 1713 — Character and Contents
of the Work — General account of the discoveries it contains — They meet with opposi-
tion from the followers of Descartes — Their reception in Foreign Countries — Progress
of the Newtonian Philosophy in England and Scotland.

Such is a brief and general view of the labours and lives of
those illustrious men who prepared the science of Astronomy
for the application of Newton's genius. Copernicus had de-
termined the form of the Solar System, and the relative posi-
tion and movements of the bodies that composed it. Kepler
had proved that the planets revolve in elliptical orbits ; that
their radii vectores describe areas proportional to the times ;
and that the squares of their periodic times are as the cubes of
their distances from the sun. Galileo had added to the uni-
verse a whole system of secondary planets. Huygens had
given to Saturn a satellite, and the strange appendage of a
ring ; and while some astronomers had maintained the doctrine
of universal gravitation, others had referred the motions to an
attractive force, diminishing with the square of the distance,

Ifi72. LIFE OF SIR ISAAC NEWTON. 253

and producing a curvilineal motion from one in a straight
line.^

We have already seen that, in the autumn of 1665, Newton
was led to the opinion that the same power by which an apple
falls from a tree extends to the moon, and retains her in her
orbit ; but upon making the calculation, he found such a dis-
(^repancy between the two forces that he abandoned the sub-
ject, suspecting that the power which retained the moon in her
orbit might be partly that of gravity, and partly that of the
vortices of Descartes.^ This discrepancy arose from the adop-
tion of an erroneous measure o^ the semi-diameter of the
earth, of which the moon's distance was taken as a multiple.
Unacquainted with the more accurate determinations of Snellius ^
and Norwood,"^ the last of which would have given Newton
the exact quantity which he required, he adopted the measure of
sixty miles for a degree of latitude, which had been employed
by the old geographers and seamen, and in which, as Mr.
Rigaud conjectures, he may have placed the more confidence, as
it agreed with the result of the observations which Edward
Wright, a Cambridge mathematician, had published in 1610.

It does not distinctly appear at what time Newton became
acquainted with the more accurate measurement of the earth,
executed by Picard in 1670, and was thus led to resume his
investigations. Picard' s method of measuring his degree, and
the precise result which he obtained, were communicated to the
Royal Society on the 11th January 1672,^ and the result of his

1 In 1673, Huvgens had announced the relations between attractive force and velocity
in circular motion.

'- Whiston's Memoirs of his own Life, p. 37.

•^ Eratosthenes Bataviis, 1617. * Seaman's Practice, 1636.

5 Mr. Rigaud remarks, that " we do not know when Norwood's determination became
known to Newton, but we are certain that he was well aware of Snellius's measures quite
as soon as he was of Picard's, — probably much sooner, since the specific mention of
them is made in Varenius's Geography (cap. iv. pp. 24-26, 1672), of which he edited a
new edition at Cambridge in 1672." — Histm-ical Essay, p. 12. " Had he adopted," as
Mr. lligaud adds, '• 28,500 Rhinlund perches, the length of a degree given bySnellius, he
would have obtained for the moon's deflexion, in a minute, 15-5 feet."

254 LIFE OF SIR ISAAC NEWTON. CHAP. XII.

observations and calculations were publislied in the Pliilosoplii-
cal Transactions for 1675. But whatever was the time when
Newton became acquainted with Picard's measurement, it seems
to be quite certain that he did not " resume his former thoughts
concerning the moon" till 1684. Pemberton tells us, that
" some years after he laid aside" his former thoughts, " a
letter from Dr. Hooke put him on inquiring what was the real
figure in which a body, let fall from an high place, descends,
taking the motion of the earth roimd its axis into considera-
tion ;" and that this gave occasion to his resuming his former
thoughts concerning the moon, and determining, from Picard's
recent measures, that " the moon appeared to be kept in her
orbit purely by the power of gravity."^ But though Hooke' s
letter of 1679 was tlie occasion of Newton's resuming his in-

1 Among the manuscripts of Couduitt, I found the following statement regarding
Newton's " resuming his former thoughts concerning the moon :" —

" In 1673, Dr. Hooke wrote to him to send him something new for the TnnisadioKs,
whereupon he sent him a little dissertation to confute the common objection that if it
were true that the earth moved from ea^t to west, all falling bodies would be left to the
west; and maintained that, on the contrary, they would fall a little eastward, and
having described a ciirce with his hand to represent the motion of a falling hod;/, he dretc
a negligent stroke with Ids pen, from whence Dr. Hooke took occasion to imagine that he
meant the curve would be a spiral, whereupon the Doctor wrote to him that the curve
would be an ellipsis, and that the body would move according to Kepler's notion, which
gave Sir Isaac Newton an occasion to examine the thing thoroughly ; and for the foun-
dation of the calculus he intended, he laid down this proposition, that the areas dti-
scribed in equal times were equal, which, though as^^umed by Kepler, was not by him
demonstrated, of which demonstration the first glory is due to Newton."

Immediately after thi'* statement, Conduitt adds : " Pembcrtou, in his preface, mentions
this in another manner," and he quotes part of that preface.

The above extraordinary story of Hooke's having considered a negligent stroke of
Newton's pen as a spiral, and on that ground having charged him with maintaining that
falling bodies would describe such a curve, could not have been given on Newton's autho-
rity, but must, have been invented by an enemy of Hooke's. Newton himself admits, in
his letter to Ilalley, July 27, 1686, that Hooke's "correcting his spiral occasioned his
finding the theorem by which he afterwards examined the ellipsis."

In the preceding extract, the date 1673 is obviously erroneous. The document wiis
copied for me by the late Henry Arthur Wallop Fellowes, the elder brother of the Earl
of Portsmouth, who kindly assisted me in the examination of Newton's papers, and
who placed.at the top of the document the words (P. 49 in Jones), which I cannot ex-
plain.

1684. LIFE OP SIR ISAAC NEWTON. ZOO

(juirics, it does nut fix the time when he employed the measures
of Picard. In a letter from Newton to Halley in 1686, he
tells him that Hooke's letters in 1679 were the cause of his
" finding the method of determining the figures, which, when
I had tried in the ellipsis, I threw the calculations by, being
upon other studies ; and so it rested for about five years, till,
upon your request, I sought for the papers." Hence Mr.
Rigaud considers it clear, that the figures here alluded to were
the paths of bodies acted upon by a central force, and that the
same occasion induced him to resume his former thoughts con-
cerning the moon, and to avail himself of Picard's measures to
correct his calculations. It was, therefore, in 1684, that
Newton discovered that the moon's deflexion in a minute was
sixteen feet, the space through which a body falls in a second
at the surface of the earth. As his calculations drew to a close,
he is said to have been so nmch agitated that he was obliged to
desire a friend to finish them.^

Sir Christopher Wren and Hooke and Halley had each of
them, from independent considerations, concluded that " the
centripetal force decreased in the proportion of the squares of
the distances reciprocally."'^ Halley had in 1683-4 derived
this law^ " from the consideration of the sesquialterate propor-
tion of Kepler," but was imsuccessful in his attempts to demon-
strate by it the laws of the celestial motions. Sir Christopher
Wren had, "very many years" before 1686, attempted by the
same law " to make out the planet's motion by a descent to-
w^ards the sun, and an impressed motion," but had " given it
over, not finding the means of doing it ;" and Dr. Hooke, as
we have already seen, though he adopted the law^ of the squares,
never fulfilled his promise of proving that it could be applied
to the motions of the planets.'^ It is therefore to Newton alone

1 Robison's Works, vol. ii. p. 94, 1822. Tradition is, we believe, the only authority
for this anecdote. It is not supported by what is known of Newton's character.
- Priiicipia, lib. i. Prop. iv. Schol.
* These various facts are stated in a letter from Halley to Jiewton, dated June 29.

256 LIFE OF SIR ISAAC NEWTON. CHAP. XII.

that we owe the demonstration of the great truth, that the moon
is kept in her orbit by the same power by which bodies fall on
the earth's surface.

The influence of such a result upon such a mind, may be
more easily conceived than described. If the force of the
earth's gravity bends the moon into her orbit, the satellites of
the other planets must be guided by the same power in their
primaries, and the attractive force of the sun must in like
manner control the movements of the comets and the planets
which surround him. In the application of this grand tmth
to the motions of the Solar System, and to the perturbations
arising from the mutual action of the bodies that compose it,
Newton must have rejoiced in the privilege of laying the foun-
dation of so magnificent a work, while he could not fail to see
that the completion of it would be the achievement of other
minds, and the glory of another age. But, however fascinating
must have been the picture thus presented to his mind, it was
still one of limited extent. He knew not of the existence of
binary and multiple systems of stars, to which the theory of

1686. " According to your desire in j'our former, I waited upon Sir Christopher Wren,
to inquire of him if he had the first notion of the reciprocal duplicate proportion from
Mr. Hooke. His answer was, that he himself very many years since had had his thoughts
upon making out the planet's motions by a composition of a descent towards the sun and
an impressed motion ; but that at length he gave over, not finding the means of doim; it.
Since which time Mr. Hooke had frequently told him that he had done it, and attemptci
to make it out to him, but that he never was satisfied that his demonstrations were cogent.
And this I know to be true, that in January 168.3-4, I, having from the consideration of
the sesquialterate proportion of Kepler,, concluded that the centripetal force decreased
in the proportion of the squares of the distances reciprocally, came on Wednesday to
town (from Islington) where I met with Sir Christopher Wren and Mr. Hooke, and fall-
ing in discourse about it, Mr. Hooke aflSrmed that upon that principle all the laws of tlie
celestial motions were to be demonstrated, and that he himself had done it. I declared
the ill success of my attempts, and Sir Christopher, to encouraj^e the inquiry, said that he
would give Mr. Hooke some two months' time to bring him a convincing demonstration
thereof, and besides the honour he of us that did it should have from him the present of
a book of forty shillings. Mr. Hooke then said he had it, but that he would conceal it
for some time, that others trying and failing mijiht know how to value it when he should
make it public However, I remember that Sir Christopher was little satisfied that he
could do it, and though Mr. Hooke then promised to show it him. I do not find that in
that particular he has been so good as his word."

1686. LIFE OF SIR ISAAC NEWTON. 2o7

universal gravitation would be extended. He could not have
anticipated that Adams and Levemer would have tracked an
unseen planet to its place by the perturbations it occasioned :
Nor could he have conjectured that his own theory of gravita-
tion might detect the origin and history of nearly thirty planet-
ary bodies, revolving within a sphere apparently destined for
one. It was enough for one man to see what Newton saw.
The service in the Temple of Science must be performed by
many priests ; and fortunate is he who is called to the humblest
task at its altar. The revelations of infinite wisdom are not
vouchsafed to man in a day. A light so effulgent would para-
lyse the noblest intellect. It must break in upon it by degrees ;
and even each separate ray must be submitted to the ordeal of
various minds, — to the apprentice skill of one age, and to the
master genius of another.

It is not easy to determine the exact time when Newton first
adopted the great truth, " that the forces of the planets from
the sun are reciprocally duplicate of their distances from him,"
but there is suflicient evidence to show that it must have been
as early as 1666, and therefore contemporaneous with his
speculations on Gravity in his garden at Woolsthorpe. " In
one of my papers," says he,^ " writ (I cannot say in what year),
but I am sure some time before I had any correspondence with
Oldenburg,^ and that's above fifteen years ago (1671), the pro-
portion of the forces of the planets from the sun, reciprocally
duplicate of their distances from him, is expressed, and the pro-
portion of our gravity to the moon's conatu8 recedendi a centro
terrce, is calculated, though not accurately enough. That when
Hugenius put out his Horologium Oscilktorium, a copy being
presented to me, in my letter of thanks to him I gave those
rules in the end thereof a particular commendation for their
usefulness in philosophy, and added, out of my aforesaid paper,

1 Letter to Halley, June 20, 1686. See also Rigaud's Hist. Essay, pp. 51, 52.

2 It appears from Birch, in his Hist, of the Royal Society, vol. ill. p. 1, that Newton
bad written to Oldenburg a letter, dated January 6, 1G73.

VOL. I, R

258 LIFE OF SIR ISAAC NEWTON. CHAP. XII.

an instance of their usefulness in comparing the forces of thv
moon from the earth, and the earth from the sun ; in deter-
mining a problem about the moon's phase, and putting a limit
to the sun's parallax, which shows that I had then my eye
upon comparing the forces of the planets arising from their
circular motion, and understood it ; so that a v/hile after when
Mr. Hooke propounded the problem solemnly in the end of hi.s
attempt to prove the motion of the earth, if I had not known
tlie duplicate proportion before, I coidd not but have found it
now." In another letter to Halley, written about three weeks
afterwards,^ he distinctly states, that " for the duplicate pro-
portion I can affirm that I gathered it from Kepler's theorem
about twentij years ago," that is, in 1666. Hence it is obvious
that the written paper referred to by Newton was, as Mr.
Rigaud says, " the result of his early speculations at Wools-
thorpe," and that "the deduction from Kepler, which is said
to have preceded the calculation ^ by a twelvemonth, took placu^
in 1665."

Such was the state of Newton's knowledge regarding the law
of gravity, when, in January 1684, Halley, Wren, and Hooke
were discussing together the subject in London. Halley had
learned from this interview that neither of his friends possessed
a " convincing demonstration" of this law, and finding, after a.
delay of some months, that Hooke " had not been so good as
his word," in showing his demonstration to Wren, he set out
for Cambridge in the month of August 1684, to consult Newton
on the subject.^ Without mentioning either his own specula-

i July 14, 1686. Rigaud's Hist. Ess. App. pp. 39, 40.

- The eiToneous calculations from his having used an incorrect measure of the earth's
diameter.

3 In both the editions of the Commercium Epistolicum, drawn up by a committee of
Newton's best friends, there occurs the following passage, which has misled several of
Newton's biographers. " Anno . . . 1683, in . . . Actis Lipsicis pro mense Octobri.
calculi diflferentialis elementa primum edidit D. Leibnitius, Uteris a. g. l. designatus.
Anno autem 1683 ad finem vergente, D. Newtonus propositiones principales, earum quae
in Philosophiaj Principiis Mathematicis habentur Loudinum misit," &c., No. LXXI.
It is certain that li>84 should have been substituted for 1683. Mr. Rigaud, who justly

l(iS4. LIFE OF SIK ISAAC NEWTON. 2-31)

tions, or those of Hooke and Wren, lie at once indicated the
object of his visit by asking Newton what would be the curve
described by tlie planets on the supposition that gravity dimi-
nished at the square of the distance. Newton immediately
answered, an ElUiyse. Struck with joy and amazement, Halley
asked him how he knew it ? Why, replied he, I have calcu-
lated it ; and being asked for the calculation, he could not find
it, but promised to send it to him. After Halley left Cam-
bridge, Newton endeavoured to reproduce the calculation, but
did not succeed in obtaining the same result. Upon examining
carefully his diagram and calculation, he found that in describing
an ellipse coarsely with his own hand, he had drawn the two
axes of the curve instead of two conjugate diameters somewhat
inclined to one another. When this mistake was corrected he
obtained the result which he had announced to Halley.^

remarks that this could not have been an error of the press, as " the argument with
reference to Leibnitz would fall to the ground if 1684 were substituted for it," has en-
deavoured successfully to find out the cause of the mistake. In the Macclesfield Collec-
tion he found two Memoranda on the first communication of the Principia to the Royal
Society, said to be " from an original paper of Newton," which we presume means in
Newton's handwriting. In the first the date of 1683 is given, and in the second the
correct date of 1684, "the 3 having been evidently altered to 4," by Newton himself, so
that the editors of the Commcrcium Episioliaun made a grave mistake in adopting the
date 1683.

Since the publication of Mr. Rigaud's Historical Essay, Mr. Edleston has thronii a
new light on this subject. The two Memoranda mentioned by Mr. Rigaud are the com-
mencement of a critique by Newton himself on three papers by Leibnitz in the Leipsic
Acts for January and February 1689. The critique, which Mr. Edleston thinks was
probably written in 1712, occupied nearly six pages, and is preserved among the Lu-
casian Papers. The first sentence is given in four different forms. In the two first the
date 1684 is used, and in the two last 1683. " Newton," says Mr. Edleston, " first of all
clearly wrote 1684, then altered the 4 to a 3, afterwards crossed all the figures out, and
wrote distinctly 1683. .... Newton, therefore, after endeavouring to recollect the
exact year in which he sent up the fundamental proposition of the Principia to London,
antedated the event by a twelvemonth," so that no blame can be cast upon the editors of
the Commercium Ejyistolictim, for the erroneous date which they adopted. The critique
is given by Mr. Edleston in his Appepdix, p. 307. See Rigaud's Ilitt. Efsaij, pp. 16-18,
and his Appendix, No. xix.

1 We have given this account of Halley's interview with Newton, nearly as we find it
in Conduit's manuscript, in which May is erroneously mentioned as the time of Halley'^
visit. Halley's own account is more brief: — " The August following when I did myself

260 LIFE OF SIE ISAAC NEWTON. CHAP. XII.

Halley returned to London with the double satisfaction that
a grand truth had been demonstrated which he himself had
anticipated, and that he had the honour of bringing it to light.
He was indeed proud of the success of his mission, and after
the Principia had excited the admiration of Europe, he used
frequently to boast to Conduit that he had been the Ulysses
who produced this Achilles.^ In the month of November,
Newton fulfilled the promise he made to Halley, by sending him
through Mr. Paget- a copy of the demonstration which he had
brought to perfection ; and very soon after receiving it, Halley
took another journey to Cambridge, " to confer with Newton
about it." Immediately after his return to London, namely,
on the 10th December, he informed the Royal Society " that
he had lately seen Mr. Newton at Cambridge, who had showed
him a curious treatise De Motu^^ which at Dr. Halley' s desire
he promised to send to the Society to be entered upon their
register. " Mr. Halley was desired to put Mr. Newton in mind
of his promise for the securing this invention to himself, till
such time as he could be at leisure to publish it," and Mr. Paget
was desired to join with Mr. Halley.

the honour to Tisit you, I then learned the good news that you had brought the demon-
stration to perfection, and you were pleased to promise me a copy thereof, which I
received with a great deal of satisfaction from Mr. Paget." — Letter to Newton, June 29,
1686.

1 " Dr. Halley has often valued himself to me," says Conduitt, " for being the Ulysses
which produced this Achilles."

2 Mr. Paget was Mathematical Master in Christ's Hospital. He was a friend of New-
ton's, and was recommended by him to Flamsteed on the 3d April 1682, as a competitor
for the Mastership. Flamsteed joined in the recommendation, and after his appointment
found him " an able mathematician." He gave such satisfaction to the Governors, in-
deed, that they sent Flamsteed " a staff," and made him one of their number. Flamsteed
has left it on record that this accomplished young man, before seven years had expired,
became a drunkard, neglected his duties, lost his character, and banished himself to
India. What a lesson to the young who are accidentally associated with great men after
whom posterity inquires ! As the bearer of the germ of the Principia to Halley, Pa get's
name has for nearly two centuries been mentioned with honour. As a protege of Newton
and Flamsteed, who failed in justifying their recommendation, a blot has been left upon
his name, which but for that honour would never have been known. See Biiily's
Flamsteed, p. 125.

1684. LIFE OP SIR ISAAC NEWTON. 261

That Halley and Paget would, without delay, remind Newton
of his promise, and that Newton would fulfil it, there can be
no doubt ; and we accordingly find that about the middle of
February he had sent to Mr. Aston, one of the Secretaries of
the Royal Society, his " notions about motion." Mr. Aston,
as a matter of course, would thank Newton for the communi-
cation, and mention the fact of its being registered ; and that
all this was done, appears from a letter of Newton's to Aston
of the 23d February 1685, written on another subject, but
thanking him for " having entered on the register his notions
about motion." Newton added, " I designed them for you
before now, but the examining several things has taken a greater
part of my time than I expected, and a great deal of it to no
purpose. And now I am to go into Lincolnshire for a month
or six weeks. Afterwards I intend to finish it as soon as I can
conveniently."

The treatise De Motu, thus registered in the books of the
Royal Society, was the germ of the Principia, and was obviously
intended to be a brief exposition of the system which that work
was to establish. It occupies twenty-four octavo pages, and
consists of four theorems and seven problems, four of the theo-
rems and four of the problems containing the more important
truths which are demonstrated in the second and third sections
of the First Book of the Principia. ^

1 Mr. Rigaud has published it in his Historical Es=ay. He is of opinion that it is not
the same paper, a copy of which was brought to Halley by Mr. Paget in November 1684,
on the ground that that paper was never mentioned to the Royal Society by Halley, and
that Halley did not see the " curious treatise De Motu till his second visit to Cambridge,
in November or December 1684." Mr. Edleston, however, is of opinion that the treatise
De Motu was part of the lectures delivered by Newton as Lucasian Professor, which
commenced in October 1684, and a copy of which is preserved in the University library ;
and that the paper sent to Halley in November was the germ of this treatise, and the
one registered by Mr. Aston. In a letter from Cotes to Jones, published in Edleston's
Correspondence, p. 209, it is stated that the manuscript at Cambridge was " the fii-st
draught of the Principia," as Newton read it in his lectures,— a statemfnt to which Mr.
Edleston refers in support of his opinion. There are certainly expre.-sious in the letters
both of Newton and Halley unfavourable to both these opinions, but we think that the
following view of the question is the most probable. Halley went to Cambridge to learn

2(}'2 LIFE OF SIR ISAAC NEWTON. CHAP. XII.

The years IG80 and 1686 will ever be memorable in the life
of Newton, and in the history of science. It was in these two
years, and in the early months of 1687, that he composed the
Principia and gave it to the world, and all the details connected
with this great event have been carefully preserved for the in-
struction and gratification of posterity. The personal history
of the philosopher, therefore, during this period, the nature of
liis correspondence and inquiries, and all the mechanical and even
commercial circumstances under which his gxeat work was
written, and printed and published, are subjects which cannot
be overlooked in any extended account of his life and writings.
Although Newton had identified the law of gravity on the earth
with the same law at the moon, yet he required the aid of the
practical astronomer in enabling him to apply his theory to the
motions of the planets and comets of the system. Fortunately
for Newton, Flamsteed was the Astronomer-Royal at Greenwich.

In November and December 1680, when the great comet
HX)peared, Flamsteed observ^ed it with peculiar care, and, before
it had ceased to be visible, he put all its observed places into

if Newton had a demonstration of a proposition that a force varying reciprocally with
the square of the distance would produce a motion in an ellipsis. Newton told him that
he " had brought this demonstration to perfection," hut that having mislaid it, he would
send him " a copy thereof." This copy was sent to Halley in November obviously for
his own information. Halley does not lay it before the Society, but is so pleased with
if, that he goes again to Cambridge in order to "confer with Newton about i<." He
now paw the treatise De Motu which Newton promised to send to the Society, and
which was registered. Now when Halley says (letter to Newton, June 29. 1686) that he
went to Newton to confer with him about it, that is, the demonstnition, and adds imme-
diately. " since which time it has been entered ui)on the register books of the Society,"
he can only mean that the demonstration was entered as part of the treatise De Motu,
of which ic was certainly the leading feature. If the two Us mean the same thing, then
Halley received in November the same treatise that was afterwards sent to Aston in the
following February, which is scarcely admissible even upon Mr. Edleston's conjecture
that Halley did produce the paper on the 10th December, though the fact is not recorded
in the journal book. In Newton's letter to Halley, July 14, 1686, he says, that having
tried the calculation in the Ellipsis, he had thrown them by for about five year.s, till
upon Dr. Halley's request " he sought for that paper (namely, the calculation in the
Ellipsis), and not finding it, did it again, and reduced it into the propositions (we read
proposition) showed you by Mr. Paget." — See Rigaud's Hist. Essay, p. 14, and Edleston's
Correspondemr, pp. Iv. and 209.

KiSO. LIFE OF SIR ISAAC NEWTON. 263

H little table, wliicli, with his thoughts on the subject of comets,
lie communicated to Mr. Crompton, Fellow of Jesus College,
Cambridge. In this letter, Flamsteed asserted that " the two
comets (as they were generally thought) were only one and the
same ; and he described the line of their motions before and
after it passed the sun." Mr. Crompton showed this letter to
Newton, who, in return, addressed a long letter to him, to be
sent to Flamsteed, containing observations on Flamsteed' s
" hypothetical notions," and endeavouring to prove " that the
comets of November and December were different comets. The
commencement of Newton's letter is very characteristic, and
though it is intended to be kind in its expressions, we can
conceive a mind like that of Flamsteed regarding it, as he did
many years afterwards, as " magisterially ridiculing the opinion
for which he thought the arguments convincing and unanswer-
able."^ "I thank Mr. Flamsteed," says Newton, "for this
kind mention of me in his letters to Mr. Crompton, and, as I
commend his wisdom in deferring to publish his hypothetical
notions till they have been well considered both by his friends
and himself, so I shall act the part of a friend in this paper,
not objecting against it by way of opposition, but in describing
what I imagine might be objected by others, and so leaving it
to his consideration. If hereafter he shall please to publish
his theory, and think any of the objections I propound need
an answer, to prevent their being objected by others, he may
describe the objections as raised by himself or his friends hi
general, without taking any notice of me." After this kind
introduction, Newton proceeds, in a long and elaborate letter,
to controvert Flamsteed's opinions, and, from the evidence of
several Cambridge scholars, to show that there were two
comets, and not one ; and also in opposition to Flamsteed, that
" more comets go northward than southward." Flamsteed
replied to this letter on the 7th March 1681, in such compli-
mentary terms, that he could not have taken any offence at

1 See Baily's Flamsifed, p. 50, note.

264 LIFE OF SIR ISAAC NEWTON. CHAP. XII.

Newton's remarks upon his views. ^ He seems to have an-
swered several of Newton's objections, and removed some of his
difficulties, but to have failed in satisfying him that there was
only one comet in 1680. Newton had been on a visit in the
country during almost the whole of March, and, after his re-
turn to Cambridge, was prevented, " by some indisposition and
other impediments," from replying to Flamsteed till the 16th
of April. In this letter "he forbears to urge further" any
objections to Flamsteed's hypothesis, and confines himself " to
the question of two comets," which he discusses at great length,
pertinaciously maintaining an opinion, which, a few years after-
wards, he was obliged to abandon. ^

When, after his return from Lincolnshire to Cambridge,
Newton was occupied with the composition of the Principia,
he renewed his correspondence with Flamsteed. Some of their

1 Mr. Baily, whose views respecting the quarrel which subsequently arose between
Newton and Flamsteed, we shall afterwards have occasion to controvert, acknowledges
that he cannot find in these two letters of Newton "any foundation for Flamsteed's
censure." It is very obvious, indeed, from the highly complimentary terms in which
Flamsteed at this time wrote to Newton, that he did not consider Newton as " magis-
terially ridiculing his opinions."

2 At this time, and even in 1684, when he wrote his treatise D« Motu, Newton had
very erroneous views regarding the motions of comets ; and it was not till September
19, 1685, that he acknowledged, in a letter to Flamsteed, that " it seemed very probable
that the comets of November and December were the same comet." In the first edition
of the Principia, p. 494, he went farther, and acknowledged that Flamsteed was right.
In giving an account of the treatise De Motu, Mr. Rigaud thus speaks of Newton's views
respecting the motions of comets : — " He certainly at this time had not resolved the
difficult question of the paths of comets. In the Arithmetica Universalis (Piob. 56).
he had proceeded on their supposed uniform rectilinear motion, and, in the present case,
he still holds expressly to that earlier theory. How, under such conditions (if strictly
adhered to), they could return, is not easy to understand ; but waiving this question, his
reasoning seems to show that if they did, they might be recognised by a similarity in
their motions. To determine this, he proposes to reduce the places of the comet to
analogous points in an imaginary ellipse, of which the focus is occupied by the sun ; and
these places having been calculated by means of the auxiliary curve, were to be verified
by their application to the rectilinear path. It seems wonderful, when we consider his
extraordinary acuteness, that such an hypothesis did not immediately lead him to the
truth ; but as he so repeatedly and so distinctly describes the supposed motion of the
comet to be in a straight line, it is impossible not to conclude, that even his most
powerful mind required the assistance of time to emancipate itself from preconceived
opinions." — Eigaud's Hist. Essa;/, p. 29.

1685. LIFE OF SIE ISAAC NEWTON. 265

letters are lost;^ but it is obvious, from one of Newton's, dated
September 19, 1685, that he had received many useful com-
munications from Flamsteed, and especially regarding Saturn,
" whose orbit, as defined by Kepler," Newton " found too little
for the sesquialterate proportions," In the other letters written
in 1685 and 1686, he applies to Flamsteed for information
respecting the orbits of the satellites of Jupiter and Saturn ; —
respecting the rise and fall of the spring and neap tides at
the solstices and the equinoxes ; — respecting the flattening of
Jupiter at the poles, which, if certain, he says, would conduce
much to the stating the reasons of the procession of the equi-
noxes ; — and respecting the differences between the observed
places of Saturn and those computed from Kepler's tables about
the time of his conjunction with Jupiter. On this last point
the information supplied by Flamsteed was peculiarly grati-
fying to Newton ; and it is obvious from the language of this
part of his letter, that he had still doubts of the universal
application of the sesquialteral proportion. "Your informa-
tion," says he, " about the errors of Kepler's tables for Jupiter
and Saturn, has eased me of several scruples. I was apt to
suspect there might be some cause or other unknown to me
which might disturb the sesquialteral proportions, for the in-
fluences of the planets one upon another seemed not great
enough, though I imagined Jupiter's influence greater than your
numbers determine it. It would add to my satisfaction if you
would be pleased to let me know the long diameters of the
orbits of Jupiter and Saturn, assigned by yourself and Mr.
Halley in your new tables, that I may see how the sesquialteral
proportion fills the heavens, together with another small pro-
portion which must he allowed for.'' '^

1 The dates of these letters, which are published in the General Dictionarp, vol. vii.
fpp. 793-797, are September 19, 1685; September 25, 1685; October 14, 1685 ; Decem-
[ber 30, 1685 (?) ; January (?) 1686 ; September 3, 1686. Excepting the second, which

is from Flamsteed, they are all from Newton. See Vol. II. Chap XVIII.

2 This letter has no date, but Flamsteed says that it was written about 1685, or
January 1685-86.

2(>G LIFE OF SIR ISAAC NEWTON. CHAP. XII.

Upon Newton's return from Lincolnshire in the beginning of
April 1685, he seems to have devoted himself to the prepara-
tion of his work, and to fulfil his intention, as expressed to
Aston, " of finishing it as soon as he conveniently could." In
the spring he had determined the attractions of masses, and
thus completed the demonstration of the law of universal gra-
vitation ; and in summer he had finished the Second Book of
the Principia,' the First Book being the Treatise De Motu,
which he had already enlarged and completed. Excepting in
the correspondence with Flamsteed, to which we have already
referred, we hear nothing more of the preparation of the Prin-
cipia till the 21st of April 1686, when Halley read to the
Royal Society his " Discourse concerning Gravity, and its Pro-
perties," in which he states " that his worthy countiyman, Mr.
Isaac Newton, has an incomparable Treatise of Motion almost
ready for the press ; " and that the reciprocal law of the
s(j[uares " is the principle on which Mr. Newton has made out
all the phenomena of the celestial motions so easily and naturally,
that its truth is past dispute." ^ The intelligence thus given
])y Halley was speedily confirmed. At the very next meeting
of the Society on the 28th of April, "Dr. Vincent presented to
the Society a manuscript treatise entitled Philosophice Naturalis
Frincipia Mathematical and dedicated to the Society by Mr.
Isaac Newton." Although this manuscript contained only the
First Book, yet such was the confidence which the Society
l)laced in its author, that an order was given " that a letter of
thanks be written to Mr. Newton ; that the printing of his
book be referred to the consideration of the Council ; and that
in the meantime the book be put into the hands of Mr. Halley,
to make a report thereof to the Council." Although there
could be no doubt of the meaning of this report, yet no progress
was made in the publication of the work. At the next meet-
ing of the Society on the 19th May, some dissatisfaction seems

1 Euleston's Correspondence, &c., p. xxix. ; and Newton's letter to Halley, June
20, 1686. - Phil. Trans. 1686, pp. C-8.

l«Sb\ LIFE OF SIR ISAAC NEWTON. 267

U) have been expressed at the delay, as it was ordered " that
Mr. Newton's work shoidd be printed foHhwith in quarto, and
that a letter should be written to him to signify the Society's
resolutions, and to desire his opinion as to the print, volume,
(tuts, and so forth." Three days afterwards, namely, on the
:32d of May, Halley communicated the resolution to Newton,
and stated to him that the printing was to be at the charge of
the Society. As the manuscript, however, had not been referred
to the consideration of the Council, as previously ordered, and
as no sum exceeding five pounds could be paid without its
authority, a farther delay took place. At the next meeting of
the Council on the 2d of June, it was again ordered " that
Mr. Newton's book be printed ;" but instead of sanctioning the
resolution of the general meeting to print it at their charge, they
added, " that Mr. Halley undertake the business of looking after
it, and printing it at his own charge, which he engaged to do."

In order to explain to Newton the cause of the delay,
Halley, in his letter of the 2 2d May, alleges that it arose from
" the President's attendance upon the King, and the abRcnce of
the Vice-Presidents, whom the good weather had drawn out of
town ;" but there is reason to believe that this was not the
real cause, and that the delay arose from the unwillingness of
the Council to undertake the publication in the present state
of their finances.^

Such was the emergency in which Halley undertook the
labour of editing, and the expense of printing, the Frincijncf,
and thus earned the gratitude of Newton and of posterity. We
cannot admit that the low state of their funds was any apology
for the conduct of the Council in refusing to carry into effect
the resolution of a general meeting of the Society. Why did

1 We here express the opinion of Mr. Rigaud, who, after a careful and repeated
examination of the Royal Society's minutes, from 1686 to 1699, " ventures to say," that
" there is no notice of any pecuniary aid having been extended to the Principia."
Halley was a married man with a family, and at " a considerable pecuniary risk pro-
vided for the disbursement, precisely at that period of his life when he could lenst afford
it."— Rigaud's Hist. Esaav, pp. 33-37.

268 LIFE OF SIR ISAAC NEWTON. CHAP. XII.

they not borrow the necessary sum on the security of their
future income, or subscribe individually to fulfil an honourable
(jbligation, and discharge an important duty 1 If the nobility
and gentry who then composed the Royal Society devolved
upon their secretary the payment of expenses which, as a body,
they had agreed to defray, let it not be said that it was to the
Royal Society that we are indebted for the publication of the
Principia. It is to Halley alone that science owes this debt
of gratitude : It was he who tracked Newton to his College,
who drew from him his great discoveries, and who generously
gave them to the world.

In Halley's letter of the 2 2d May, announcing to Newton
the resolution of the Society, he found it necessary to inform
him of the conduct of Hooke when the manuscript of the
Principia was presented to the Society. Sir John Hoskyns,
the particular friend of Hooke, was in the chair, when Dr.
Vincent presented the manuscript, and passed a high encomium
on the novelty and dignity of the subject. Another member
remarked that Ne^vi;on had carried the thing so far that there
was no more to be added, to which Sir John replied, that it
was so much the more to be prized, as it was both invented
and perfected at the same time. Mr. Hooke was offended
because Sir John did not menti(jn what he had told him of his
own discovery ; and the consequence was, as Halley says,
" that these two, who, till then, were inseparable cronies, have
since scarce seen one another, and are utterly fallen out."
After the meeting broke up and adjourned to the coffee-house,
Mr. Hooke endeavoured to persuade the members " that he
had some such thing by him, and that he gave Newton the
first hint of this invention." Although this scene passed at
the Royal Society, Halley only communicated to Newton the
fact, " that Hooke had some pretensions to the invention of
the rule for the decrease of gravity being reciprocally as the
squares of the distances from the centre," acknowledging at the
same time, that though Newton had the notion from him,

1686. LIFE OF SIR ISAAC NEWTON. 269

" yet the demonstration of the curves generated thereby be-
longed wholly to Newton." " How much of this," Halley
adds, " is so, you know best, as likewise what you have to do
in this matter ; only Mr. Hooke seems to expect you should
make some mention of him in the preface which 'tis possible
you may see reason to prefix. I must beg your pardon that
'tis I that send you this ungrateful account ; but I thought it
my duty to let you know it, that so you might act accordingly,
being in myself fully satisfied that nothing but the greatest
candour imaginable is to be expected from a person who has of
all men the least need to borrow reputation." In thus appeal-
ing to Newton's candour, Halley obviously wished that some
acknowledgment of Hooke should be made. He knew indeed,
that before Newton had announced the inverse law, Hooke and
; Wren and himself had spoken of it and discussed it, and there-
fore justice demanded that though none of them had given a
demonstration of the law, Hooke especially should receive credit
for having maintained it as a truth of which he was seeking
the demonstration.

Newton's reply to Halley,^ written after a month's delay, is
a remarkable production. He acknowledges that Hooke told
him of the duplicate proportion, but that his views were erro-
neous, as he conceived it "to reach down from hence to the
centre of the earth." He confesses " that he himself had
never extended the duplicate proportion lower than to the svptr-
Icies of the earth,^'' and that " before a certain demonstration
\he found last year (1685) he suspected it did not reach accu-
^rately enough down so low.'' In the rest of the letter he shows
very satisfactorily, from letters to Oldenburg and Huygens, and
[even from this theory of gravity, that he must have been
[acquainted with the duplicate proportion before his conversation
fwith Hooke.

When Newton had finished this letter, he was informed " by
one who had it from another lately present at one of the

1 June 20, 1686. Appendix, No. IX.

270 LIFE OF SIR ISAAC NEWTON. CHAP. XII.

Society's meetings, that Mr. Hooke had there made a great
stir, pretending that Newton had all from him, and desiring
they wonld see that he had justice done him." Roused by
what he considered " a veiy strange and undeserved carriage
towards him," he writes an angry postscript to his letter,
putting forward the claims of Borelli and BuUialdus to the
duplicate proportion, and ungenerously charging Hooke with
having derived his knowledge of it from them, and even with
liaving been led to it by perusing his own letter to Huygens,
which might have come into his possession after the death of
Oldenburg. " My letter," says he, " to Huygens was directed
to Mr. Oldenburg, who used to keej) tlie originals. His pajjers
came into Mr. Hooke's possession. Mr. Hooke, knowing my
hand, might liave the curiosity to look into that letter, and
thence take the notion of comparing the forces of the planets
from their circular motion ; and so what he wrote to me after-
wards about the rate of gravity might be nothing but the fruit
of my own garden. And it's more than I can affii-m, that the
duplicate proportion was not expressed in that letter." ^ This
reasoning is certainly far from being sound. If Hooke had tlie
law of gravity from Borelli and BuUialdus, Ne\Hon might have
had it from them also ; and if Hooke obtained it by the pro-
cess indicated in the letter to Huygens, which he probably
never saw, it follows that Hooke's views were as soimd as those
expressed in that letter, and that he then knew as much about
the law as Newton did. But there is no evidence whatever
that Hooke saw the letter.

Halley was much annoyed with the contents of this post-
script, and lost no time in replying to it. He gives Newton an
account of the interview between Hooke, Wren, and himself,
previously described, and which led him to go to Cambridge.
He tells him that Hooke's manner of claiming the discovery
lias been represented in worse colours than it ought, " for lie

1 It was not expressed in the letter, as Newton afterwards admits. See Appknimx.
No. X. Letter, July 27, 16S6.

1686. LIFE OF SIR ISAAC NEWTON. 271

neither made application to the Society for jnstice, nor pre-
tended you had all from him ;" and he gives " the truth," by
telling what really happened at the meeting of the Society, and
of the little quarrel between Hooke and his friend Sir John
Hoskyns. Halley concludes his letter by begging Newton
" not to let his resentments run so high" as to deprive the
world of his Third Book, on the theory of comets.

Though ruffled for a moment, Newton's excellent temper
)on recovered its serenity. When he understood from Halley
bhat Hooke had been in some respects misrepresented to him,
le " wished that he had spared the postscript in his last ;"
id he goes on to acknowledge that Hooke's " letters occa-
sioned his finding the method of determining figures which he
tried in the ellipsis ;" — that Hooke told him of the experiment
dth " Halley' s pendulum clock at St. Helena, as an argument
bhat gravity w^as lessened at the equator by the diurnal motion ;"

-and that he also told him a third thing which was new to
lim, and which he would acknowledge if he made use of it,
lamely, " the deflexion of fallen bodies to the south-east in
)ur latitude." Having thus sincerely told Mr. Halley the ca«e
itween him and Mr. Hooke, " he considered how best to
)mpose the present dispute," which he thought might be done
3y the enclosed scholium to the fourth proposition. " The
iverse law of gravity holds in all the celestial motions, as was
liscovered also independently by my countrymen. Wren, Hooke,
md Halley."

On the 30th June, the President w^as desired by the Council

license Mr. Newton's book, entitled Philosophice Naturalis
^rincipia Mathematica, and after Halley had obtained the
luthor's leave about the middle of July to substitute wooden
Buts for copperplates, the printing of it was commenced and
went on with considerable regularity. The Second Book,
though ready for the press in autumn, was not sent till Marcli
1687. The Third Book was presented to the Society on the
6 th of April, and the whole work published about midsummer

272 LIFE OF SIR ISAAC NEWTON. CHAP. XTI,

of 1687.^ It was dedicated to the Royal Society as flourish-
ing under his august Majesty James vii.,^ and there was pre-
fixed to it a set of beautiful Latin hexameters, addressed by
Halley to its immortal author.^ They began thus —

En tibi norma poli, et divae libramina molis,
Computus atque Jovis ; quas, dum primordia rerum
Pangeret, omniparens leges violare creator
Jfoluit, aeternique operis fundamina fixit,

and ended with the following lines —

Talia monstrjin'.em mecum celebrate camoenis,
Vos qui coelesti gaudetis nectare vesci,
Newtonum clausi reserantem scrinia veri;
Nbwtonum Musis charum, cui pectore puro
Phoebus adest, totoque incessit numine mentem,
Nee fas est propius mortal! attingere divos.

This great work, as might have been expected, excited a
warm interest in every part of Europe. The impression was

1 The manuscript of the Principia, v?ithout the preface, bound in one volume, is in
the possession of the Royal Society. Mr. Edleston is of opinion that the manuscript is
not in Newton's autograph, and he believes it to be of the same hand as the first draught
of the Principia in the University library, the author's own handwriting being easily
recognised in the additions and alterations in both manuscripts. Edleston's Corre-
spondence, &c., pp. Mi. Iviii. In a very interesting letter from Dr. Humphrey Newton to
Conduitt, which is printed in our second volume, he informs him, that " he copied
out the Principia before it went to press." Pemberton states that the Principia was
written in a year and a half. In reference to this point I found the following memo-
randum in Sir Isaac's handwriting : —

" in the tenth proposition of the second book, there was a mistake in the first edition,
by drawing the tangent of the arch g h from the wrong end of the arch, which caused an
error in the conclusion ; but in the second edition I rectified the mistake. And there
may have been some other mistakes occasioned by the shortness of the time in which
the book was written, and by its being copied by an amanuensis who understood not
what he copied, besides the press faults ; for I wrote it in seventeen or eighteen months,
beginning in the end of December 1684, and sending it to the Royal Society in May 1686,
excepting that about ten or twelve of the propositions were composed before, viz., the
1st and 11th in December 1679, the 6th, 7th, 8th, 9th, 10th, 12th, 13th, and 17tb, Lib. L,
and the 1st, 2d, 3d, and 4th, Lib. II., in June and July 1684."

2 A copy of the Principia was presented to the King by Halley, accompanied with a
paper giving a general account of the Book, and more especially an explanation of the
tides, a subject in which the King was likely to take a deep interest, from his having a,s
Lord High Admiral comm.nded the British fleet in the war with the United Provinces.
See Phil. Trans, vol. xix. p. 445, and Rigaud's Hist. Essay, App. p. 77.

3 See Appendix, No. XI.

1691 1704. LIFE OF SIR ISAAC NEWTON. 273

quickly sold.^ A copy of the Principia could scarcely be pro-
cured in 1691, and at that time an improved edition was in
contemplation. Newton himself, though pressed by his friends,
had refused to undertake it, and M. Facio D'Huillier, who had
studied it with the most minute attention, had intimated to
Huygens his design of publishing a new edition.^ In 1694,
Newton resumed the study of the lunar and planetary theories,
with the view of rendering more perfect a new edition of his
book ; but the difficulty which he experienced in getting the
accessary observations from the Astronomer-Royal, interfered
with his investigations, and contributed more than any other
cause to prevent him from bringing them to a close. Flam-
steed did not sufficiently appreciate the importance of Newton's
labours ; but while we deeply regret that he should have
treated so ungraciously the importunities of his friend, we are
disposed to find some apology for his conduct in the infirmities
of his health and of his temper.

Mr. Edleston has stated, with much appearance of truth,
that the steps taken by Newton's friends at the close of 1695,
may have interfered as much as the infirmities of Flamsteed
with the completion of the lunar theory ; 3 but whether or not
this was the case, there can be no doubt that his appointment
to the Wardenship of the Mint in 1696, and to the Mastership
in 1699, deferred to a distant day the appearance of a new
edition of the Principia. Even in November 1702, when he
was visited by Bd. Greves, who saw in his hands an interleaved
and corrected copy of the Principia, he would not acknowledge
that he had any intention to reprint it.* The preparation of
his Optics, which was published in April 1704, must have in-
terfered with his revision of the Principia, and it appears, from
his letter to Flamsteed, in November 1694, that he was then

1 The number of copies printed is not kaown. The original price seems to have been
ten shillings.
• 2 See Rigaud's Hist. Essai/.'pp. 89-95.

5 Correspondence, &c., Free/, p. xi. * Ibid. Prcef. p. xir.

VOL. I. S

274 LIFE OF SIR ISx\AC NEWTON. CHAP. XJI.

occupied in preparing a new edition of his great work.^ His
duties at the Mint allowed him but little time for the per-
formance of so laborious a task ; and when his consent was at
last obtained to put the work to press, they greatly interrupted
its progress.

Dr. Bentley, the distinguished Master of Trinity College, had
for a long time solicited and even urged Newton to give his
consent to the re-publication of the Priucipia.^ In the middle
of 1708 he succeeded in removing his scruples, but it was not
till the spring of 1709 that he prevailed upon him to intrust
the superintendence of it to a young mathematician of great
pi'omise, Roger Cotes, Fellow of Trinity College, who had been
recently appointed Professor of Astronomy and Experimental
Philosophy. On the 21st May 1709, after having been that
day with Newton, Bentley annoimced this anangement to
Cotes. " Sir Isaac Newton," he said, " will be glad to see you
in June, and then put into your hands one part of his Book
coiTccted for the press." About the middle of July, Cotes went
to London, in the expectation doubtless to bring down with
him to Cambridge the corrected portion of the Principia.
Newton, however, had some farther improvements to make
upon it, and promised to send it down in about a fortnight.
Cotes was impatient to begin his work, and when a whole
month had passed without any intelligence from Newton, he
addressed to him the following letter : —

" Cambeidge, August 18th, 1709.
" S^' — The earnest desire I have to see a new Edition of
y"" Princip. makes me somewhat impatient till we receive your
Copy of it whicli You was pleased to promise me about the

1 Baily's Flamstecd, \\ 138.

'^ It would api>e:ir from a conversation tictween Sir Isaac and Couduitt, that Bentley
was at the expense of printing the second edition of the Principia, and received the
protitsof the work. •'! ji.*king him (Newton)," says Conduitt, "how he came to let
Bentley print his Principia, which he did not undersUmd — ' Why,' said he, ' he wb»
covetous, and I let him do it to get nionev."'—Conduitt's MS. See Vol. II. ch. xxL

1709. LIFE OF SIR ISAAC NEWTON. 275

middle of the last Month, You would send down in about a
Fourtnights time. I hope you will pardon me for this uneasi-
ness from which I cannot free myself & for giving You this
Trouble to let You know it. I have been so much obliged to
You by Y'^self & by Y'" Book y* (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 I take this Opportunity

to return You my most hearty thanks for Y'" many Favours
and Civilitys to me who am

Your most obliged humble Servant,
;. Roger Cotes.

"For Sir Isaac Newton at His House in
.leniiin Street near St. James's Church
Westminster."

No answer was returned to this letter from Cotes, and a
long month had passed away when one evening his next-door
neighbour, William Whiston, about the end of September, put
into his hands " the greatest part of the copy of the Principia,"
ending with the thirty -second Proposition of the Second Book.
In a letter dated October 1 1 , Newton intimated to Cotes that
he had sent him by Mr. Whiston " the greatest pa.rt of the
<;opy of his Principia, in order to a new edition," thanked him
for his letter of the 1 8th of August, and requested him not to
he at the trouble of examining all the Demonstrations, but " to
print by the copy sent him, correcting only such faults as occur
in reading over the sheets," which would entail upon him
" more labour than it was fit to give him." These were the
two first letters of that celebrated correspondence between
Newton and Cotes, which has lain in Trinity College Libraiy
for nearly a century and a half, in spite of the wishes expressed
l>y Dr. Monk,^ and felt by other admirers of the Principia,
^'that one of the many accomplished Newtonians who are
resident in that society would favour the \^^orld by publishing

» Monk's Life of Berdley, p. 180.

276 LIFE OF SIR ISAAC NEWTON. CHAP. XII.

the whole collection." Through the liberality of the present
Master and Seniors of Trinity College, this has at last been
done, and in a manner highly creditable to the learning and
talents of Mr. Edleston, by whom the correspondence is edited.^
The printing of the Principia went on very slowly, and w^as not
finished till the first w^ek of March 1713. Cotes expressed a
wish that Dr. Bentley should write the preface to it, but it was
the opinion of Sir Isaac and the Master of Trinity, that the
preface should come from the pen of Cotes himself. Tliis he
readily undertook, but previous to writing it he addressed the
following letter to Dr. Bentley, in order to learn " with wiiat
view he thought proper to have it written."

TO DE. BENTLEY.

" March 10/A,1712-13.
" S^' — I received what you wrote to me in S'" Isaac's letter.
I will set about the Index in a day or two. As to the Preface,
I shoidd be glad to know from S' Isaac with what view he
thinks jn'oper to have it written. You know the book has
been received abroad with some disadvantage, and the cause of
it may easily be guessed at. The Commercium Epistolicum,
lately published by order of the Eoyal Society, gives such in-
dubitable proofs of Mr. Leibnitz's want of candour, that I shall
not scruple in the least to speak out the full tmth of the matter
if it be thought convenient. There are some pieces of his look-
ing this way which deserve a censure, as his Tentamen de
Motuum Coelestium caiisis.'^ If S*" Isaac is willing that some-

' These letters, relating to questions connected with the new edition of the Principia,
tiXQ xevmiy-ttco in number, and extend from May 21, 170$), to March 31, 1713. Mr.
Edleston has added <)ther J'fty, connected with the Principia, from Newton, Cotes,
Keill, Jones, Brook Taylor, and others, and in an Appendix he has published thirty-four
letters, chiefly from Newton, and collected principally from original sources. Mr.
Edleston has enriched this valuable work with an excellent synoptical view of Newton's
life, and a large number of notes of the highest interest.

2 The critique by Newton, already mentioned, bore upon this paper by Leibnitz ; see
p. 258, Note.

1713. LIFE OF SIE ISAAC NEWTON. 277

thing of this nature may be done, I should be glad of it, whilst
I am making the Index, he would be pleased to 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 would be much more adviseable
that you or he or both of you should write it whilst you are in
town. You may depend upon it that I will own it, and
defend it as well as I can, if hereafter there be occasion. — I
am, S--' " &c.

Immediately after the arrival of this letter on the 1 2th, Sir
Isaac happened to call upon Dr. Bentley, and they agreed to
meet in the evening at Sir Isaac's house, to write a reply to it.
They objected to any joint preface " to be fathered by Cotes :"
they suggested as the subject of the Preface an account of the
work itself, and of the improvements of the new edition, and
they answered that he has Sir Isaac's consent " to add what he
thought proper about the controversy of the first invention, you
■yourself being full master of it, and want no hints to be given
;you." Cotes was also instructed " to spare the name of M.
Leibnitz, and abstain from all words and epithets of reproach."
In reply to this letter on the 18th March, Cotes sketched the
plan of the Preface in conformity with the directions already
given him, and asks Newton for permission to appeal to the
[judgment of the Society in the Commercium Epistolicum, To
this Newton answers, that if any farther Preface is written,
" he must not see it, as he finds he shall be examined about
it." The plan of the Preface is therefore altered, and the pro-
posed notice of the dispute respecting the discovery of fluxions
is abandoned. Cotes confines himself to an exposition of " the
manner of philosophizing made use of" in the Principia, and
to an examination of the objections of Leibnitz and of the
[theory of vortices.

The general Preface thus drawn up by Cotes, is dated 1 3th
I May, 1713, and in a subsidiary Preface, dated March 2d, Sir
Isaac himself mentions the leading alterations which have been

278 LIFE OF SIR ISAAC NEWTON. CHAP. XII.

ina(ie in tlio New Edition. " In the second section of the First
Book," he says, " the determination of the force by which bodies
may revolve in given orbits, is simplified and enlarged. In the
seventh section of the Second Book, the theory of the resistance
of fluids is more accurately investigated, and confirmed by new
experiments ; and in the Third Book the theory of the moon,
and the precession of the equinoxes, are more fully deduced
from their principles, and the theorj^ of comets is confirmed by
several examples, and their orbits more accurately computed."

On the 25th of June, Cotes * announces to its author, through
Dr. Samuel Clarke, " that the book is finished," and on the
27th of July, Newton waited on the Queen to present a copy
of the Principia to her Majesty.

Such is a brief notice of the composition and printing of the
first and second editions of a work which will be memorable
not only in the annals of one science or of one countiy, 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, — a work, may we not add, which would be read with
delight in every planet of our system, — in every system of the
universe. What a glorious privilege was it to have been the
author of the Principia ! There was but one earth upon whose
form and tides and movements the philosopher could exercise
his genius, — one moon, whose perturbations and inequalities
and actions he could study, — one sun, whose controlling force
and apparent motions he could calculate and determine, — one
system of planets, whose mutual disturbances could tax his
highest reason,'"^ — one system of comets, whose eccentric paths
he could explore and rectify, — and one universe of stars, to

1 Some account of this interesting and distinguished person, whose name is so indis-
solubly associated with that of Newion, and with the Principia, will be found in Appkn-
Dix, No. XII.

* The celebrated Lagrange, who frequently asserted that Newton was the greatest
genius that ever existed, used to add— and the most fortunate, for v/e cannot find more
than once a system of the world to establish.— Delambre, Notice sitr la Vic de Lactrange.
M&m. dc r hislitul. 1 81 2, p. Ixv.

1713. LIFE OF SIR ISAAC NEWTON. 279

whose binary and multiple combinations he could extend tlie
law of terrestrial gravity. To have been the chosen sage sum-
moned to the study of that earth, these systems, and that uni-
verse, — the favoured lawgiver to worlds unnumbered, the high-
priest in the temple of boundless space, — was a privilege that
could be granted but to one member of the human family ; —
and to have executed the task was an achievement which in its
magnitude can be measured only by the infinite in space, and
in the duration of its triumphs by the infinite in time. That
Sage — -that Lawgiver — that High-priest was Newton. Let us
endeavour to convey to the reader some idea of the revelations
which he made, and of the brilliant discoveries to which they
conducted his successors.

The Principia consists of three Books. The First and Second,
which occupy three-fourths of the work, are entitled, On the
Motion of Bodies ; the First treating of their motions in free
space, and the Second of their motions in a resisting medium.
The Third bears the title, On the System of the World.

The First Book, besides the definition and axioms, or laws
of motion, with which it begins, consists oi fmirteen sections, in
the first of which the author explains the method of prime and
ultimate ratios, used in his investigations, and which is similar
to the method of fluxions, more fully explained in the Second
Book. The other sections treat of centripetal forces, and mo-
tions in fixed and moveable orbits.

The Second Book consists of nine sections, and treats of bodies
moving in resisting media, or oscillating as pendulums.

The Third Book is introduced by the " Rules of Philoso-
phizing." It consists of five sections, on the Causes of the
System of the World, — on the Quantity of Lunar Errors, — on
the Quantity of the Tides, — on the Precession of the Equinoxes,
— and on Comets ; and it concludes with a general scholium,
containing reflections on the constitution of the universe, and
on the " Eternal, Infinite, and perfect Being" by whom it is
governed.

280 LIFE OF SIR ISAAC NEWTON. CHAP. XII.

The great discovery which characterizes the Principia, is that
of the principle of universal gravitation, that every particle of
matter in the universe is attracted hy, or gravitates to every other
particle of matter^ with a force inversely proportional to the
squares of their distances. In order to establish this principle,
Newton begins by considering the curves, which are generated
by the composition of a direct impressed motion with a gravita-
tion or tendency towards a centre ; and having demonstrated,
that in all cases the areas described by the revolving body are
proportional to the times of their description, he shows how to
find, from the curves described, the law of the force. In the
case of a circular orbit passing through the centre of tendency,
the force or tendency towards the centre will be in every point
as the fifth power of the distcmce. If the orbit is the propor-
tional spiral, the force will be reciprocally as the cube of the
distance. If it is an ellipse, the force towards the centre of it
will be directly as the distance. If it is any of the conic sec-
tions, the centripetal force, or tendency towards the focus, will,
in all points, be reciprocally as the square of the distance from
the focus. If the velocity of the impressed motion is of a cer-
tain magnitude, the curve described will be a hyperbola, — if
diff'erent to a certain degree, it will be a parabola, — and if slower,
an ellipse, or a circle in one case.

In order to determine whether the force of gravity resided in
the centres of the sun and planets, or in each individual par-
ticle of which they are composed, Newton demonstrated 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 centre alone.
But as the bodies of the solar system are very nearly spherical,

1687. LIFE OF SIE ISAAC NEWTON. 281

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 be-
tween spherical bodies, namely, that one sphere will act upon
another with a force directly proportional to their quantities of
matter, and inversely, as the square of the distance between the
centres of the spheres. From the equality of action and re-
action, 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 pro-
portional 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 com-
|posed, — results which Adam Smith pronounced to be " above
[the reach of human reason and experience." 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
bhe earth, and that the density of the earth was four times
[greater than that of the sun, the planets increasing in density
tas they are nearer the centre of the system.

If the peculiar genius of Newton has been displayed in his
i investigation of the law of universal gravitation, it shines with
10 less histre in the patience and sagacity with which he traced
le consequences of this fertile principle.
The discovery of the spheroidal form of Jupiter by Cassini
id probably directed the attention of Newton to the determi-
lation of its cause, and consequently to the investigation of the
le figure of the earth. The spherical form of the planets
lad been ascribed by Copernicus to the gravity or natural

•2S'2 LIFE OF SIR ISAAC NEWTON. CHAP. XII.

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 ten-
dency increases with the velocit}^ Hence arises a centrifugal
force, which acts in combination with the 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 lati-
tude, 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 com-
municate 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 conse-
quently that it diminishes from the equator to the poles, — a
result which he confirmed by the fact, that clocks required to

1687. LIF?: OF Sill ISAAC NEWTON. 28-}

liave 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 had 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 a short time after she is in the meri-
dian 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

tthe sun conspires with that of the moon ; and that the lowest
tides take place when the lines drawn from the sun and moon

ito 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

fmost perplexing phenomenon in the tides of the ocean, and one
diich is still a stumbling-block to persons slightly acquainted
dth the theory of attraction, is the existence of high water on
le side of the earth opposite to the moon, as well as on the
jide next the earth. To maintain that the attraction of the
lOon at the same instant draws the waters of the ocean to-
wards herself, and also draws them from the earth in an oppo-
site 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,

1 This was first observed by Richer, who found that a clock regulated to mean time
at Paris lost 2' 28" daily at Cayenne.

284 LIFE OF SIR ISAAC NEWTON. CHAP. XII.

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 then will 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 moon 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 pro-
duced a tide of 8-63 feet ; — that of the sun one of 1-93 feet ;
— and both combined, one of lOJ 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

1687. LIFE OF SIR ISAAC NEWTON. 285

globe, he found that the quantity of water 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 line 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 by the action of the
sun in every quarter of a revolution ; and he had also ascer-
tained the existence of the annual equation. Of these two
inequalities, Newton gave a most satisfactory explanation,
making the first 36' 10", and the other 11' 51", differing only
a few seconds from the numbers adopted by Tobias Mayer in
his celebrated Lunar Tables. The force exerted by the sun
upon the moon may be always resolved into two forces, one
acting in the direction of the line joining the moon and the
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
syzygies or quadratures, so that at these four points the de-
scribed areas are proportional to the times. The instant, how-
ever, that the moon quits these positions, the force under
consideration, which we may call the tangential force, begin.=,
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 thirty minutes, and therefore affects the an-
gular motion of the moon, the motion being accelerated in
passing from the quadratures to the syzygies, and retarded in
passing from the syzygies to the quadratures. Hence the

286 LI¥E OF SIR ISAAC NEWTON. CHAP. XII.

velocity is in its mean state in the octants, a maximum in the
syzygies, and a minimum in the quadratures.

, Upon considering the influence of the solar force in dimi-
nishing or increasing the moon's gravity to the earth, Newton
saw that her distance and 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 was
an angular progressive motion of 3° 4' nearly in the course of
one lunation ;i and he showed that the retrogradation of the
nodes, amounting to 3' 10" daily, arose from one of the ele-
ments 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 inter-
section of these two planes, to move in a direction opposite to
that of the moon.

The lunar theory thus sketched 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 one of the most striking of all his
discoveries, namely, 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

' Newton made it only 1° 31' 2S", just one-half of its real value. Clairaut obtained
the (^ame result, but afterward!?, by a more accurate calculation, found it to be 3*" 4 ',
j^rroeing exactly viith observation.

Ifi87. LIFE OF SIR ISAAC NEWTON. 287

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 beiug above
the plane of the ecliptic, and the other half below it. Consi-
dering this excess of matter as a system of satellites adhering
to the earth's surface, Newton now saw that the combined
actions of the sun and the moon upon these satellites tended to
produce a i-etrogradation 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 eft'ect produced by the motion of the sun he found to be
forty seconds, and that produced by the action of the moon ten
seconds.

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 not easy 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 obtain approximate results
by repeated observation. Newton, however, though he at first
imagined that comets moved in straight lines, 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. This method consists of an easy
geometrical construction, founded on the supposition that the
paths of comets are so nearly parabolic, that the parabola may
be used without any sensible error, although he considers it
more probable that their orbits are elliptical, and that after a
long period they may return. 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

288 LIFE OF SIR ISAAC NEWTON. CHAP. XII.

were observed, lie 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 ex-
tends far beyond the limits of the solar system, it demonstrated
the existence of gravity in spaces beyond the planets, and
proved that the law of the inverse ratio of the squares of the
distance was true in eveiy possible direction, and at very re-
mote 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 simi)licity 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 insured 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 everywhere
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 imagi-
nation more than to reason, 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 difl'used
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 difiiculty in conceiving how the planets might re^

ir,S7. LIFE OF SIR ISAAC NEWTON. 289

volve 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, con-
tributed powerfully to its adoption, while it derived a still
higher sanction from the excellent character and the unaffected
piety of its author.

Thus entrenched as the Cartesian system was, in the strong-
liolds of the human mind, and fortified by its most obstinate pre-
judices, it was not to be wondered at that the pure and sublim<3
doctrines of the Principia were distrustfully received and perse-
veringly 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
(pialities of the ancient physics, and resisted their introduction
with a pertinacity which it is not easy to explain. Prejudicetl,
no doubt, in favour of his own metaphysical views, Leibnitz
himself misapprehended the principles of the Newtonian philo-
sophy, and endeavoured to demonstrate the truths in the
Principia by the application of different principles. Even two
years after the publication of the Principia, he publislied a
dissertation in which he explained the motions of the planets
by an ethereal fluid. 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, also, one of the first mathematicians
of the age, opposed the philosophy of Newton. Mairan, in the
early part of his life, was a strenuous defender of the system of

VOL. I. T

290 LIFE OF SIR ISAAC NEWTON. CHAP. XII.

vortices. Cassini and Maraldi were quite ignorant of the
Principia, and occupied themselves with the most absurd
methods of calculating the orbits of the comets long after the
Newtonian method had been established on the most im-
pregnable basis ; 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, in his memoir " On the construction
and Theory of Tables of the Sun," had applied the doctrine of
central force to the motions of the planets, so early as 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, zealously defended
it in his. Treatise on the Figures of the Celestial Bodies. 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 in Engknd.2 With regard to the pro-
gress 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 resist-
ance, they had been supplanted by the Cartesian, which became
jfirmly 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 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

1 M^m. Acad. Par. 1720.

2 In 1738, Voltaire published a popular exposition of Newton's discoveries, wbich con-
tributed greatly to their reception on the Continent.

1718-20. LIFE OF SIR ISAAC NEWTON. 291

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 subjects of dis-
cussion, 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 uncer-
tain, 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 anything to
alarm prejudice, or awaken from its lethargy the dread of in-
novation. Thus, therefore, the Newtonian philosophy first
entered the University of Cambridge, under the protection of
(the Cartesian." To this passage Professor Play fair adds the
Ifollowing as a note.

" The Universities of St. Andrews and Edinburgh were, I
[believe, the first in Britain where the Newtonian philosophy
ras made the subject of the academical prelections. For this
listinction they are indebted to James and David Gregory, the
[first in some respects the rival, but both the friends of Newton.
'Whiston bewails, in the anguish of his heart, the difference in
this respect between those universities and his own. David
Gregory taught in Edinburgh for several years prior to 1690,
when he removed to Oxford ; and Whiston says^ ' he had
already caused several of his scholars to keep Acts, as we call
them, upon several branches of the Newtonian philosophy,
while we at Cambridge, poor wretches, were ignominiously
studying the fictitious hypotheses of the Cartesians.'^ I do

^ " Whiston's Memoirs of his own Life," p. 36.

* It does not appear at what time the Newtonian Philosophy was received at Oxford,
Judging from Addiaon's " Oration in Defence of the New Philosophy," spoken in the

292 LIFE OF SIR ISAAC NEWTON. CHAP. XII.

not, however, mean to say that from this date the Cartesian phi-
losophy was expelled from those universities ; the Physics of
Rohaiilt 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 afterwards." Adopting the same view of
the subject, Mr. Dugald Stewart has stated, " that the philo-
sophy of Newton was taught by David Gregory at Edinburgh,
and by his brother, James Gregory, at St. Andrews,^ before it
was able to supplant the vortices of Descartes in that very
university of which Newton was a member. It was in the

Theatre at Oxford, July 7, 1693, six years after the publication of the Principia, we have
no doubt that the Cartesian Philosophy, which is obvious;ly the " New Philosophy,"
defended by Addison, was in full force at that date. This omtion, " done from the
Latin original," is appended to the English translation of Fontenelle on the Plurality of
Worlds ; and on the title-page to that work it is called " Mr. Addison's Defence on the
Newtonian Philosophy/." Our readers will decide from the following extract whether
the New Philosophy means the Newtonian or the Cartesian Philosophy : —

" IIow long, gentlemen of the University, shall we slavishly tread in the steps of the
ancients, and be afraid of being wiser than our ancestors ? IIow long shall we religiously
worship the triflings of antiquity as some do old wives' stories ? It is indeed shameful,
when we survey the great ornament of the present age (Nkwton), to transfer our ap-
plauses to the ancients, and to take pains to search into ages past for persons fit for
panegyrick." So far the New Philosophy may mean that of Newton, but the followiug
passage contradicts any such inference : — " The ancient philosophy has had more
allowed than it could reasonably pretend to ; how often has Sheldon's Theatre rung
with encomia on the Stagyrite, who, greater than his own Alexander, has long, un-
opposed, triumphed in our school desks, and had the whole world for his pupils ? At
length rose Cartesius, a happier genius, who has bravely asserted the truth against the
united force of all opposers, and has brought on the stage a new method of pMloso})hiz-
ing. But shall we stigmatize with the nume of iiovelty, that philosophy which, though
but lately revived, is more ancient than the peripatetic, and as old as the mother from
whence it is derived ? A great man indeed he was, and the only one we envy France
(Descartes). He solved the difficulties of the universe almost as well as if he had been its
architect." The name of Newton or liis ]>hilosophy is never again mentioned. — Author.

1 Dr. Reid states, that James Gregory, Professor of Philosophy at St Andrews, j Tinted
a Thesis at Edinburgh in ] 690, corit;.ining twenty-five positions, of which twenty-two
were a compend of Newton's Principia.

1099-1739. LIFE OF SUl ISAAC NEWTON. 293

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 Priiicipia ; 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 capa-
cities, 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 pub-
lished, — 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 " On the Principia, Optics,
[and Universal Arithmetic of Newton," and the popularity of
these lectures was so great, that Sir Isaac corresponded on the

ibject of them with their author ; and on the ejection of

''histon from the Lucasian chair in 1711, Saunderson was
ippointed his successor. In this important ofiice he continued
teach the Newtonian philosophy till the time of his death,

rhich took place in 1739.

But while the Newtonian philosophy was thus regularly taught
■■in Cambridge, after the publication of the Principia, there were

294 LIFE OF SIE ISAAC NEWTON". CHAP. XH.

not wanting other exertions for accelerating its progress. About
1694, the celebrated Dr. Samuel Clarke, while an under-gra-
duate, 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 Saunder-
son informs us, that public exercises or acts, founded on every
part of the Newtonian system, were very common about 1707,
and so general were such studies in the University, that the
Principia rose to four times its original price. ^ 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 pro-
bable 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 in that college, instead of appointing a
moderator, he discharged the office himself, and devoted his
most active exertions to the promotion of mathematical know-
ledge. 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 popu-
larity of his college. 2 About the same time the learned Dr.
Bentley, who first made known the philosophy of his friend to
general readers, filled the high office of Master of Trinity
College, and could not fail to have exerted his influence in pro-
pagating doctrines which he so greatly admired. Had any
opposition been ofi'ered to the introduction of the true system

1 Cotes states, in his preface to the second edition of the Principia, that copies of the
first edition were scarce, and could only be obtained at an immense price. Sir William
Brown, when at college, gave more than two guineas for a copy, and owing to the diflB-
cully of procuring one at a reasonable price, the father of Dr. John Moore of Glasgow
transcribed the whole work with his own hand. See Nichol's Literary Anecdotes, vol.
iii p. S22, and Encyc. Brit. Art. Moore.

2 See the Museum Criticum, vol. ii. p. 514.

1707-10. LIFE OF SIR ISAAC NEWTON. 295

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 patronized the study
of the Physics of Rohault, yet it is probable that similar per-
sons existed in the Universities of Edinburgh and St. Andrews ;
and we cannot regard their adherence to error as disproving the
general fact, that the philosophy of Newton was quickly intro-
duced 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 physi-

1 The following passage in Wbiston's Life of Dr. Clarke, is not in accordance with
some of the preceding statements. " About the year 1697, while I was chaplain to Dr.
John Moor, then Bishop of Norwich, I met at one of the coffee-houses in the market'
place at Norwich, a young man, to me then wholly unknown ; his name was Clarke,
pupil to that eminent and careful tutor, Mr. Ellis, of Gonvil and Caius College in Cam-
bridge. Mr. Clarke knew me so far at the university, I being about eight years elder
than himself, and so far knew the nature and success of my studies, as to enter into a
conversation with me about that system of Cartesian philosophy his tutor had put him
to translate, — I mean Rohault's Physics ; and to ask my opinion about the fitness of
such a translation. I well remen.ber the answer I made him, that, ' since the youth of
the university must have, at present, some system of Natural Philosophy for their
studies and exercises ; and since the true system of Sir Isaac Newton's was not yet
made easy enough for the purpose ; it was not improper, for their sakes, yet to translate
and use the system of Rohault (who was esteemed the best expositor of Descartes), but
that as soon as Sir Isaac Newton's philosophy came to be better known, that only ought
to be taught, and the other dropped.' Which last part of my advice, by the way, hns
not been followed, as it ought to have been, in that university. But, as Bishop Hoadley
truly observes. Dr. Clarke's Rohault is still the principal book for the young students
there. Though such an observation be no way to the honour of the tutors in that uni-
versity, who. in reading Rohault, do only read a philosophical romance "to their pupils,
almost perpetually contradicted by the better notes thereto belonging. And certainly to
use Cartesian fictitious hypotheses at this time of day, after the principal parts of Sir
Isaac Newton's certain system have been made easy enough for the understanding of
ordinary mathematicians, is like the continuing to eat old acorns after the discovery of
new wheat, for the food of mankind. However, upon this occasion, Mr. Clarke and I
fell into a discourse about the wonderful discoveries made in Sir Isaac Newton's philo-
sophy ; — and the result of that discourse was, that I was greatly surprised that so young
a man as Mr. Clarke then was, not much, I think, above twenty-two years of age, should
know so much of those sublime discoveries which were then almost a secret to all, but
to a few particular mathematicians."

206 LIFE OF SIR ISAAC NEWTON. CHAF. XII.

cal truths had been studied by some of the most distinguished
scholars and philosophers of the times, and were subsequently
explained and communicated to the public by various lecturers
on experimental philosophy. The celebrated Locke, who was
incapable of understanding tiie Principia from his want of
geometrical knowledge, inquired of Huygens if all the mathe-
matical 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 phj^sical 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 him-
self master of every part of it which was not mathematical.^
From a manuscript of Sir Isaac Newton's, entitled, " A Demon-
stration that the Planets, by their gravity towards the Sun,
may move in Elli})ses,2 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 proposition. This manuscript is endorsed,
" Mr. Newton, March, 1G89." It begins with three hypothe-
ses (the two first being the two laws of motion, and the third
the parallelogram of motion), which introduce the proposition
of the proportionality of the areas to the times in motions
round an immovable centre of attraction.^ Three lemmas, con-
taining the properties of the ellipse, then prepare the reader for
the celebrated proposition, that when a body moves in an
ellipse,* the attraction is reciprocally as the square of the dis-
tance 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

1 Preface to Desaguliers' Course of Experimental Philosophy, toI. i. p Tiii. Dr: Des-
aguliers says that he was told this anecdote several times by Sir Isaac Newton himself.
- The Life of John Locke. Edit. 1830, vol. i. pp. 389-400.
3 Principia, lib. i. prop. i. < Ibid. lib. i. prop. xi.

jl692. LIFE OF SIR ISAAC NEWTON. 297

their present modified form, they were beyond the cajjacity of
Mr. Locke.

Among the learned men who were desirous of understanding
the truths revealed in the Principia, Richard Bentley was one
of the most distinguished. In 1691, when only thirty years
of age, he applied to John Craige, a mathematician of some
eminence, and a friend of Newton, for a list of works which
would enable him to study the Principia. Alarmed at the list
which Craige sent him, he was induced to apply to Newton
himself, who drew up the directions which, along with those of
Craige, we have given in the Appendix.^ When Bentley was
appointed, in 1692, the first Lecturer on Robert Boyle s Foun-
dation, he chose as the subject of his discourse, "A Confutation
of Atheism." The insidious doctrines of Spinoza and Hobbes
had at that time made considerable progress among the upper
ranks of society, and as these authors denied a Divine Provi-
dence, and considered the existence of the universe as the result
of necessity, Bentley proposed to conclude his course of lectures
with the demonstration of a Divine Providence from the physi-
cal constitution of the universe, as demonstrated by Newton.
Before printing his discourses, he consulted Newton on some
points which required elucidation, and it was in reply to the
Queries thus addressed to him, that Newton wrote the five re-
markable letters already alluded to. By this means some of
tlie great truths of the Newtonian philosophy were promulgated
among a class of readers who would not otherwise have heard
of them. 2

1 See Appendix, No. XIII. The original of these directions was given by Richard
Cumberland, the relation of Bentley, to Trinity College, along with the originals of the
four celebrated letters from Newton to Bentley, to which our attention will be after-
wards directed.

' Lord Aston, "a great lover of the mathematics, who would gladly be satisfied in a
difiBculty or two on that science," requested Mr. Greves and Sir E. Southcote to submit
these difficulties to Sir Isaac Newton. Mr. Greves accordingly went on Monday, the 30th
November 1702, and gives the following account of the conversation. " He owns there
are a great many faults in his book, and has cros^^ed it and interleaved it, and writ in the
mars^in of it, in a great many places. It is talked he des^igns to reprint it, though he
would not own it I asked bim about his proof of a vacuum, and said that if there is

298 LIFE OP SIR ISAAC NEWTON. CHAP. XII.

About the year 1718, Isaac Watts speaks of the exploded
Physics of Descartes, and the noble inventions of Sir Isaac
Newton, in his " hypotheses of the heavenly bodies and their
motions ;" and he refers to previous writers who have explained
Nature and its operations in a more sensible and geometrical
manner than Aristotle, especially those who have followed the
principles of that wonder of our age and nation, Sir Isaac
Newton.^

Dr. John Keiil was the first person who publicly taught
natural philosophy " by experiments in a mathematical man-
ner." 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, con-
cerning 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 new philosophy by
experiments. He commenced his lectures at Harthall, in Ox-
ford, in 1710, and delivered more than a hundred and twenty
discourses ; and when he went to settle in London in 1713,
he informs us that he found " the Newtonian philosophy gene-
rally received among persons of all ranks and professions, and
even among the ladies by the help of experiments."^

such a matter as escapes through the pores of all sensible bodies, this could not be
weighed. ... I find he designs to alter that part, for he has writ on the margin, Materia
sensibilis ; perceiving his reasons do not conclude in all matter whatsoever." — Edleston's
Correspondence, Pref p. xiv., and Tixall's Letters, II. 152, quoted there.

1 Improvement of the Mind, Part I. chap. xx. Art. vi. and xvi., or his Works, vol. v.
pp. 301, 306.

2 These lectures were first published in Latin in 1718, and afterwards in English in
1721 and 1739, under the title of An Introduction to the true Astronomy, or Astronomi-
cal Lectures read in the Astronomical School of the University of Oxford. By John
Keill, M.D. F.R.S.

2 Desaguliers, ut supra, Preface, pp. viii. x.

1710-13. LIFE OF SIR ISAAC NEWTON. 299

Such were the steps by which the philosophy of Newton 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 over-
turned ; and long before his death, Newton enjoyed the high
satisfaction of seeing his philosophy triumphant in his native
land.

In closing our account of the Principia, and in justification
of the high eulogium we have pronounced upon it, we may
quote the opinions of two of the most distinguished men of the
past or the present age. " It may be justly said," observes
Halley, " that so many and so valuable philosophical truths, as
are herein discovered, and put past dispute, were never yet
owing to the capacity and industry of any one man." ^ " The
importance and generality of the discoveries," says Laplace,
"and the immense number of original and profound views
which has been the germ of the most brilliant theories of the
philosophers of this century, and all presented with much
elegance, will insure to the work, on the Mathematical
Princijjles of Natural Philosophy, a pre-eminence above all
the other productions of human genius." 2

1 PMl. Trans, vol. xvi. p. 296.

2 Systeme du Monde, Edit. 2<ie, 1799, p. 336.

300 LIFE OF SIR ISAAC NEWTON. CHAP. XITT.

CHAPTER XIII.

The Newtonian Philosophy stationary for half a Centurj-, owing to the imperfect state
of Mechanics, Optics, and Analysis — Developed and extended by the French Mathe-
maticians — Influence of the Academy of Sciences — Improvements in the Infinitesimal
Calculus— Christian Mayer of the Arithmetic of Sines— D'Alembert's Calculus of
Partial Differences — Lagrange's Calculus of Variations — The Problem of Three
Bodies— Importance of the Lunar Theory — Lunar Tables of Clairaut, D'Alembert,
and Euler — The Superior Tables of Tobias Mayer gains the Prize offered by the
English Board of Longitude — Euler receives part of the English Reward, and also a
Reward from the French Board — Laplace discovers the cause of the Moon's Accelera-
tion, and completes the L ;nar Theory — Lagrange's Solution of the Problem of Three
Bodies as applied to the Planets — Inequalities of Jupiter and Saturn explained by
Laplace — Stability of the Solar System the proof of Design — Maclaurin, Laplace, and
others, on the Figure of the Earth —Researches of Laplace on the Tides, and the stable
Equilibrium of the Ocean — Theoretical Discovery of Neptune by Adams and Leverrier
— New Satellites of Saturn and Neptune— Extension of Saturn's Ring and its partial
fluidity — Twenty-seven Asteroids Discovered — Leverrier's Theory of them — Comets
with Elliptic Orbits within our System— Law of Gravity applied to Double Stars-
Spiral Nebulae— Motion of the Solar System in Space.

When Halley remarked that the author of the Principia
" seemed to have exhausted his argument, and left little to be
done by those who should succeed him," he committed a mis-
take which, though it had a tendency to check the progress of
inquiry, was yet one into which philosophers are apt to fall
when their science has made a great start by the discovery of
some general and comprehensive law. Had Halley ventured to
make this remark at the close of his life, rather than in 1687,
he might have found some justification of it in the long interval
which elapsed before any brilliant addition had been made to
physical astronomy. During the half century which had
passed away since the discovery of universal gravitation, no
application of it of any importance had been made, and, as

LIFE OF Sm ISAAC NEWTON. 301

Laplace lias observed, " all this interval was required for this
great truth to be generally comprehended, and for surmounting
the opposition which it encountered from the system of vortices,
and from the prejudices of contemporaneous mathematicians."
The infinitesimal analysis, as it was left by Newton and Leib-
nitz, was incapable of conducting the physical astronomer to
any higher results than those which were consigned in the
Principia ; and it is a remarkable fact in the history of science,
that the very men who spurned the new philosophy of gravita-
tion, were strenuously engaged in improving that very calculus
which was destined to establish and extend those great truths
which they had so rashly denounced.

It has been remarked by Laplace, that " with the exception
of his researches on the elliptical motion of the planets and
(iomets, of the attraction of spherical bodies, and of the intensity
of gravity at the surface of the sun, and of the planets that are
accompanied by satellites, all the other discoveries which we
have described were only blocked out by Newton. His theory
of the figures of the planets was limited by the supposition of
their homogeneity. His solution of the problem of the preces-
sion of the equinoxes, though very ingenious and accordant with
observations, is in many respects defective. In the great num-
ber of perturbations in the celestial motions, he has considered
only those of the lunar motions, the most important of which,
namely, the evection, had escaped his researches. He has com-
pletely established the existence of the principle which he dis-
covered, but the development of its consequences and of its
advantages has been the work of the successors of this great
geometer."!

In thus completing the great work of which Newton laid the
foundation, it was necessary, as Laplace observes, " to bring to
perfection at once the sciences of mechanics, optics, and analy-
sis ; and though physical astronomy may still be improved and
•gimplified, yet posterity will gratefully acknowledge that* the

1 SytUme du Monde, p. 336.

302 LIFE OF SIR ISAAC NEWTON. CHAP. XIII.

geometers of the eighteenth century have not transmitted to us
a single astronomical phenomenon of which they have not de-
termined the cause and the law. We owe to France the justice
of observing, tliat if England had the advantage of giving birth
to the discovery of universal gravitation, it is principally to the
French geometers, and to the encouragement held out by the
Academy of Sciences, that we owe the numerous developments
of this discovery, and the revolution which it has produced in
astronomy."^

In submitting to our readers a brief history of these develop-
ments, and of that revolution, we shall gather fresh laurels for
the author of the Priucipia. It is from what he left undone,
and what he enabled others to do, that we can rightly estimate
the magnitude and appreciate the value of his achievement.
The importance of a great discovery does not lie in its intrinsic
novelty and beauty : It is the number of its applications, and
the ubiquity of its range, that stamps its value ; and when we
proclaim Newton the Father of the Philosophy of the Universe,
we must regiird the Eulers, the Clairauts, the D'Alemberts, the
Lagranges, and the Laplaces of another age, as the intellectual pro-
geny which he educated and reared. A distinguished philosopher
has asked the question, why no British name is ever mentioned
in the list of mathematicians who followed Newton in his brilliant
career, and completed the magnificent edifice of which he laid
the foundation 1 ^ May we not make the question more special
by asking why the University which he instructed and adorned,
which possessed such noble endowments, and which claims the
honour of having first adopted and taught his philosophy, did
not rear a younger son, or even a sickly child, that could be
ranked in the great family we have named ? Scotland contributed

1 Laplace, Syslcme dii Mon le, p. 340.
Professor Playfair adds, that this was " the more remarkable, as the interests of
navigation were deeply involved in the question of the lunar theory, so that no motiv«
which a regard to reputation or to interest could create was wantiug to engage the ma-
thematicians of England in the inquiry."— ii:dt7i6Mrp/i Review, vol. xL p. 280. Jan.
1808.

LIFE OF SIR ISAAC NEWTON. 303

her Maclaiirin, but England no European name ; and a century
and a half passed away till Airey and Adams adorned the birth-
place of Newton's genius. In the same spirit in which we have
asked these questions, M. Arago, equally jealous of the glory of
his country, has freely confessed, " that no Frenchman can
reflect, without an aching heart, on the small participation of
his own country in the memorable achievement of the discovery
of universal gravitation ;" and Mr. Grant, the latest historian
of physical science,^ in responding to this liberal sentiment, has
added, in the language of just severity, that " if an English-
man could he supposed to he equally sensitive, he has ample
reason to regret the inglorious part his country played during
the long period which marked the development of the Newto-
nian theory." 2

In the imperfect state in which the differential calculus was
left by Newton and Leibnitz, its inventors, it was not fitted to

1 History of Phtjsical Astronomy, kG.^.ld^. London, 1852. Mr. Grant also remarks,
*' that with the exception of Maclaurin and Thomas Sim[)Son, hardly any individual of
these islands deserves even to he mentioned in connexion with the history of physical
astronomy during that period ;" and that, at the beginning of the present century, " there
was hardly an individual in this country who possessed an intimate acquaintance with
the methods of investigation which had conducted the foreign mathematicians to so
many sublime results."

Referring our readers to the statements at the end of Chapter IV., as showing the
f>robable cause of the success of the French mathematicians, and of the inglorious failure
)f our own, we beg their attention to the following confirmation of our views by one of
the wi-sest and most eminent of our Scottish mathematicians. In a review of Laplace's
Si/steme dii Monde, Professor Playfair makes the following observations.

■ The literary institution which has most completely produced its effect of any in mo-
j;dem times, and that has been most successful in promoting the interests of science, is
that of the Royal Academy of Sciences of Paris, yihere small pensions and great honours,
bestowed on a few men for devoting themselves exclusively to works of invention and
discovery, have been the means of advancing the mathematical sciences in France to a
•tate of unexampled prosperity.

" In England, where such an institution as that just mentioned was wanting, and where
the public is perpetually prepared, with the question, cuibono, to repress what seems the
luxury of science, the same progress has not been made ; and our mercantile prejudices
have so far defeated our own purpose, that if the matter had been left to us, the theory
of the moon's motion would still have been extremely imperfect, and the great nautical
problem of finding the longitude could have received nothing like an accurate solution."
—Edinburgh Review, vol. xv. p. 39. Jan. 1810.

304 LIFE OF Sm ISAAC NE\\"rON. CHAP. XIII,

grapple with the higher problems in physical astronomy which
still remained to be solved ; and it was fortunate for the future
progress of the science, that distinguished mathematicians directed
themselves to the improvement of the infinitesimal calculus, and
to the discovery of new mechanical principles, or extended appli-
cations of those already known.

In 1727, the very year in which Newton died, Christian
Mayer published in the Petersburg Commentaries, a valuable
memoir on the application of algebra to geometry ; and the geo-
metrical theorems which he demonstrated, formed the basis of
the Arithmetic of Sines, for which Euler provided a notation
and an algorithm, which has rendered it one of the most simple
and valuable instruments of astronomical research. The inven-
tion of the calculus of Partial Differences by D'Alembert., which
he first made known in 1747, was particularly applicable to
the more difficult problems in physical astronomy, and when im-
proved and extended by Euler, it became an invaluable instru-
ment in every inquiry which demanded the aid of the pure or
mixed mathematics.

But however valuable were these instruments of analysis, the
calculus of variations discovered by Lagrange in 1760, was
the greatest step in the improvement of the infinitesimal cal-
culus which was made in the last century. It not only afforded
the most complete solution of the problems that gave rise to it,
but had an application of' the most extensive kind, exceeding
even the expectations of its inventor. Euler, who had made
some progress in the same subject, at once acknowledged the
superiority of his youthful rival, and with a nobility of mind
not frequently displayed even by the greatest men, he renounced
his own less perfect methods, and devoted himself to the study
and extension of the new calculus.^

Nearly twenty years after the death of Newton, Euler,
Clairaut, and D'Alembeii; were engaged in solving what has

I See the Article Mathematics in the Edinburgh Encpclopa-dia, Tol. xiii. p. .^80,
where Sir John Herschel pronounces a beautiful eulogy on the conduct of Euler.

1746. LIFE OF SIE ISAAC NEWTON. 305

been called the prohlem of three bodies, — that is, the determin-
ation of the motion of one body revolving round a second body,
such as the moon round the earth, and disturbed by the attrac-
tions of a third body, such as the sun. The rigorous solution
of this problem is beyond the reach of human genius, and the
imperfect solution which has been obtained is only an approxi-
mate one depending for its accuracy on the more or less advanced
state of the infinitesimal calculus. But even if the problem of
three bodies had been susceptible of an accurate solution, it
would not have diminished the difficulty of solving the more
general problem of finding the motion of a planet, when simul-
taneously acted upon by all the other planets of the system.
In this case the disturbances are very small, and when the
separate action of each planet upon the disturbed body is deter-
mined, the sum of the perturbations, when applied to the place
of the planet in its elliptic orbit, will give its true place in the
heavens as seen from the centre of the sun.

When the three bodies are the sun, the moon, and the earth,
the disturbance of the moon's motions by the action of ttiC sun
is very considerable, and hence the theory of the moon was
the first subject to which the continental mathematicians directed
their attention. The determination of the longitude at sea by
observing the distance of the moon from the stars, had given a
peculiar interest to the construction of accurate tables for com-
puting the moon's place, and the Board of Longitude in England
liad offered a high reward. Mathematicians were urged to the
inquiry by the united motives of wealth and fame. Newton
had explained only five of the principal equations of the moon's
orbit, and it was obvious that there were many other irregu-
larities which observation alone was incapable of detecting.
Clairaut seems to have been the first of the three mathemati-
cians who undertook this inquiry ; but however this may be,
the competitors arrived at the same goal with nearly equal
success. Clairaut had at first endeavoured to compute the lunar
inequalities by the method of Newton, but he was obliged to
VOL, I. u

306 LIFE OF SIR ISAAC NEWTON. CHAP. XIII.

abandon it, and appeal to the higher powers of analysis. In
1746, Euler drew up a set of lunar tables, founded on the results
of his researches, but they were not found to be very superior
to those in common use. In 1754, Clairaut and D'Alembert
published lunar tables, embodying the results of their theory.
Those of Clairaut were far superior to any that had hitherto
l)een published, while those of D'Alembert were very inferior in
accuracy. Encouraged by the failure of his rivals, Euler resumed
his investigations in 17-55, and published a more complete set
of lunar tables, along with his researches on the lunar theory ;
but though more conformable with observation than his former
set, they had not that degree of accuracy which was required
for the determination of the longitude.

While the mathematicians, trusting too much to theory, were
thus baffled in the useful application of their own results, a
sagacious practical astronomer directed his attention to the im-
jjrovement of the lunar tables, and carried off the prize. Tobias
Mayer of Gottingen, comparing the results obtained by Euler
with a number of accurate observations made by himself and
others, produced a set of tables which, wdien compared with the
observations of Bradley, gave the moon's place within thirty
seconds. These tables were sent to the English Board of Lon-
gitude in 1755, in competition for the prize ; but they did not
possess that degree of precision which was required. Mayer,
however, continued till the day of his death to add to their
accuracy, and he left behind him a complete set of solar and
lunar tables, for which the Board of Longitude awarded his
widow the sum of th7re thousand 'pounds, a portion of the
reward which they had offered for the discovery of the longitude.
These tables were first published in 1770, and their greatest
error was found never to exceed one minute and a quaiiei'. As
these tables were founded on Euler's theorems, the Board pre-
sented this distinguished mathematician with the sum of thre(^
hundred pounds. Though advanced in years, Euler was full
of intellectual life, and having continued to labour at the \\\m\x

1771. LIFE OF SIR ISAAC NEWTON. 307

theory, lie constructed a new set of tables, which were published
in 1771, and were rewarded by the Board of Longitude in
France.

Notwithstanding the accuracy of Mayer's tables, an irregu-
larity had been discovered by observation which was not indicated
by the theory of gravity. Halley and other astronomers had
placed it beyond a doubt that the moon performed her monthly
revolution round the earth in a shorter time than formerly.
This acceleration of the moon, as it was called, amounted to
nearly ten seconds in a century, and various hypotheses were
framed to account for it. The most plausible of these was, that
all space v/as filled with an ethereal medium which opposed such
a resistance to the motions of the planets, that the force which
kept them in their orbit would gradually overpower their dimi-
nished velocity, and thus shorten their period round the central
body. This hypothesis was supported by Euler, and by the
abettors of the undulatory theory, who required the existence of
a medium for the propagation of light, and it was adopted with
equal eagerness by another class of theorists, who saw in the
acceleration of the celestial motions the process by which the
Almighty was to dest»Oy the solar system, by precipitating the
secondary planets upon their primaries, and the primary planets
upon the sun. Laplace admitted the sufficiency of the hypo-
thesis, but as he saw no reason for admitting the existence of a
resisting medium, he did not consider himself warranted in
adopting such an hypothesis till it was found that gravitation
was incapable of accounting for the fact. Another theory of
the moon's acceleration was founded on the supposition that the
daily motion of the earth was retarded by the continued blowing
of the easterly winds of the tropics against the mountain ranges
which extend from the equator to the poles ; but Laplace satis-
fied himself, from a rigorous examination of this supposition,
that no retardation of the earth's motion could be thus produced.
Another hypothesis still remained to which astronomers ndght
appeal not only for the explanation of the moon's acceleration,

308 LIFE OF SIR ISAAC NEWTON. CHAP. XIII.

but also of some considerable inequalities in the motions of
Jupiter and Saturn, which appeared not to have a periodical
character, and therefore to be in the same category with the
moon's acceleration. Newton and every other philosopher had
taken it for granted that the force of gravity was propagated
instantaneously from bodies, and not in time like the rays of
light ; but it occurred to Laplace that if time was required for
the transmission of gravity, it would affect the intensity of the
force. He therefore computed the velocity of gravity that
would be required to produce the observed acceleration, and he
found it to be eight millions of times greater than the velocity
of light, that is 192,500 miles multiplied by 8,000,000, or
1,540,000,000,000 miles in a second — a velocity which no
language can express. After arriving at this result, Laplace
found that if the acceleration is produced by another cause, then
the effect of the successive transmissions would be insensible,
and consequently the velocity of gravity, if it is not instanta-
neous, must at least he Jifty millio7is of times greater than that
of light, that is, must be at least 9,625,000,000,000 miles in
a second.

In the course of these investigations fi had been placed be-
yond a doubt that every inequality in the motion of the planets,
and in the form of their orbits produced by their mutual gravi-
tation, must be periodical, that is, that the inequality, after
reaching its maximum, will diminish according to the same law
by which it increased, and hence it became doubly interesting
to discover the cause of phenomena which had this character.
Although foiled in so many attempts to refer the moon's acce-
leration to the action of gravity, Laplace returned to the
inquiry with fresh zeal, and about the end of 1787, his labours
were crowned with success. It was well known to Lagrange
and to himself, that the eccentricities of the planetary orbits
underwent extremely slow changes, which had a very long
period. To such a change the eccentricity of the earth's orbit
is subject from the action of the planets. The mean action

1H93. LIFE OF SIR ISAAC NEWTON. 309

of the sun must therefore vary with the earth's eccentricity,
and the earth, thus exerting a greater or a less force over the
moon, will accelerate or retard her, and thus produce the se-
cular inequality which has been observed in her mean motion.
When the eccentricity is diminishing, which it has been doing
since the date of the earliest astronomical observations, the
moon's mean motion will be accelerated : but when the dimi-
nution ceases, and the orbit returns to its former ellipticity, the
sun's action will increase, and the moon's mean motion will be
retarded.^ Laplace found the acceleration to be ten seconds
during a century, — a rate which, notwithstanding its variable
character, may be considered as uniform for two thousand
years.

Although Halley suspected the existence of this inequality so
early as 1693, yet it is to Mr. Dunthorne that we owe the first
accurate determination of its magnitude. By means of lunar
eclipses observed at Babylon in 721 B.C., and at Alexandria in
201 B.C., — a solar eclipse observed by Theon, a.d. 364, and
other two by Ibyn Jounis at Cairo, about the end of the tenth
century, he found the acceleration to be ten seconds in a
hundred years. 2 The consequence of this inequality is, that
the moon is about two hours later in coming to the meridian
than she would have been had she performed her monthly revo-
lution in the same time that she did when the earliest Chaldean
observations were made. "It is indeed a wonderful fact in the
history of science," as Mr. Grant remarks, " that these rude
notes of the priests of Babylon should escape the ruins of suc-
cessive empires, and finally, after the lapse of three thousand
years, should become subservient in establishing a phenomenon
of so refined and complicated a character as the inequality we

1 M. Leverrier has recently shown that the earth's eccentricity will diminish during the
period of twenty-four thousand years !

'^ Mr. Airy has more recently found by discussing three ancient total eclipses (Aug. 16,
B.C. 309 ; May 19, B.C. 556 ; May 28, B.C. 584), that the secular acceleration is at least
12' 12", as adopted by Hansen in his Lunar Tables. See Memoirs of the Astronomical
Society, vol, xxvi.

310 LIFE OF SIR ISAAC NEWTON. CHAP, XIII.

have just been considering."^ And in referring to the long
period of the same inequality, Professor Playfair remarks, that
"two thousand years are little more than an infinitesimal in
this reckoning ; and as an astronomer thinks that he commits
no error when he considers the rate of the sun's motion as
uniform for twenty-four hours, so he commits none when he
regards the rate of this equation as continuing the same for
twenty centuries. That man, whose life, nay, the history of
whose species occupies such a mere point in the duration of the
world, should come to the knowledge of laws that embrace
myriads of ages in their revolution, is perhaps the most astonish-
ing fact that the history of science exhibits. "^

By this great discovery, which had eluded the grasp of Euler
and Lagrange,^ Laplace may be regarded as having completed
the lunar theory exactly one hundred years after it had been
sketched out in the first edition of the Principia.

The curious subject of the moon's acceleration has recently
excited much interest in consequence of Professor Adams* having
proposed an important correction upon the theory of Laplace,
by which the secular acceleration was reduced to 6"-ll.
M. Delaunay, by a different process, has since found it to be
6"-ll, exactly the same as that obtained by Mr. Adams.*''
M. Plana, the distinguished Sardinian mathematician, and M.
Pontecoulant,^ still adhere to the theory of Laplace, on grounds
which are not yet published. M. Delaunay is of opinion that

1 History of Phijskal Axtronomij, pp. 63, 64.

'- Edinburgh Review, vol xi. p. 261

3 The Academy of Sciences proposed the moon's acceleration as the subject of their
prize for 1770. Euler gained it, but came to the conclusion ihat it was not produced by
the force of gravity. The same subject was again proposed in 1772, and the prize was
divided between Euler and Lagrange. Euler ascribed the acceleration to a resisting
medium, and Lagrange evaded the difficulty. The prize was again offered in 1774, and
was gained by Lagrange, and he now doubted the existence of the inequality. It was
under these circumstances that Laplace took up the subject, and obtained the results
which we have mentioned.

* Phil. Tram. 1853, p. 398.

s Comptes Rendus, torn, xlviii. pp. 137, 249, 817, 1031 ; torn. xlix. p. 309.

c Id. torn, xlviii. p. 1023.

1748-52. LIFE OF SIR ISAAC NEWTON. 311

this difference has arisen from M. Plana having regarded the
equal description of areas as constant, whereas it is variable.
The difference between the results of MM. Adams and Delaunay,
if correct, and those obtained from ancient eclipses, is very re-
markable, and indicates the operation of some cause w^hich
remains to be discovered.

The theory of the lunar motions being thus completed, Euler,
Lagrange, and Laplace directed all the powers of their mind,
and all the refinements of analysis, to the determination of the
mutual action of the primary planets. In this case the three
bodies were the sun, the disturbed and the disturbing planet.
In 1748, the Academy of Sciences proposed the Inequalities of
Jupiter and Saturn as the subject of their prize. In his Memoir,
which gained the prize, Euler proved that both Jupiter and
Saturn were subject to considerable inequalities, arising from
their mutual action, but all of them periodical, and returning
nearly in the same order after short intervals of not much more
than twenty or thirty years. But though these results accorded
with observation, they afforded no explanation of the great
secular inequalities which in twenty centuries had produced in
Jupiter an acceleration of 3° 33', and in Saturn a retardation
of 5" 13'. The Academy, therefore, again offered their prize
of 1752 for the best Memoir on the same subject. Euler a
second time carried off the prize ; but though he found two in-
equalities of long periods depending on the angle formed by the
line of the apsides of each planet, yet he made them equal and
additive, c(mtrary to observation. Lagrange failed in the same
inquiry ; and Laplace, after carrying his approximation farther
than either of his rivals, came to the conclusion that no change
in the mean motion of J upiter and Saturn could be produced by
their mutual action. Under this grave embarrassment, appa-
rently threatening the truth or accuracy of the law of gravity,
but really heralding a great discovery, Lagrange appeared with
a, new solution of the problem of three bodies. At the age of
twenty-seven he published this solution in the Turin Memoirs

312 LIFE OF SIR ISAAC NEWTON. CHAP. XIII.

for 1763, and, in applying it to the motions of Jupiter and
Saturn, he obtained for the former an additive secular equation
of nearly three seconds, and for the latter a subtractive one of
fourteen seconds ; but though this result was in its general
character superior to that of Euler, it yet afforded no explana-
tion of the great inequalities we have mentioned. Having
observed that the calculus had never given any inequalities but
periodical ones, Lagrange now set himself to inquire, whether
in the planetary system, continually increasing or continually
diminishing inequalities, affecting the mean motions, could be
produced by the mutual action of the two planets. Inde-
pendently of any approximation, and by a method peculiarly his
own, he found that all inequalities produced by gravity must
be periodical, and that amid all the changes arising from the
umtual action of the planets, two elements are unchangeable —
the length of the major axis of the planet's elliptical orbit, and
the time in which that orbit is described. The inclination of
the orbit to the ecliptic changes, the ellipse and its eccentricity
change, but its greater axis and the time of the planet's revo-
lution are unalterable. This grand discovery, excluding every
source of disorder, and securing the stability of the system, is
doubtless one of the noblest in physical astronomy, and more
than any other displays the wisdom of the Creator.

But though Lagrange had made this great step in celestial
physics, he failed in discovering the cause of the inequalities of
Jupiter and Saturn, and left to Laplace the honour of solving
this perplexing problem. By a more rigorous inquiry into the
effects of their mutual action, Laplace found that the mean
motion of Jupiter would be accelerated, while that of Saturn
would be retarded, and that the relative derangement of the
two planets would be as five to ten, the ratio of their mean
motion, or as 3° 58' to 5° 16', the result for Jupiter differing
only nine minutes from that given by Halley. In continuing
the inquiry, he found that each planet was subject to an
inequality whose period was 969 years ; — that of Saturn, when

1763. LIFE OF SIR ISAAC NEWTON. 313

a maximum, being 48' 44", and that of Jupiter 20' 49", with
an opposite sign. These inequalities were a maximum in 1560,
and from that epoch the apparent mean motions of the two
planets have been approaching to their true mean motions, and
became the same in 1790. By a comparison of these results
with forty -three observed oppositions of Saturn, Laplace found
them generally correct, and the error never exceeding two
minutes of a degree. This difference he afterwards reduced in
the case of both planets to twelve seconds, although the best
tables of Saturn often erred twenty minutes. By these brilliant
researches theory and observation were reconciled, — the last
difficulty which beset the Newtonian theory was removed, —
every inequality in the Solar System was explained, — and the
law of gravitation established as a law of the universe.

In concluding this brief notice of the progress of physical
astronomy since the time of Newton in a few of its leading
features, we are naturally led to ponder on the great truth of
the stability and permanence of the solar system as demon-
strated by the discoveries of Lagrange and Laplace. In the
present day, when worlds and systems of worlds, when life
physical and life intellectual are supposed to be the result of
general law, it is interesting to study those conditions of the
planetary system which are necessary to its stability, and to
consider whether they appear to be the result of necessity or
design. It follows, from the discoveries of Laplace, that there
are three conditions essential to the stability and permanence of
the solar system, namely, the motion of all the planets in the
same direction, — their motion in orbits slightly elliptical, or
nearly circular, — and the commensurability of their periods of
revolution. That these conditions are not necessary is very
obvious. Any one of them may be supposed different from
what it is, while the rest remained the same. The planets,
like the comets, might have been launched in different direc-
tions, and moved in planes of various and great inclinations to
the ecliptic. They might have been propelled with such varie-

314 LIFE OF SIR ISAAC NEWTON. CHAP. XIII.

ti(?s of tangential force as to have moved in orbits of great
ellipticity ; and no reason, even of the most hypothetical nature,
can be assigned why their annual periods might not have been
incommensurable. The arrangements, therefore, upon which
the stability of the system depends, must have been the result
of design, the contrivance of that omniscience which foresaw all
that was future, and of that infinite skill which knew how to
provide for the permanence of His work. How far the comets,
whose motions are not regulated by such laws, and which move
in so many directions, may in the future interfere with the
order of our system, can only be conjectured. They have not
interfered with it in the past, owing no doubt to the smallness
of their density ; and we cannot doubt that the same wisdom
which has established so great a harmony in the movements of
the planetary system, that the inequalities which necessarily
arise from their mutual action arrive at a maximum, and tlien
disappear, will also have made provision for the future stability
of the system.

Although it is only a general view that we can take of the
important discoveries in physical astronomy which have sprung
from those of Newton, yet we should scarcely be justified in
omitting those which relate to the figure of our earth and the
tides of its ocean. Newton inferred that the figure of the earth
was an oblate spheroid, whose equatorial diameter was to its
polar axis in the ratio of 231 to 230, but it was reserved for
Maclaurin to demonstrate, a priori^ that the earth, if homo-
geneous, might assume such a form. The method which he
employed, though synthetical, was remarkable for its accuracy
and elegance. In 1743, Clairaut published his Treatise on the
Figure of the Earth, in which he investigated the form it would
assume on the supposition of its density being heterogeneous.
He found that the earth would have the form of an elliptic
spheroid, if its mass was arranged in homogeneous concentric
strata of the same form ; and he investigated the beautiful
theorem which bears his name, by which we can determine the

174(1. LIFE OF SIR ISAAC NEWTON. 31.5

cllipticity of the earth from measures of the force of gravity,
taken in two different latitudes by the aid of the pendulum.
D'Alembert, Lagi'ange, Legendre, Laplace, Ivory, Plana, Gauss,
P(nsson, and Airy, have directed their attention to the subject
of the earth's figure, but without adding much, to the results
obtained by Clairaut. In his Mecanique Celeste, Laplace has
applied the deductions of his calculus to the determination of
the figure of the earth, from the measurement of degrees on its
surface, and the observations made in different latitudes on the
length of a pendulum vibrating seconds, and he finds that the
result cannot be reconciled with the hypothesis of an elliptic
spheroid, unless a greater error than is probable be admitted in
some of the measurements.^ Upon discussing, however, all the
more recent measurements of a degree, and all the observations
with the pendulum, the ellipticity of the earth in the former
case has been found to be ^^, and, in the latter, 2 J-o? the
ellipticity indicated by the lunar perturbation being 3 J^, an
agreement which is very remarkable, when we consider the
local causes which necessarily affect the observations with the
pendulum, as first noticed by General Sabine, and the measure-
ment of an arc of the meridian.

The theory of the tides of our ocean, though treated by a
master mind in the Principia, was nevertheless susceptible of
extension and improvement. The Academy of Sciences proposed
it as the subject of their prize for 1740. Four dissertations
competed for the prize, three of them of great merit, by Euler,
Daniel Bemouilli, and Maclaurin, and a fourth by Father Ca-
valleri, a Jesuit, who founded his investigation on the system
of Vortices. The prize was divided among all the four com-
T)etitors, — a proof, doubtless, that the Cartesian doctrines were
not entirely exploded. These dissertations, and others on the
same subject, are founded on what is called the equilibrium
theory, which supposes that the sun and moon draw the waters
of the ocean into the form of an aqueous spheroid, in which

1 Mecanique CHeste, tora. ii. liv. iii. chap, v.; and Systeme du Monde, liv. iv. chap. vii.

316 LIFE OF SIR ISAAC NEWTON. CHAP. XIII.

the molecules of water are maintained at rest by the action of
these forces. In consequence, however, of the daily motion of
the earth, such a spheroid never can be formed, — there can
only be a tendency to it ; and hence the tides are the conse-
quence of the perpetual oscillation of the waters of the ocean, —
a result which the state of mechanical and mathematical science
will not allow us to determine. Laplace, however, undertook
the task, and communicated to the Academy of Sciences in
1755, 1779, and 1790, a series of valuable memoirs on the
subject. The theory to which he was led by these researches
rests upon two suppositions not strictly true, namely, that the
earth is covered with water, and that the depth of the ocean is
uniform under the same parallel of latitude. Regarding every
particle of water as under the influence of three forces, namely,
the attraction of the earth, the attraction of the sun and moon,
and that which arises from the earth's rotation, he found that
three kinds of oscillation are produced ; the first depending on
the sun and moon, and varying periodically, so as not to return
tiU after a long interval ; the second depending on the earth's
rotation, and returning in the same order after the interval of
about a day ; and the third depending on double the angular
rotation of the earth, and returning after an interval of about
half a day. As the oscillations of the second class are affected
by the depth of the sea as well as the earth's rotation, and as
the differences between the two tides in the same day depend
chiefly upon them, Laplace has from this been able to determine
that the mean depth of the sea is about foiu* leagues. The
general correctness of this theory has been placed beyond a
doubt by a comparison of its results, with observations on the
tides made at Brest during a long succession of years. ^

As the ocean is often agitated by several irregular causes,
such as storms and earthquakes, which raise it to great heights,
and sometimes make it overstep its limits, Laplace has eiidea-

' Micaniqm Celeste, parti, liv. iv. chap. i. torn. ii. p. 171 ; and St/steme dv Monde,
liv. iv. chap. x. p. 248.

1779. LIFE OF SIK ISAAC NEWTON. 317

voured to ascertain the " stability of the equilibrium of our
seas." Although we find that the sea falls into its hollow bed
after the ordinary commotions to which it is subject, yet we
may reasonably fear that some extraordinary cause may com-
municate to it such a disturbance, that, though inconsiderable
in its origin, may go on increasing till it raises it above the
highest mountains. As such a result would afford an explan-
ation of several phenomena of natural history, it becomes in-
teresting to determine the conditions necessary to the absolute
stability of the equilibrium of our seas, and to see if these
conditions exist in nature. In submitting this question to
analysis, Laplace has found that the equilibrium of the ocean is
stable if its density/ is less than the mean density of the earth,
and that its equilibrium cannot be subverted unless these two
densities are equal, or that of the earth less than that of its
waters. The experiments on the attraction of Schehallion and
Mount Cenis, and those made by Mr. Cavendish, Reich, and
Bailey, with balls of lead, demonstrate that the mean density of
the earth is at least five times that of water, and hence the
stability of the ocean is placed beyond a doubt. As the seas,
therefore, have at one time covered continents which are now
raised above their level, we must seek for some other cause of
it than any want of stability in the equilibrium of the ocean. ^

We have already seen how Newton deduced the precession
of the equinoxes from the action of the sun and moon upon the
excess of matter accumulated at the equator of the terrestrial
spheroid. This investigation, however, was founded on principles
not rigorously correct, and therefore the complete solution of
the problem was left to his successors. The discovery, too, of
the nutation and of its cause, by Bradley, gave a new character
to the investigation, which now required the aid of the calculus
of partial differences. It fell to the lot of D'Alembert to give
a complete solution of the problem, whatever were the figure

1 See Mecanique Cdeste, part i. liv. iv. chap. ii. torn. ii. p. 204 ; and Systeme du
Monde, liv. iv. chap. xi. p. 265.

3 1 8 LIFE OF SIR ISAAC NEWTON. CHAP. XIII.

and the density of the strata of the terrestrial spheroid. The
results which he obtained agreed accurately with observations
on the precession, and he obtained also the true measure of the
nutation, or the dimensions of the small ellipse described by
the pole of the equator, which the observations of Bradley had
left in some uncertainty.

In viewing the subject under a more general aspect than
D'Alembert, Laplace was led to some very interesting results.
From his researches on the oscillations of the ocean, he was led
to the remarkable theorem, " that whatever be the law of tlie
depth of the sea, and the form of the spheroid which it covers,
the phenomena of the precession and the nutation are the same
as if the sea formed a solid mass with this spheroid." Laplace
has also shown tliat the rotation of the earth upon its axis, or
the length of the day, cannot be affected either by currents on
the ocean, rivers, trade-winds, or even earthquakes, or in general
any force which can shake the earth either in its interior or
upon its surface. It might have been expected that the trade-
winds blowing between the tropics would, by their action upon
the sea, and upon the continents and mountains which they
meet, insensibly diminish the rotatory motion of the earth ; but
upon the same principle the other motions of the atmosphere,
which take place beyond the tropics, would accelerate that
motion by the same quantity. In order to produce any sensible
change in the length of the day, a very considerable displace-
ment in the parts of the earth would be required. A great
mass of matter, for example, transported from the poles to the
equator, would increase the length of the day, and it would be
diminished if dense bodies approached either pole, or the axis
of the earth. But as there appears to be no cause which is
capable of displacing masses sufficiently large to produce such
effects, we may regtird the length of the day as one of the most
unchangeable elements in the system of the world. " The same
thing is true," as Laplace observes, " with respect to the points
where the earth's axis meets its surface. If this planet turned

1799. LIFE OF SIR ISAAC NEWTON. 319

successively round different diameters inclined to one another
at considerable angles, the equator and the poles would change
their place upon the earth ; and the seas on rushing to the new
equator, would cover and uncover alternately the highest moun-
tains ; but all the researches which I have made on the dis-
placement of the poles of rotation at the surface of the earth,
have proved to me that it is insensible.""^ After discussing the
consequences respecting the constitution of the earth, which
are accordant with his theory of the precession and nutation,
Laplace states, that though it does not enable us to determine
the ellipticity of the earth, it fixes its limit between ^^^ and
sTF P^^"* ^f *^^ radius of the equator. The same theory in-
dicates as the most probable constitution of the earth, that the
density of its strata increases from its surface to its centre. ^

Such is a brief and general view of the important discoveries
in physical astronomy, which have illustrated the century that
followed the publication of the Principia. Brilliant as they are,
and evincing as they do the highest genius, yet the century in
which we live has been rendered remarkable by a discovery
which, whether we view it in its theoretical relations, or in its
practical results, is the most remarkable in the history of physical
astronomy. In the motions of the planet Uranus, discovered
since the time of Newton, astronomers had been for a long time
perplexed with certain irregularities, which could not be deduced
from the action of the other planets. M. Bouvard, who con-
structed tables of this planet, seeing the impossibility of reconciling
the ancient with the modern observations, threw out the idea
that the irregiilaiities from which this discrepancy arose might
be owing to the action of an unknown planet. Our countryman,
the Kev. Mr. Hussey, conceived " the possibility of some dis-
turbing body beyond Uranus ;" and Hansen, with whom Bouvard
corresponded on the subject, was of opinion that there must be

1 SyiUme dn Monde, liv. iv. chap. xiii. pp. 276, 277. See also M^eanique Celeste,
part i. liv. v. chap. i. torn. ii. p. 347. 2 j^^^c. Cdkste, torn. ii. pp. 354, 355.

320 LIFE OF SIR ISAAC NEWTON. CHAP. XIII.

two new planets beyond Uranus to account for the irregularities.
In 1834, Mr. Hussey was anxious that the Astronomer-Royal
should assist him in detecting the invisible planet, and other
astronomers expressed the same desire, to have so important a
question examined and settled. On his return to Berlin from
the meeting of the British Association in 1846, the celebrated
astronomer, M. Bessel, commenced the task of determining the
actual position of the planet ; but in consequence of the death
of M. Flemming, the young German astronomer to whom he
had intrusted some of the preliminary calculations, and of his
own death not long afterwards, the inquiry was stopped.

While the leading astronomers in Europe were thus thinking
and talking about the possible existence of a new planet beyond
the orbit of Uranus, two young astronomers, Mr. Adams of St.
John's College, Cambridge, and M. Leverrier of Paris, were
diligently engaged in attempting to deduce from the irregularities
which it produced in the motions of Uranus, the elements of
the planet's orbit, and its actual position in the heavens. In
October 1845, Mr. Adams had solved this intricate problem —
the inverse problem of perturbations, as it has been called,
placing beyond a doubt the theoretical existence of the planet,
and assigning to it a place in the heavens, which was afterwards
found to be little more than a single degree from its exact place !
Anxious for the discovery of the planet in the heavens, Mr.
Adams communicated his results to the Astronomer-Royal and
Professor Challis ; but more than nine months were allowed to
pass away before a single telescope was directed in search of it
to the heavens. .On the 29th July, Professor Challis began
his observations, and on the 4th and 1 2th of August, when he
directed his telescope to the theoretical place of the planet as
given him by Mr. Adams, he saw the planet, and obtained two
positions of it.

While Mr. Adams was engaged in this important inquiry, M.
Leverrier, Avho had distinguished himself by a series of valuable
memoirs on the great inequality of Pallas, — on the perturbations

1845-47. LIFE OF SIR ISAAC NEWTON. 321

of Mercury, — and on the rectification of the orbits of comets,
was busily occupied with the same problem. In the summer
of 1845, M. Arago represented to Leverrier the importance of
studying the perturbations of Uranus. Abandoning his researches
on comets, he devoted himself to the task suggested by his
friend, and on the 10th November 1845, he communicated to
the Academy of Sciences his First Memoir on the Theory of
Uranus, In the following June he submitted to the Academy
his Second Memoir, entitled, Researches on the Motio')is of
Uranus, in which, after examining the different hypotheses that
had been adduced to explain the irregularities of that planet, he
is driven to the conclusion that they are due to the action of a
planet situated in the ecliptic at a mean distance double that of
Uranus. He then proceeds to determine where this planet is
actually situated, what is its mass, and what are the elements
of the orbit which it describes : After giving a rigorous solution
of this problem, and showing that there are not two quarters of
the heavens in which we can place the planet at a given epoch,
he computes its heliocentric place on the 1st January 1847,
which he finds to be in the 325th degree of longitude, and he
boldly asserts that in assigning to it this place, he does not
commit an error of more than 10°. The position thus given
to it is within a degree of that found by Mr. Adams. Anxious,
like Mr. Adams, for the actual discovery of the planet, M. Le-
verrier naturally expected that practical astronomers would exert
themselves in searching for it. The place which he assigned to
it was published on the 1st of June, and yet no attempt seems
to have been made to find it for nearly five months. The exact
position of the planet was published on the 31st August, and
on the 1 8th September was communicated to M. Galle, of the
Royal Observatory of Berlin, who discovered it as a star of the
eighth magnitude the very evening on which he received the
request to look for it. Professor Challis had secured the dis-
covery of this remarkable body six weeks before, but the honour
of having actually found it belongs to the Prussian astronomer.

VOL. I. X

322 LIFE OF SIR ISAAC NEWTON. CHAP. XIII.

With the universal concurrence of the astronomical world, the
new planet received the name of Neptune. It revolves round
the sun in about 172 years, at a mean distance of thirty, that
of Uranus being nineteen, and that of the Earth one ; and by
its discovery the Solar System has been extended one thousand
millions of miles beyond its former limits.

The honour of having made this discovery belongs equally to
Adams and Leverrier. It is the greatest intellectual achieve-
ment in the annals of astronomy, and the noblest triumph of
the Newtonian Philosophy. To detect a planet by the eye, or
to track it to its place by the mind, are acts as incommensur-
able as those of muscular and intellectual power. Recumbent
on his easy chair, the practical astronomer has but to look
through the cleft in his revolving cupola, in order to trace the
pilgrim star in i\;s course ; or by the application of magnifying
power, to expand its tiny disc, and thus transfer it from among
its sidereal companions to the planetary domains. The physical
astronomer, on the contrary, has no such auxiliaries : he cal-
(;ulates at noon, when the stars disappear under a meridian
sun : he computes at midnight, when clouds and darkness
shroud the heavens ; and from within that cerebral dome,
which has no opening heavenward, and no instrument but the
Eye of Reason, he sees in the disturbing agencies of an unseen
planet, upon a planet by him equally unseen, the existence of
the disturbing agent, and from the nature and amount of its
action, he computes its magnitude and indicates its place. If
man has ever been permitted to see otherwise than by the eye,
it is when the clairvoyance of reason, piercing through screens
of epidermis and walls of bone, grasps, amid the abstractions of
number and of quantity, those sublime realities which have
eluded the keenest touch, and evaded the sharpest eye.

Although the philosophy of Newton has since his day en-
joyed such signal triumphs, it has yet other strongholds to
storm, and other conquests to achieve. In his survey of the
sidereal and planetary domains, the practical astronomer has in

1S52. LIFE OF SIR ISAAC NEWTON. 323

the present century laid open new fields of research ripe for the
intellectual sickle, and fitted to yield to the accomplished
analyst the richest harvest of discovery.

Within our own system the detection of a satellite to Nep-
tune, by Mr. Lassels, — of an eighth satellite to Saturn, by Mr.
Lassels and Mr. Bond, between the orbits of the 4 th and 5th
of these bodies, — and of a new fluid ring gradually advancing
to the body of the planet, will furnish interesting materials to
the physical astronomer. This new and remarkable feature in
the system of Saturn has been recently studied by Mr. Bond of
the United States, and M. Otto Struve, at the observatory of
Pulkova, with the great Munich telescope. With that fine
instrument they saw distinctly the dark interval which separates
this new ring from the two old ones, and the boundaries of this
interval were so well marked, that they succeeded in measuring
its dimensions. They perceived, also, at the inner margin of
the new ring, an edge or border feebly iUuminated, which they
conceived might be the commencement of another similar
appendage, though the line of separation had not yet become
visible. The following are the principal results which these
two able astronomers have obtained : — " 1. The new ring is
not subject to very rapid changes. 2. It is not of very recent
formation ; for it is quite certain that it has been seen, if not
recognised, according to its true character, ever since the im-
provements upon astronomical telescopes have enabled astrono-
mers to see the belts upon the surface of the planet, or at least
since the beginning of the last century. 3. That the inner
border of the annular system of Saturn has, since the time of
Uuygen^, been gradually approaching to the body of the planet^
and therefore it follows, that there has been a successive en-
largement of this system. 4. That it is at least very probable
that the approach of the rings towards the planet is caused
particularly by the successive extension of the inner or middle
ring. Hence it follows, that Saturn's system of rings does not
exist, as has been generally supposed, in a state of stable

324 LIFE OF SIR ISAAC NEWTON. CHAP. XIII.

equilibrium, and that we may expect sooner or later, perhaps
in some dozen of years, to see the rings united with the body of
the planet."^

Of all the celestial phenomena which have been discovered
since the time of Newton, the most remarkable are thojifty-
six small planets which have been discovered between the
orbits of Mars and Jupiter. Dr. Olbers of Bremen, who dis-
covered two of them, hazarded the idea that a large planet
which had once occupied the same place, had been burst in
pieces by some internal force. This opinion, which has been
long considered as a very probable one, has only recently been
called in question. M. Leverrier, the first mathematician who
has directed his attention to the theory of this remarkable
group of bodies, considers the opinion of Olbers as contradicted
by the great inclination of the orbit of Pallas ; and in place of
explaining the existence of these planets by an alteration of the
primitive system of the universe, he believes " that they have
been regularly formed like all the other planets, and in virtue
of the same laws." In a very interesting communication on
this subject, lately made to the Academy of Sciences, 2 M.
Leverrier has endeavoured to ascertain the limit of the sum of
the magnitudes of the whole group, known and unknown, by
the disturbing action which they exercise on the motion of the
perihelion of Mars and the Earth. If the perihelions of these
small planets were distributed uniformly in all the regions of
the zodiac, the action of these masses of matter, situated in one
half or semi- circumference of the heavens, would be destroyed
by the action of the equal masses situated in the opposite half

1 Laplace has shown that the stability of the equilibrium of the rings requires that
they be irregular solids, unequally wide in different parts of their circumference, so that
their centres of gravity do not coincide with their centres of figure. — See M^caniqite
(Xleste, part i. liv. iii. chap. vi. torn. ii. p. 155 ; Systime du Monde, liv. chap. Till p.
342.

2 Considerations sur Vensemble du Systeme des petites Planetes situt'es cntre Mars et
Jupiter, par M. U. J. LavEBaiBa. Lu 28 Nov. 1853. Comptes Rendus, inc., torn,
xxxvii. pp. 793-798.

1801-53. LIFE OF SIR ISAAC NEWTON. 325

or semi-circumference. But M. Leverrier finds that twenty out
of twentT/six of the planets have the longitudes of their peri-
helion between 4° and 184°, a semi-circumference of the
heavens, and hence their action as one mass on Mars and the
Earth is not destroyed by the action of the other six planets.
It is possible that the small planets, which may yet be disco-
vered, may have more of their perihelions in the latter of their
semi-circumferences than in the former ; but the possibility is
that there will be more of them conjoined with the larger than
the smaller group, or, at least, that they will be equally diffused
over the zodiac in reference to their perihelion points.

Having shown that the perihelion of Mars is placed much
more advantageously than that of the Earth, in relation to the
mean direction of the perihelions of the small planets, and that
the greater eccentricity of the orbit of Mars is more favourable
for determining the amount of their action, he finds that if the
total mass of the small planets were equal to the mass of the
Earth, it would produce in the heliocentric longitude of the
perihelion of Mars, an inequality which in a century would
amount to eleven seconds, a quantity which could not have
escaped the notice of astronomers. Considering, therefore, that
this inequality would become particularly sensible at the oppo-
sitions of Mars, M. Leverrier is led to believe, that though the
orbit of Mars has not received its final improvements, yet it
will not admit of an error in longitude greater than one-fourth
of the above quantity, and hence he concludes, that the sum
total of the matter constituting the small planets situated between
the mean distances 2-20 and 3-16, cannot exceed about the
fourth part of the mass of the Earth.

In examining the place of the nodes of twenty-six of the small
planets, M. Leverrier finds that twenty-two of the ascending nodes
of their orbits have their longitudes between 36* and 216°, that
is, within a semi-circumference of the heavens,^ a result almost

1 M. Leverrier takes occasion to remark, "that we might perhaps find some systematic
difference between the mean direction of the ascending nodes of the planets near the

326 LIFE OF SIR ISAAC NEWTON. CHAF. XIH.

the same as that which takes place in their perihelions. From
this fact he observes, that in considering the motion of the plane
of the ecliptic, we may arrive at conclusions of the same kind
respecting the magnitude of the mass of the small planets,
though the limit would be less strict than in that which is
derived from the grouping of their perihelions.

In his theory of the motion of comets. Sir Isaac Newton did
not anticipate that bodies of this kind would be discovered
moving in elliptical orbits, contained within the limits of our
own system, and thus affording a new application of the law of
gravity, and remarkable examples of the action of the planets
upon this new class of wandering stars. It had long been the
universal belief among astronomers, that every comet strayed
far beyond the limits of our system, the shortest period being
about seventy years. In 1818, however, M. Pons announced
the discovery of a very faint comet, without a tail, the motions
of which could not be reconciled with a parabolic orbit. After
its fourth appearance. Professor M. Encke of Berlin, whose name
is now attached to the comet, found that it moved in an elliptic
orbit with a period of about 1211 days, or three years and a
third, and that its orbit was included within our system, ex-
tending inward as far as Mercury, and outward only a little
beyond the orbit of Pallas. He computed the perturbations
produced by the action of Venus, the Earth, Mars, Jupiter, and
Saturn, and he found that its periods had been diminishing
between 1786 and 1838, at the rate of about 21 hours in each
revolution — an effect which he ascribed to the resistance of an
ethereal medium.

A still more remarkable comet, supposed to be the same as
that of 1772, 1805, 1839, &c., was discovered in 1826 by
M. Biela. Its period was found to be about 2410 days, or
6} years, and its orbit did not reach so far as that of Saturn.

Sun, and that of the ascending nodes of the more distant planets, and that we may thus
conjecture that these planets belong in reality to three distinct groups." — Comptcs Hendtts,
&c., torn, xxzvii. p. V95.

1832-48. LIFE OF SIR ISAAC NEWTON. 327

M. Damoiseau found that its arrival at its perihelion would be
retarded nine days and sixteen hours by the action of Saturn,
Jupiter, and the Earth ; and that on the 29th October 1832,
about a month before its perihelion passage, it would cross the
plane of the ecliptic, within 18,000 miles of a point in the
Earth's orbit. The announcement of this fact excited such an
alarm in Paris, that M. Arago was summoned to allay the fears
of the community. According to prediction, the comet returned
in 1839 and 1846 ; but, strange to say, it was on this last
occasion separated into two distinct comets, the one a little fainter
than the other. Their tails were parallel, and their distance,
which was the same till the comet became single by the gradual
disappearance of the smaller one, was found by M. Plantamour
to be equcil to about two -thirds of the radius of the moon's orbit,
that is, about 160,000 miles !^

Another comet belonging to our system was discovered by
M. Faye in November 1843. Dr. Goldsmicht found that its
period was about 2718 days, or 7 J years, and M. Leverrier
computed that its arrival would be delayed 7 days and 1 5 hours
by the action of the planets. Its orbit is more circular than
that of any other comet, and is included between the orbits of
Mars and Saturn. It had been suggested by M. Valz, that this
comet might be Lexell's comet of 1770,^ which had been ren-
dered visible by the action of Jupiter in 1767, and which was
afterwards thrown into a larger orbit and rendered invisible in
1779 by the action of the same planet. M. Leverrier, however,
has shown that the two bodies cannot be identical.

Before another year had expired, a fourth comet belonging to
our system was discovered by M. De Vico of Rome. He first

1 Sir John Herschel has ventured to say, " that the orbit of Biela's comet so nearly
intersects that of the Earth, that an actual collision is not impossible, and indeed (sup-
posing neither orbit variable) must, in all likelihood, happen in the lapse of some
millions of years," — Outlines of Astronomy, § 585.

2 This comet ought to have appeared thirteen times since 1770, and, as it has not been
since seen, it must be lost. Burckhardt supposed that it might have become a satellite
to Jupiter, from its aphelion being near that planet !

328 LIFE OF SIE ISAAC NEWTON. CHAP. XIII.

saw it on the 29tli August 1844, and M. Faye found that it
revolved in an elliptic orbit with a period of about 2000 days,
or 5i years. It was supposed by some astronomers that this
comet was the same as that of 1585, observed by Tycho ; but
M. Leverrier has shown that they are not identical, and that
the comet of De Vico is not the same as that of Lexell. He
discovered, however, such a striking similarity between it and
the comet observed by De la Hire in 1678, that he considers
them clearly identical. It is strange, however, that this comet
should only have been seen once previous to 1844, although it
has frequently come very near the Earth.

Another comet of the Solar system was discovered l^y M.
Brorsen on the 26th February 1846. Its period is 2042 days,
or about 5^ years. It is very faint, and is almost identical in
its elements with the comet of 1532.

A seventh comet, discovered by M. Peters on the 26th June
1846, has been placed by the calculations of M. Arrest among
those having elliptic elements and a short period, and therefore
belonging to our system. Its period is 5804 days, or about
16 years.

Such are some of the important celestial phenomena within
the limits of our own Solar system, to which the Newtonian
theory is applicable, and to which it has been to some extent
successfully applied. The sidereal phenomena which have been
discovered beyond our system, in which movements of long
periods, round visible and invisible centres, have been traced and
measured, possess a higher interest, and to some of them also
the Newtonian law of gravitation has been actually extended.

The most important of this class of phenomena are those of
binary and multiple systems of stars. Among the many stars
of this kind which have been discovered by Sir William Herschel
and succeeding observers, there must be a large number in
which the two, three, or four stars constituting a group have
no other connexion than that of being placed nearly in the
same line. There are others, however, in which, as Sir W.

1830. LIFE OF SIR ISAAC NEWTON. 329

Herschel long ago announced, one of two stars revolves
round the other in regular orbits, and with periods which have
been determined — that of Castor, being 334 years, y Virginis
708 years, and y Leonis 1200 years. Although the list of
double stars has been greatly extended, yet those whose orbits
and periods have been determined with any accuracy, amount
only to twenty-one. Nine of these have been computed by Mr.
Madler of Dorpat, five by Sir John Herschel, four by Mr. Hind,
and one by M. Savary.^ The first calculation of the orbit of a
double star was made in 1830 by M. Savary (in the case of ^
of the Great Bear), who showed that the changes of place in
one of the stars could be explained by an elliptic orbit, and a
period of 58 J years. The periods of the other twenty double
stars vary from 3 1^ to 737 years, eleven having their periods
below 100 years, three below two hundred, two below 300,
and three between 600 and 700 years. These orbits are cal-
culated on the supposition that the force exerted by the stars
varies inversely as the square of the distance, and the accuracy
with which the observations are represented allows us to con-
clude that the Newtonian law of gravity extends to the distant
region of the double stars.^

Another sidereal phenomenon, in which we have the appear-
ance of motion round a centre, is displayed in the spiral nebuli3e
discovered by Lord Rosse ; that the stars which compose these
spirals have been placed there in virtue of some movement
related to the central mass, cannot be doubted, although it is
vain for man to attempt the solution of such a problem. To
suppose these spirals to be nothing more than vaporous matter,
like the tail of a comet, whirled round into spiral branches,
because we cannot find any explanation compatible with the
almost universally admitted fact, that every nebula is composed

1 A table of the elements of their orbits is given by Sir John Herschel in his Outlines
of A$tronomy, § 843.

2 M. Madler has adduced an instance (p Ophiuchi), where he regards the deTiations
from an elliptic orbit too considerable to be accounted for by an error of observation ; but
we cannot view a single fact of this kind as affecting the generality of the law of gravity.

330 LIFE OF SIR ISAAC NEWTON. CHAP. XIII.

of stars, is to renounce all faith in the great truths of astronomy,
and seek for some resting-place to the mind, when reason stands
aghast amid the infinite and the incomprehensible.

Beside the motions of one of the bodies which compose a
binary system, a proper motion of a very peculiar kind has
been observed in the stars. In one region of the heavens the
distance between the stars is increasing, and in the opposite
region diminishing, while in intermediate localities little or no
change of place is observed. It is obvious that such changes
indicate a motion of our earth, and consequently of the whole
Solar system, to a point in the heavens where the increasing
distance of the stars is a maximum. Before the proper motion
of the fixed stars had been measured, various speculators, among
whom Hooke was the earliest, hazarded the supposition that
the whole Solar system wa« in continual motion. Tobias
Mayer, in 1771, attempted in vain to deduce such a move-
ment of the system from the proper motions of eighty stars :
but a few years afterwards, in 1783, when better observations
were accessible. Sir W. Herschel and M. Provost came to the
conclusion that the Solar system was advancing to a point in
the heavens whose right ascension was 257°,^ and north de-
clination 25°. Although both Biot and Bessel came to the
same conclusion as Tobias Mayer, that no such motion existed,
yet the existence of a proper motion has been more recently
placed beyond a doubt by the observations made at the obser-
vatories of Dorpat, Abo, and Pulkova : And it has been shown
by the united studies of Argelander, Otto Struve, and Peters,
that the point to which the Solar system is advancing at the
epoch of 1840, is situated in, —

Right ascension, 259° 35', with a probable error of 2° 57'
North declination, 'ii° 33', with a probable error of 3° 24'

Not content with determining the direction of the solar
motion. Otto Struve has computed the angular value of this
motion, as seen at a right angle to the Sun's path, and at the

1 M. Prgvost, who used Mayer's proper motions, made the right ascension only 230*.

1738-1850. LIFE OF SIE ISAAC NEWTON. 331

mean distance of the stars of the first magnitude. His results
are as follows : —

From the right ascension of the stars, 0"' 32122, with a probable error of 0"- 03684
From their declination, . . '25719, with a probable error of • 03662

Or, taking the mean of these results, 0"- 33920 0"- 03623

But as the parallax of stars of the first magnitude is 0"-209,
we can change the angular motion of the Sun into a linear
motion in space ; and hence taking the radius of the Earth's
orbit as unity, M. Struve finds that the annual motion of the
Sun in space is ^t§^ = 1-G23 radii of the Earth's orbit, with
a probable error of 0-229.

In his interesting work on Stellar Astronomy,^ he has ex-
pressed these results in the following manner : — " The motimi
of the solar system in space is directed to a point of the celestial
vault situated on the right liiie which joins the two stars tt and
fjb Herculis at a quarter of the apparent distance of these stars,
reckoning from tt Hercidis. The velocity of this motion is
such, that the Sun, with all the bodies which depend upon it,
advances annually in the above direction 1-623 times the
radius of the EartJis orbit, or 33,550,000 geographical miles.
The possible error of this last number amounts to 1,733,000
geographical miles, or to a seventh part of the whole. We may
then wager 400,000 to 1 that the Sun has a proper progres-
sive motion, and 1 ^o 1 that it is comprised between the limits
of thirty-eight and twenty-nine millions of geographical miles.

If we take 95 millions of English miles as the mean radius
of the Earth's orbit, we have 95 x 1-623 = 154-185 millions
of miles, and, consequently,

The velocity of the Solar system is 154,185,000 miles in the year.
„ „ 422,424 miles in a day.

„ „ 17,601 miles in an hour.

„ „ 293 miles in a minute.

„ „ 4-9 miles in a second.

As none of the celestial motions are rectilineal, the advance

1 Etudes d' Astronomie Stellaire, of which we have given a copious abstract in the
North British Review, vol, viii. pp. 623-634.

332 LIFE OF SIR ISAAC NEWTON. CHAP. XIII.

of the system in space must be round some distant centre,
which M. Madler, without much reason, supposes to be Alcyone,
the brightest star in the Pleiades. In the course of time,
however, the point to which the system is advancing must
change its place, and from the nature and magnitude of that
change, its curvilineal motion, and perhaps the form of its
orbit, may be established. But even if so grand a result were
obtained, we may never be able to ascertain whether our Sun and
planets revolve like a multiple star round a single centre, or,
as in our planetary system, they form only one of a number of
systems revolving round the same centre. On such a subject
speculation is vain. We must rest satisfied with the simple
truth, that since the earliest observation of the stars, our system
has described so small a portion of its curvilineal orbit, that it
cannot be distinguished from a straight line. If the buried
relics of primeval life have taught us how brief has been our
tenure of this terrestrial paradise, compared with its occupanc}'
by the brutes that perish, the gi-eat sidereal truth which we
have been expounding, impresses upon us the no less humbling
lesson, that from the birth of man to the extinction of his race,
the system to which he belongs will have described but an
infinitesimal arc of that immeasurable circle in which it is
destined to revolve.

Such are the great sidereal movements to some of which the
law of gravitation has been already applied, and nobody has
ventured to doubt that all of them will, in due time, come
under its rule. Every new satellite, every new asteroid, every
new comet, every new planet, every new star circulating round
its fellow, proclaims the universality of Newton's philosophy,
and adds fresh lustre to his name. It is otherwise, however,
in the general history of science. The reputation achieved by
a great invention is often transferred to another which super-
sedes it, and a discovery which is the glory of one age is
eclipsed by the extension of it in another. The fame of having
invented the steam-engine has disappeared beside the reputation

LIFE OF SIR ISAAC NEWTON. 333

of the philosophers who have improved it ; and the laurels
which the discoverer of Ceres has worn for half a century, have
been almost withered by the discovery of fifty-six similar
bodies. It is the peculiar glory of Newton, however, that
every discovery in the heavens attests the universality of his
laws, and adds a greener leaf to the laurel chaplet which he
wears.

334 LIFE OF SIE ISAAC NEWTON. CHAP. XIV.

CHAPTER XIV.

History of the Infinitesimal Calculus — Archimedes— Pappus — Napier — Edward Wright
— Kepler's Treatise on Stereometry — Cavalieri's Geometria Indivisibilium — Roberval
— Toiicelli — Fermat — Wallis's Arithiiietica Infinitorum — Eludde — Gregory — Slusius —
Newton'a discovery of Fluxions in lt;55— General Account of the Method, and of its
Applicjitious — His Analysis per Kquationes, etc. — His Discoveries communicated to
English and Foreign Mathematicians— The Method of Fluxions and Quadratures-
Account of bis other Mathematical Wrifings — He solves the Problems proposed by
Bemouilli and Leibnitz — Leibnitz visits London, and corresponds with the Engli>»h
Mathematicians, and with Newton through Oldenburg — He discovers the Difi'erential
Calculus, and communicates it to Newton — Notice of Oldenburg — Celebrated Scholium
respecting Fluxions in the Principia— Account of the Changes upon it — Leibnitz's
Manuscripts in Hanover.

In the history of Newton's optical and astronomical dis-
coveries, which we have given in the preceding chapters, we
have seen him involved in disputes with his own countrymen as
well as with foreigners, in reference to the value and the priority
of his labours. Such extreme sensitiveness as that with which
he felt the criticisms and discussed the claims of his oiDponents,
has been seldom exhibited in the annals of science ; and so
great was his dread of controversy, and so feeble his love of
wealth and of fame, that, but for the importunities of his
friends, his most important researches would have been with-
held from the world. If he had been warned of the dangers of
a scientific career by the troubled lives of Galileo and of Kepler,
he must have learned from their history that great truths have
never been received with implicit submission, and that in every
age and every state of society the newest and the highest must
undergo more than one ordeal — the ordeal of the ignorant,

LIFE OF SIK ISAAC NEWTON,

whose capacity they transcend — the ordeal of philosophy, .^
which they are to be tested and confirmed — and the ordeal of
personal jealousy and rival schools, by which they are to be
misrepresented and condemned. The discoveries of Newton
were tried by all these tests : they emerged purer and greater
from the opposition of the Dutch savans : they were placed on
a firmer basis by the skilful analysis of Hooke and of Huygens ;
and they were more warmly received and more widely extended
after they had triumphed over the rival speculations of the
followers of Aristotle and Descartes.

/"^n the history of Newton's mathematical discoveries, which
the same dread of controversy had induced him to withhold
from the world, we shall find him involved in more exciting
discussions, — in what may even be called quarrels, in which
both the temper and the character of the disputants were
severely tried. In the controversy respecting the discovery of
fluxions, or of the differential calculus, Newton took up arms in
his own cause, and though he never placed himself in the front
rank of danger, he yet combated with all the ardour ef his
comrades. Hitherto it had been his lot to contend with indivi-
duals unknown to science, or with the philosophers of his own
country who were occupied with the same studies ; but interests
of a larger kind, and feelings of a higher class, sprung up
around him. National sjnnpathies mingled themselves with
the abstractions of number and of quantity. The greatest
mathematicians of the age took the field, and statesmen and
princes contributed an auxiliary force to the settlement of ques-
tions upon which, after the lapse of nearly 200 years, a verdict
has not yet been pronounced.

Painful as the sight must always be when superior minds are
brought into collision, society gains from the contest more than
the parties lose. We are too apt to regard great men, of the
order of Newton and Leibnitz, as exempt from the common
infirmities of our nature, and to worship them as demigods more
than to admire them as sages. In the history upon which we

336 LIFE OF SIR ISAAC NEWTON. CHAP, XIV.

are about to enter we shall see distinguished philosophers upon
the stage, superior, doubtless, to their fellows, but partaking in
all the frailties of temper, and exposed to all the suspicions of
iryuatice, which embitter the controversies of ordinary life.
'{Although the honour of having invented the calculus of
fluxions, or the differential calculus, has been conferred upon
Newton and Leibnitz, yet, as in every other great invention,
they were but the individuals who combined the scattered lights
of their predecessors, and gave a method, a notation, and a
name, to the doctrine of quantities infinitely small.4

By an ingenious attempt to determine the area of curves the
ancients made the first step in this interesting inquiry. Their
principles were sound, but their want of an organized method
of operation prevented them from even forming a calculus. The
method of exhaustions which they employed for this purpose
consisted in making the curve a limiting area, to which the
inscribed and circumscribed polygonal figures continually ap-
proached by increasing the number of their sides. The area
thus obtained was obviously the area of the curve. In the case
of the parabola, Archimedes showed that its area is two-thirds
of its circumscribing rectangle, or of the product of the ordinate
and the abscissa ; and he proved that the superficies of the
sphere was equal to the convex superficies of the circumscribing
cylinder, or to four times one of its great circles, and that the
solidity of the sphere was two-thirds of that of the cylinder.
His writings abound in trains of thought, which are strictly
conducted on the principles of the modern calculus, but in place
of this calculus we have only an imperfect arithmetic.

Pappus of Alexandria, who flourished about the close of the
fourth century, followed Archimedes in the same inquiries, and
his celebrated theorems on the centre of gravity ^ is the only

1 Guldinus gave this theorem in 1635, and seeing that he was acquainted with Pappus,
Montucla and others were disposed to regard him as a plagiarist. Had they studied
Pappus in Condamine's Latin, in place of that of Halley, they never would have known
the theorem but from Ouldinus.

1615. LIFE OF SIR ISAAC NEWTON. '^ 3.37

fruit which sprung from the seed sown by the Greek geometer
till we reach the commencement of the seventeenth century.
We search in vain the writings of Cardan, Tartaglia, Yieta, and
Stevinus, for any proof of their power to employ the infinitesimal
principle.

Our countryman, John Napier of Merchiston, and his con-
temporary, Edward Wright, were not only the first to revive
the use of the infinitesimal principle, but the first who applied
it in an arithmetical form. They distinctly apprehended the idea
of a sufficient approach to the calculation of gradual change by
the substitution of small and discontinuous changes. In this
way Napier arrived at the representation of the results of arith-
metical and geometrical progression taking place continuously
in two diff'erent magnitudes, and associated the logarithm of any
quantity with its primitive. In this manner, too, Wright ex-
hibited what we now call an integration by quadrature, in his
celebrated construction of the meridional parts. Both of these
geometers fully conceived the idea, as it was embodied in their
several problems ; and though we cannot ascribe to either a
distinct conception of it, we cannot withhold from them the
honour of being the first of modern writers who assisted their
successors in its conception.

In his treatise on Stereometry, published in 1615, Kepler
made some advances in the doctrine of infinitesimals. In con-
sequence of a dispute with a wine-merchant he studied the
mensuration of round solids, or those which are formed by the
revolution of the conic sections round any line whatever within
or without the section. He considered the circle as consisting
of an infinite number of triangles, having their vertices in the
(centre, and their infinitely small bases in the circumference.
In like manner, he considered the cone as composed of an infi-
nite number of pyramids, and the cylinder of an infinite number
of prisms, and by thus rendering familiar the idea of quantities
infinitely great and infinitely small, he gave an impulse to this
branch of mathematics.

VOL. I. Y

338 -^ LIFE OF SIR ISAAC NEWTON. CHAP. XIV.

The failure of Kepler in solving some of the more difficult
problems which he himself proposed, drew the attention of
geometers to the subject of infinitely small quantities, and seems
particularly to have attracted the attention of Cavalieri. This
celebrated mathematician, who Avas the friend as well as the
disciple of Galileo, was born at Milan in 1598, and was pro-
fessor of geometry at Bologna. Although he had invented his
method of indivisibles so early as 1629, his work entitled
Geometria Indivisihilium did not appear till 1635, nor his
Exercitationes, containing his most remarkable results, till
1647. He considers 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 assumes as an axiom,
that the infinite sums of such lines and surfaces have the same
ratio, existing in equal numbers in different surfaces or solids,
as the surfaces or solids to be determined. As it is not tme
that an infinite number of infinitely small points can make a
line, nor an infinite number of infinitely small lines a surface,
Pascal proposed to return to the idea of Kepler 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. If Cavalieri had been more advanced in
algebra he might, perhaps, have gone farther ; but he was un-
doubtedly the first who applied the algebraical process to the
quadrature of parabolas of an integer order ; and his chief
instrument, as it was afterwards that of Wallis, was the
theorem, that 1" + 2'' + . . . x'\ divided by a?» + x" . . . x"^
is 1 : (?i -j- 1) when x is infinite.

Previous to the publication of Cavalieri's work, Roberval had
adopted the same principle, and proved that the area of the
cycloid was equal to three times that of its generating circle.
He determined also the centre of gravity of its area, and the
solids formed by its revolution about its axis or its base. We
owe to the same mathematician a general method of drawing

1644. LIFE OF SIR ISAAC NEWTON. 339

tangents to certain curves, mechanical and geometrical, which
was in some respects similar to that of fluxions. Regarding
every curve as described by a point, RobervaP considered the
point as influenced by two motions, by the composition of
which it moves in the direction of a tangent ; and had he pos-
sessed the method of fluxions he could have determined in every
case the relative velocities of these motions, which depend on
the nature of the curve, and, consequently, the direction of the
tangent, w^hich he assumed to be the diagonal of a parallelogram
whose sides were as the velocities.

Without knowing what had been done by Eoberval, Toricelli,
a pupil of Galileo, published, in 1644, a solution of the
cycloidal problems ; but though the demonstrations were so
different as to prove that he had not seen those of Roberval,
and though his character and talents might have protected him
from so ungenerous a charge, the French mathematician did not
scmple to accuse him of plagiarism. Toricelli made much use
of the infinitesimal methods, and was one of those who most
clearly foresaw the approach of a new calculus.

The methods of Peter Feimat, counsellor of the Parliament
of Toulouse, for obtaining maxima and minima, and for draw-
ing tangents to curves, had such a striking resemblance to those
of the diff'erential calculus, that Laplace, and, in a more quali-
fied manner, Lagrange, have pronounced Fermat^ to be the in-
ventor. We need not say that this is an exaggeration : Fermat
and others came so close to the calculus as actually to invent
cases of it ; but none before Newton and Leibnitz ever ima-
gined, far less organized, a general method which should com-
bine the scattered cases of their predecessors into a uniform and
extensible system.

1 Robervars concealment of his discovery, and his forgery of a work of Aristarchus,
greatly lower his credit, when he bears testimony in his own favour.

2 These methods were published in the sixth or supplemental volume of the second
edition of Herigon's Cursus, Paris, 1644, 8vo ; and an example was given by Schooten
in the second edition of his Commentary on the second Book of Descartes's Geometry,
in 1669.

340 LIFE OF SIR ISAAC NEWTOX. CHAP. XIV.

As the time for the real invention approached, the anticipa-
tory cases were multiplied. The Arithmetica Injinitoimm of
Wallis (1655), not to speak of any other of his writings,
applied and extended the ideas of Cavalieri, and produced an
ample field of results. It appears, in modern language, like a
treatise on fx^dx for all values of n except — 1, and on
/ {g? — x'^ydx for all integer values of n. It gives the first
description of the method of rectifying a curve. In the work
before cited, Schooten publishes a letter from Henry Van
Heuraet, written in 1659, giving the algebraic rectification of
every parabola of the form y'*=a.r"+\ except in the case of w=l,
which case is shown to depend on the quadrature of the hyper-
bola. This had been completed a year or two before, about the
same time at which William Neile communicated to Wallis his
rectification of the semicubical parabola. Fermat also did the
same as Neile, under the forms of the old geometry. Descartes,
in 1648, showed that he had made progress in a method of
finding areas, centres of gravity, and tangents ; and he after-
wards determined the character of a curve by what we should
now call a transformation of a diff"erential equation.

In his Commentary on Descartes, Schooten published two
letters of John Hudde, the second of which is dated January
27, 1658. It shows how to make a rational function integral
or fractional, a maximum or minimum, and even treats the case
in which the function and its variable are connected by an un-
solved rational equation. The rules are, for the first time,
extricated from algebraical process, and presented in calcular
form. These very remarkable results were well known to both
Newton and Leibnitz, and are freely cited by both.

James Gregory, in 1668, gave two of what we should now
call integrations of trigonometrical functions. He demonstrated
the connexion which had been observed between Wright's meri-
dional parts and the logarithms of cotangents.

The methods of drawing tangents, invented by Barrow and
by Slusius, were published in 1670 and in 1673. Such

1663-9. LIFE OF SIR ISAAC NEWTON. 341

methods were then common ; and Barrow, m announcing his,
says he scarcely perceives the use of publishing it, because
several similar methods were well known. But both these
methods obtained an undue importance in the great controversy,
and this probably arose from their being both published in
England.

Such are the methods which Newton and Leibnitz received
from their predecessors, and, were we obliged to describe them
in modern terms, we should call them isolated instances of dif-
ferentiation and integration, of calcular rules of differentiation,
of quadrature, rectification, and determination of centres of
gravity, of determination of maxima and minima, both of ex-
plicit and implicit functions, &c. But we can hardly permit
ourselves to invite the reader to look back under general terms,
because he can hardly use the general terms without having the
idea of a general system. Some will almost be inclined to ask
what was left for Newton and Leibnitz to do 1 The best
answer is, that it was left for them to put the querist in a
position to ask the question. Had it not been for Newton and
Leibnitz, that is, supposing their place had never been supplied,
the close approach of the investigators to each other, and to a
common method, would never have been visible.

We have already seen^ that the attention of Newton had
been directed to these subjects so early as 1663 and 1664.
Upon reading Dr. Wallis's work in the winter of 1664-5, he
obtained an expression in series for the area of circular sectors ;
and from the consideration that the arch has the same propor-
tion to its sector that an arch of 90° has to the whole quadrant,
he found an expression for the length of the arch. At the
same time he determined the area of the rectangular hyperbola
intercepted between the curve, its asymptote, and two ordinates
parallel to the other asymptote ; and it was by this series that
he computed the area of the hyperbola to fifty-two figures,
when the plague had, in the summer of 1669, driven him from

1 See pp. 20-22.

342 LIFE OF SIR ISAAC NRWTON. CHAP. XIV.

Cambridge to Boothby. At the same time he was led, by the
happy thought of substituting indefinite indices of powers for
definite ones, to give a more general form to the 59th proposi-
tion of Dr. Wallis's Arithmetic of Infinites. In the beginning
of 1665, he likewise discovered a method of tangents similar to
those of Hudde, Gregory, and Slusius, and a method of finding
the curvature of curve lines at any given point ; and, con-
tinuing to pursue the method of interpolation, he found the
quadrature of all curves whose ordinates are the powers of
binomials affected with indices whole, fractional, or surd, affir-
mative or negative ; together with a rule for reducing any
power of a binomial into an approximating or converging
series. In the spring of the same year he discovered a method
of doing the same thing by the continual division and extrac-
tion of roots ; and he soon after extended the method to the
extraction of the roots of adfected equations in species.

Having met with an example of the method of Fermat, in
Schooten's Commentary on the Second Book of Descartes,
Newton succeeded in applying it to adfected equations, and
determining the proportion of the increments of indeterminate
quantities. These increments he called moments, and to the
velocities with which the quantities increase he gave the names
of motions, velocities of increase, and fluxions. He considered
quantities not as composed of indivisibles, but as generated by
motion ; and as the ancients considered rectangles as generated
by drawing one side into the other, that is, by moving one side
upon the other to describe the area of the rectangle, so Newton
regarded the areas of curves as generated by drawing the ordi-
nate into the abscissa, and all indeterminate (juantities as gene-
rated by continual increase. Hence, from the flowing of time
and the moments thereof, he gave the name of flotoing quan-
tities to all quantities which increase in time, that of fluxions
to the velocities of their increase, and that of fnonients to their
parts generated in moments of time. He considered time as
flowing uniformly, and represented it by any other quantity.

16(56. LIFE OF SIR ISAAC NEWTON. 343

which is regarded as flowing uniformly, and its fluxion by a
unit. These moments of time, or of its exponent, he considers
as equal to one another, and represents by the letter o, or l)y
any other mark multiplied by unity. The other flowing quan-
tities are represented by any letters or marks, but most com-
monly by the letters at the end of the alphabet ; while their
fluxions are represented by any other letters or marks, or by
the same letters in a different form or size, and their moments
by their fluxions multiplied by a moment of time.

In a manuscript, dated 13th November 1665, the direct
method of fluxions is described with examples, and the follow-
ing problem is resolved : — " An equation being given expressing
the relation of two or more lines, x, v/, z, &c., described in the
same time by two or more moving bodies. A, B, C, &c., to
find the relation of their velocities, yj>, q, r, &c., with which
these lines are described." In the same manuscript we find
an application of this method to the drawing of tangents, by
determining the motion of any point which describes the curve,
and also to the determination of the radius of curvature of any
curve line, by making the perpendicular to the curve move
upon it at right angles, and finding that point of the perpen-
dicular which is in least motion, for that point will be the
centre of curvature of the curve at that point upon which the
perpendicular stands. On another leaf of the same book,
dated May 20, 1665, the same method is given, but in differ-
ent words, and fluxions are represented with dots superfixed.
In another leaf, dated May 16, 1666, there is given a general
method, consisting of seven propositions, of solving problems
by motion, the seventh proposition being the same, though
diff"erently expressed, from that in the paper of November 13,
1665.

In a small tract, written in October 1666, we find the same
method in the same number of propositions ; but the seventh
is improved by showing how to proceed in equations involving
fractions and surds, and such quantities as were afterwards

344 LIFE OF SIR ISAAC NEWTON. CHAP. XIV.

called transcendental. To this tract there is added an eighth
proposition, containing the inverse method of fluxions, in so far
as he had then attained it, namely, by the method of quadra-
tures, and by most of the theorems in the Scholium to the
tenth proposition of his Book of Quadratures, which with many
more are contained in this tract. Newton then proceeds to
show the application of the propositions to the solution of the
twelve following problems, many of which were at that time
entirely new : —

"1. To draw tangents to curve lines.

" 2. To find the quantity of the crookedness of lines.

"3. To find the points distinguishing between the con-
cave and convex portions of curved lines.

"4. To find the point at which lines are most or least
curved.

"5. To find the nature of the curve line whose area is ex-
pressed by any given equation.

" 6. The nature of any curve line being given, to find other
lines whose areas may be compared to the area of that given
line.

" 7. The nature of any curve line being given, to find its
area when it may be done ; or two curved lines being given, to
find the relation of their areas when it may be.

" 8. To find such curved lines whose lengths may be found,
and also to find their lengths.

"9. Any curve line being given, to find other lines whose
lengths may be compared to its length, or to its area, and to
compare them.

"10. To find curve lines whose areas shall be equal, or have
any given relations to the length of any given curve line drawn
into a given right line.

"11. To find the length of any curve line when it may be.

"12. To find the nature of a ciu-ve line whose length is ex-
pressed by any given equation when it may be done."

Such were the improvements in the higher geometr}^ which

1666. LIFE OF SIR ISAAC NEWTON. 345

Newton had made before the end of 1666. His analysis, con-
sisting of the method of series and fluxions combined, was so
universal as to apply to ahnost all kinds of problems. He had
not only invented the method of fluxions in 1665, in which
the motions or velocities of flowing quantities increase or de-
crease, but he had considered the increase or decrease of these
motions or velocities themselves, to which he afterwards gave
the name of second fluxions, — using sometimes letters with one
or two dots, to represent first and second fluxions.

It does not appear that Newton imparted any of these
methods to his mathematical friends ; but in order to com-
municate some of his results, he composed his treatise entitled
Analysis per Equationes Numero Terminorum Infinitas, in
which the method of fluxions and its applications are supposed
by some to be explained ; while others are of opinion, that it
treats only of moments or infinitely small increments, and ex-
hibits the algebraical processes involved in their use. In June
1669, he communicated his work to Dr. Barrow, who, in let-
ters to Collins of the 20th June, the 31st July, and the 20th
August, mentions it, as we have already seen,^ as the produc-
tion of Newton, a young man of great genius. Having taken
a copy of this treatise, Collins returned the original to Dr.
Barrow, from whom it again passed into the hands of Newton.
At the death of Collins, Mr. William Jones found the copy
among his papers ; and having compared it with the original
given him by Newton, it was published, along with some other
analytical tracts of the same author, in 1711, nearly fifty years
after it was composed.

Although the discoveries contained in this treatise were not
at first given to the world, yet they were generally known to
mathematicians by the correspondence of Collins, who com-
municated them to James Gregory in Scotland ; to M. Bertet,
and an English gentleman, Francis Vernon, secretary to the
English ambassador in Paris ; to Slusius in Holland ; to Bo-

1 See p. 32, and note 3. p. 24

34 G LIFE OF SIR ISAAC NEWTON. CHAP. XIV.

relli in Italy ; and to Thomas Strode, Oldenburg, Daiy, and
others in England, in letters dated between 16 GO and 1672.

In the years 1669 and 1670, Newton had prepared for the
press a new and enlarged edition of Kinckhuysen's Introduction
to Algebra.^ He at first proposed to add to it, as an introduc-
tion, a treatise entitled, a Method of Fluxions and Quadratures ;
but the fear of being involved in disputes as annoying as those
into which his optical discoveries had led him, and which were
not yet concluded, prevented him from giving this treatise to
the world. At a later period of our author's life. Dr. Pem-
berton had prevailed upon him to publish it, and for this
purpose had examined all the calculations and prepared the
diagrams. The latter part of the treatise, however, in which
he intended to show the manner of resolving problems which
cannot be reduced to quadratures, was never finished ; and
when Newton was aljout to supply this defect, his death put a
stop to the plan. 2 It was therefore not till the year 1736
that a translation of the work appeared, with a commentary
by Mr. John Colson, Professor of Mathematics in Cambridge.^

Between the years 1671 and 1676, Newton did not pursue
his mathematical studies. His optical researches, and the
disputes in which they involved him, occupied all his time ;
and there is reason to believe, that as soon as these disputes
were over, he directed the whole energy of his mind to those
researches which constitute the Principia.

Hitherto the method of fluxions was known only to the

1 This task seems to have been pressed upon him by some friends in London. In
sending to Collins the notes upon the book, in July 1670, he v,i!ihe8 his name to be suj)-
pressed, and suggests that in the title-jiau-e, after the words Nunc e Belpico Laline versa,
the words et ah alio authore locupldata should be added. In a letter to Collins, date<i
September 5, 1676, he thus speaks of the work : — " I have nothing in the press, only
Kinckhuysen's Algebra, I would have got printed here, to satisfy the expectation of
some friends in London, but our pre.^s cannot do it. This, I suppose, is the book Dr.
Lloyd means. It is now in the hands of a bookseller here to get it printed ; but if it do
come out, I shall add nothing to it. — Macclesfield Correspondence, vol. ii. p. .'^98.

2 Pemberton's Accovnt of Sir Isaac NeictoDS Discoveries, Pref. p. 6.

3 It is entitled Method of Fluxions and Infinite Series. Lond. 1736, 1737. 4to.

16S7 S)3. LIFE OF SIR ISAAC NEWTON. 347

friends of Newton and their correspondents ; but in the first
edition of the Frincipia, which appeared in 1687, he published
for the first time one of the most important rules of the fluxion-
ary calculus, which forms the Second Lemma of the Second
Book, and points out the method of finding the moment of the
products of any power whatsoever.

In writing the Frincipia, Newton made great use of both
the direct and the inverse method of fluxions ; but though all
the difficult propositions in that work were invented by the
aid of the calculus, yet the calculations were not put down,
and the propositions were demonstrated by the method of the
ancients, shortened by the substitution of the doctrine of limits
for that of exhaustions. No information, however, is given in
the Frincipia respecting the algorithm or notation of the cal-
culus ; and it was not till 1693 that it was communicated to
the mathematical world, in the Second Volume of Dr. Wallis's
Works, which was published in that year. The friends of
Newton in Holland had informed Dr. Wallis that Newton's
" Method of Fluxions " had passed there with great applause
by the name of Leibnitz's Calculus Differentialis. The Doctor,
who was at that time printing the Preface to his First Volume,
inserted in it a brief notice of Newton's claim to the discovery
of fluxions, and published in his second volume some extracts
from the Quadratura Curmrum, with which Newton had
furnished him.^

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 Jigurarum curviline-
arum, 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

1 Wallisii Opera, torn. i. Praef. pp. 2, 3 ; and torn. iii. cap. xciv. xcv. See also Letter of
Wallis to Newton, April 10, 1695, in Edleston's Correspondence, &c., p. 309, and part of
it in Raphson's Hist, of Fluxions, pp. 120, 121.

- Newtoni Opera, torn. i. pp. 333-386. » Ibid. torn. i. pp. 531-5C0.

348 LIFE OF SIR ISAAC NEWTON. CHAP. XIV.

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 publishiug 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 ciurvilinear
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 delivered at Cambridge, under the
title of Arithmetica Universalis^ sive de Compositione et Reso-
lutione Arithmetica Liber?- This work, which is still in the
University Library, was soon afterwards translated into English
by Mr. Raphson ; 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 admir-
able work, the celebrated S'Gravesande published a tract, en-
titled, Specimen Gommentarii in Arithmeticam Universalem ;
and Maclaurin's Algebra seems to have been drawn up in con-
sequence of this appeal.

Among the mathematical works of Newton we must not
omit to enumerate a small tract entitled, Methodus Difeven-
tiaiis, which was published with his consent in 1711. It

I Newtoni Opera, torn. i. pp. 1-251.

1696. LIFE OF SIR ISAAC NEWTON. 349

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 was published for
the first time in 1799, in Dr. Horsley's edition of his works.
It is entitled, Ai-tis Analyticce Specimina, vel Geometria Ana-
lytica} 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 un-
known hand, was given by Mr. William Jones to the Honour-
able 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 afiected 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 length
of curves.

In enumerating the mathematical works of our author, we
must not overlook his solutions of the celebrated problems
proposed by John Bernoulli and Leibnitz. In June 1696,
John Bernoulli addressed a 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.

1 Newtoni Opera, torn. i. pp. .^88-519.

3 " Acutissimis qui toto orbe florent Mathematicis."

350 LIFE OF SIR ISAAC NEWTON. CHAP. XIV.

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 togetlier, may make
everywhere the same sum.^

This challenge was first made in the Leipsic Acts, for June
1 696. 2 Six months were allowed by Bernoulli for the solution
of the problem, and in the event of none being sent to him he
promised to publish his own. The six months, however, elapsed
without any solution being produced ; but he received a letter
from Leibnitz, stating that he had " cut the knot of the most
beautiful of these problems," and requesting that the period for
their solution shoidd be extended to Christmas next, that the
French and Italian mathematicians might have no reason to
complain of the shortness of the period. Bernoulli adopted the
suggestion, and publicly announced the prorogation for the in-
formation of those who might not see the Leipsic Acts.

On the 29th January 1696-7, Newton received from France
two copies of the printed paper containing the problems, and on ,
the following day he transmitted a solution of them to Charles
Montague, Chancellor of the Exchequer, and then President of
the Royal Society.^ 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 pro-
perties. Solutions were also obtained from Leibnitz and the
Marquis de I'Hopital ; and although that of Newton was anony-
mous, yet Bernoulli recognised in it his powerful mind ; " tai}-

1 John Bernoulli had already published, in the Leipsic Acts for June, p. i'oQ, a'solu-
tion of the most simple case in which the exponent of the power was unity.

2 Acta Lipsknsia, in June, p. 269.

8 The original manuscript of this letter with the solution of the problem is preserved
at the Royal Society ; and one of the two papers, a folio printed half-sheet, still exists
in their archives. At the bottom, in Newton's hand, are the words, " Chartam banc ex
(Jallia raissam accepi, Jan 29, 1696-T." — Edleston's Correspond€nc*\ &c. &c., p. Ixvjii.
For a copy of the document, see Newtoni Op^ra, torn. iv. pp. 411-418.

1716. LIFE OF SIR ISAAC NEWTON. 351

quam^'' says he, " ex ungue leonem,'' as the lion is known by
his claw.

One of the last mathematical efforts of our author was made,
with his usual success, in solving a problem which Leibnitz
proposed in 1716, in a letter to the Ahh6 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
difficult, and he himself fatigued with business, he reduced it
to a fluxional equation before he went to bed.

In his reply to Leibnitz,^ Conti does not even mention the
solution of Newton ; but as if such a problem had been beneath
the notice of the English geometers, he says : — " Your problem
was very easily resolved, and in a short time. Several geometers,
both in London and Oxford, have given the solution. It is
general, and extends to all sorts of curves, whether geometrical
or mechanical. The problem is proposed somewhat equivocally ;
but I believe that M. De Moivre is not wrong when he says
that we must fix the idea of a series of curves, and suppose, for
example, that they have the same subtangent for the same
abscissa, which would correspond not only with the conic sec-
tions, but with an infinity of other curves, both geometrical and
mechanical."

Such is a brief account of the mathematical writings of Sir
Isaac Newton, not one of which was voluntarily communicated
to the world by himself. The publication of his Universal
Arithmetic is said to have been made by Whiston against his
will ; and, however this may be, it was an unfinished work,
never designed for the public. The publication of his Qwidra-
ture of Curves, and of his Enumeration of Curve Lines, was in
Newton's opinion rendered necessary, in consequence of plagiar-

i Dated London, March 1716.

352 LIFE OF SIR ISAAC NEWTON. CHAP. XIV.

isms 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 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, nor with the communications which he so
freely made to Barrow, Collins, and others. If he withheld his
labours from the world in order to avoid the disputes and con-
tentions 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 whole of
his design ; but no apology can be made for the imprudence of
withholding it any longer from the public, — an imprudence
which is the more inexplicable, as he was repeatedly urged by
Wallis, Haltey, and his other friends, to present it to the world. ^
Had he published this noble discovery previous to 1673, when
his great rival had made but little progress in those studies
which led him to the same method, he would Imve 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, might have directed the attention of

1 Wallis to Newton, April 10, 1695. See Edleston's Correspondence, pp. 301, 302.

1073. ' LIFE OF SIR ISAAC NEWTON. 353

mathematicians to subjects to which they would not have other-
wise ajjplied their powers. The discoveries which he had
previously made were made subsequently by others ; and
Leibnitz, instead of appearing on the theatre of science as the
disciple and the follower of Newton, stood forth with all the
dignity of a second inventor ; 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 nature of this work 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, when Leibnitz came to London in
the suite of the Duke of Hanover, he became acquainted with
the great men who then adorned the capital of England.
Among these was Henry Oldenburg, a countryman of his own,
who was at that time Secretary to the Royal Society, Leibnitz
had not then, as he himself assures us,^ entered upon the study
of the higher geometry, but he eagerly embraced the opportu-
nity Avhich was now offered to him of learning the discoveries of
the English mathematician. With this view he kept up a corre-
spondence with Oldenburg, communicating to him freely certain
arithmetical and analytical methods of his own, and receiving
in return an account of the discoveries in series made by James
Gregory and Newton. In the two letters^ written in London
to Oldenburg, and in the first four which he addressed to him
from Paris,^ he refers only to certain properties of numbers
which he had discovered ; but in those of a subsequent date,
he mentions a theorem of his own for expressing the area of a
circle, or of any given sector of it, by an infinite series of

1 Two years before this, in 1671, Leibnitz presented to the Academy of Sciences a
paper containing the germ of the differential method, so that he must have been able to
appreciate the information he received in England. — See page 11.

2 Dated February 3d and 20th, 1673.

3 March 30, April 26, May 26, and June 8, 16V3.

VOL. I. Z

354 LIFE OF SIR ISAAC NEWTON. CHAP. XIV.

rational numbers ;^ and of deducing, by the same method, the
arc of a cu'cie from its sine.^ In reply to these letters, Olden-
burg acquainted him with the previous discoveries of Newton,
and transmitted to him a communication from Collins, describ-
ing several series which had been sent to him by Gregory on
the 15th February 1671. Leibnitz stated in reply,^ that he
was so much distracted with business, that he had not time to
compare these series with his own ; and he promises to com-
municate his opinion to Oldenburg as soon as he has made the
comparison. In continuing his correspondence with Oldenburg,
Leibnitz requested farther information respecting the analytical
discoveries recently made in England ; and it was in compliance
with this request that Newton, at the pressing solicitation of
Oldenburg and Collins, wrote a long letter, dated 13th June
1676, to be communicated to Leibnitz.

This letter, which was sent to Leibnitz in Paris, along with
extracts from Gregory's letters, on the 26th June, contained
Newton's method of series, and, after describing it, he added,
" that analysis, by the assistance of infinite equations of this
kind, extends to almost all problems except some numerical
ones like those of Diophantus, but does not become altogether
universal without some farther methods of reducing problems
to infinite equations, and infinite equations to finite ones, when
it might be done."

Leibnitz answered this letter on the 27th August, and, in
return for Newton's method of series, he sent to Oldenburg a
theorem for transmuting figures into one another ; and thus
demonstrated the series of Gregory for finding the arch from
its tangent. In consequence of Leibnitz having requested still
farther information, Newton addressed to Oldenburg his cele-
brated letter of the 24th October 1676. In this letter he gave
an account of his discovery of the method of series before the
plague in the summer of 1665. He stated, that on the pub-
lication of Mercator's LogaHthmotechnia, he had communicated

1 July 15, 1673. » October 26, 1673. 3 May 20, 1675.

1677. LIFE OP SIR ISAAC NEWTON. 355

a compendium of tliis method through Dr. Barrow to Mr.
Collins, and, that five years after, he had, at the suggestion
of the latter, written a large tract on the same subject, joining
with it a method from which the determination of maxima and
minima, and the method of tangents of Slusius and some others
flowed. "This method," he continued, "was not limited to
surds, but was founded upon the following proposition, which
he communicated enigmatically in a series of transposed let-
ters. Data equatione quotcunque fluentes quantitates involvente,
fluxiones invenire, et vice versa. This proposition," he added,
" facilitated the quadrature of curves, and afforded him infinite
series, which broke off and became finite when the curve was
capable of being squared by a finite equation." In the con-
clusion of this letter, Newton stated that his method extended
to inverse problems of tangents, and others more difiiculfc, and
that in solving these he used two methods, one more general
than the other, which he expressed enigmatically in transposed
letters, which formed the following sentence : — " Una methodus
consistit in extractione fluentis quantitatis ex equatione simul
involvente fluxionem ejus : altera tantum in assumptione seriei
pro quantitate qualibet incognita, ex qua cetera commode de-
rivari possunt, et in coUatione terminorum homologorum
aequationis resultantis, ad eruendos terminos assumptse seriei."

This letter, though dated 24th October, had not been for-
warded to Leibnitz on the 5th March 1677. At the time
Newton was writing it, Leibnitz spent a week in London, on
his return from Paris to Germany ; but it must have reached
him in the spring of that year, as he sent an answer to it dated
June 21, 1677.

In this remarkable letter he frankly describes his differential
calculus and its algorithm. He says that he agrees with
Newton in the opinion that Slusius's methods of tangents is not
absolute, and that he himself had long ago (a multo tempore)
treated the subject of tangents much more generally by the
differences of ordinates. He gives an example of drawing

356 LIFE OF SIR ISAAC NEWTON. CHAP XIY.

tangents, and shows how to proceed, as Newton expresses it,
" without sticking at surds." He then expresses the oj^inion,
that the method of drawing tangents, which Newton wished to
conceal, does not differ from his ; and he regards this opinion
as confirmed by the statement of Newton, that his method
facilitated the quadrature of curves.

No answer seems to have been returned to this communica-
tion either by Oldenburg or Newton, and, with the exception
of a short letter from Leibnitz to the former, dated 1 2 th July
1677, no farther correspondence between them seems to have
taken place. This no doubt arose from the death of Oldenburg
in the month of September 1677 ;i and the two rival geome-
ters, having through him become acquainted with each other's
labours, were left to pursue them with all the ardour which
the importance of the subject could not fail to inspire.

In the hands of Leibnitz, the differential calculus made rapid
progress. In the Acta Eruditorum, which appeared at Leipsic
in October 1684, he describes its algorithm in the same manner
as he had done in his letter to Oldenburg. He points out its

1 Henry Oldenburg, whose name is so intimately associated with the history of New-
ton's discoveries, was born at Bremen, and was consul from that town to London during
the usurpation of Cromwell. Having lost his office, and been compelled to seek the
means of subsistence, he became tutor to an English nobleman, whom he accompanied
to Oxford in 1656. During his residence in that city he was introduced to the philoso-
phers who established the Royal Society, and, upon the death of William Crown., the
firs!; secretary, he was appointed, in 1663, joint secretary along with Mr. Wilkins. He
kept up an extensive correspondence with more than sevc.ntp i)hilosophers and literary
men in all parts of the world,— a privilege especially given to the Society in their char-
ter. The suspicions of the Government, however, were, somehow or other, excited
against him, and he was committed to the Tower on the 20th June 1667, " for dangerous
designs and practices." Although no evidence was produced to justify so harsh a pro-
ceeding, he was kept a close pri.soner till the 26 th August 1667. when he was discharged.
" This remarkable event," as Mr. Weld remarks, " had so much influence on the Society
as to cause a suspension of the meetings from the 30th May to the 3d October." It is
remarkable that there is no notice of this fact in the coimcil or journal-books of the
Society.

Oldenburg was the author of several papers in the Philosophical Transactions, and of
some works which have not acquired much celebrity. He died at Charlton, near
Greenwich, in August 1678. See Weld's History of the Royal Society, vol. L pp.
200-204.

1686. LIFE OF SIR ISAAC NEWTON. 357

application to the drawing of tangents, and the determination
of maxima and minima ;^ and he adds, that these are only the
beginnings of a much more sublime geometry, applicable to the
most difficult and beautiful problems even of mixed mathema-
tics, which, without his differential calculus, or one similae to
it, could not be treated with equal facility. The suppression of
Newton's name in this reference to a similar calculus, which
was obviously that of Newton, indicated in the letters of 1676,
was the first false step in the fluxionary controversy, and may
be regarded as its commencement.

While Leibnitz was thus making known the principles of his
Calculus, Newton was occupied in preparing his Principia for
the press. In the autumn of 1684, he had sent the principal
propositions of his w^ork to the Royal Society ; but it would
appear from his letter to Halley of the 20th June 1686, that
the second book of the Principia had not then been sent to
him. He must therefore have been acquainted with the paper
of Leibnitz in the Acta Eruditorum, before he sent the manu-
script of the second book to press ; and it was doubtless from
this cause that he was led to compose the second lemma of
that book, in which he, for the first time, explains the funda-
mental principle of the fluxionary calculus. This lemma, which
occupies only three pages, was terminated with the following .
scholium, which has been the subject of such angry discussion.

" The correspondence which took place about ten years ago,
between that very skilful geometer G. G. Leibnitz and myself,
when I had 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
surds and to rational quantities, and concealed the same in
transposed letters, involving this sentence (Data jEquatione
quotcunque Fluentes quantitates involvente, Fluxiones invenirey

1 This article was entitled, " Nova methodus pro maxlmis et minimis, itemque
tangentibus quae nee fractas nee irrationales moratar, et singulare pro iliis calculi genus,
per G. G. L."— Jcto Erudit. 1684, pp. 472, 473.

358 LIFE OF SIR ISAAC NEWTON. CHAP. XIV.

et vice versa), this illustrious man replied that he also had
fallen on a method of the same kind, and he communicated his
method, which scarcely differed from my own,^ except in the
forms of words and notation (and in the idea of the generation
of quantities^). The fundamental principle of both is contained
in this lemma."

This celebrated scholium has been viewed in different lights
by Leibnitz and his followers. Leibnitz asserts,^ that Newton
" has accorded to him in this scholium the invention of the
differential calculus independently of his own ;" and M. Biot
considers the scholium as " eternalizing the rights of Leibnitz
by recognising them in the Principia." But the scholium has
no such meaning, and it was not the intention of the author
that it should be thus understood. It is a statement of the
simple fact, that Leibnitz communicated to him a method which
was nearly the same as his own, — a sentiment which he might
have expressed whether he believed that Leibnitz was an inde-
pendent inventor of his calculus, or had derived it from his
communication and correspondence with his friend.*

The manuscripts of Newton furnish us with some curious
information on this subject, and place it beyond a doubt that
he regarded the silence of Leibnitz, in his communication of
1684, as an aggressive movement, which he was bound to
repel. " After seven years," says Newton,^ " viz., in October

'^" A mea vix abludentem" — the same expression which Leibnitz used in his letter
to Oldenburg of June 21, 1677, " ab his non abludcre." The similarity of the Method
of Fluxions and the Differential Calculus, may be considered as admitted both by New-
ton and Leibnitz.

2 These words were inserted in the 2d edition of the Principia.

8 Letter to the Abbg Conti, April 9, 1716, and to Madame de Kilmarisegg, April

18, me.

4 We have, fortunately, Newton's own opinions on the subject. " And as for the
scholium upon the second lemma of the second book of the Principia Philosophia
Matfiematica, which is so much wrested against me, it was written not to give away that
lemma to Mr. Leibnitz, but, on the contrary, to assert it to myself. Whether Mr.
Leibnitz invented it after me, or had it from me, is a question of no consequence : for
second inventors have no right." — Raphson's History of Fluxions, 1715, p. 122, see also
p. 115 ; and Newtoni Opera, torn. iv. p. 616.

5 In a manuscript of seven closely written pages, entitled, " A Supplement to the

1724. LIFE OF SIR ISAAC NEWTON. 359

1684, he pubiished the elements of this method (the method
mentioned to Leibnitz in his letter of October 24, 1676), as
his own, without referring to the correspondence which he
formerly had with the English about these matters. He men-
tioned, indeed, a methodus similis, but whose that method was,
and what he knew of it, he did not say, as he should have done.
And thus his silence put me upon a necessity of writing the
scholium upon the second lemma of the second Book of Prin^
ciples, lest it should be thought that I bon'owed that lemma
from Mr. Leibnitz. In my letter of 24th October 1676, when
I had been speaking of the Method of Fluxions, I added,
Fundamentum harum operationum, satis obvium quidem, quo-
niam non possum explicationem ejus prosequi, sic potius celavi
Qceccdoe Ideff 7i SI 9n 4o 4:qrr 4s 9t 12vx. And in the said
scholium I opened this enigma, saying, that it contained the
sentence, Data cequatione quotcunque fluentes quantitates in-
volvente, fluxiones invenire, et vice versa ; and was written in
the year 1676, for I looked upon this as a sufficient security,
without entering into a wrangle; but Mr. Leibnitz was of
another opinion."

In 1724, when the third edition of the Principia was pre-
paring for the press, Newton had resolved to substantiate his
claims to the first, if not the sole invention, of the new calcu-
lus, and we have found several rough draughts of the changes
which he intended to have made upon the scholium. In one
of these ^ he gives an account of the fundamental principle of
the fluxionary calculus, and distinctly states that it " might
have been easily collected even from the letter which he wrote
to Collins on the 10th December 1672,^ a copy of which was
sent to Leibnitz in 1676."^

Remarks;" that is, to some observations upon Leibnitz's letter to Conti, dated Qih
April 1716, published in Raphson's Fluxions, p. 111.

1 The title of this addition, which occupies more than a folio page, is, " In the end
of the Scholium in Princip. Philos., p. 227, after the words, Vtriusque fundamentum
continetur in hoc Lemmate, add, Sunto quantitates datce, a, h, c ; fluentes x, y, z," &c.

2 A copy of this letter was sent to Tschirnhausen in May 1675, thirteen months before
it was sent to Leibnitz.

3 " Doubts have been expressed," Mr. Edleston remarks, " whether these papers wore

360 LIFE OF SIR ISAAC NEWTON. CHAP. XIV.

In another folio sheet, we have the scholium in three dif-
ferent forms, including the substance of the one previously
published.^ In all of them it is distinctly stated that Newton's
letter to Collins, of the 10th December 1672, containins: the

actually sent to Leibnitz." That papers were sent and received by Leibnitz, his own
testimony and that of others prove ; but there is some reason to believe, as first indi-
cated by Mr. Edleston, and made much more probable by Professor De Morgan, that
Newton's letter of the 10th December was sent, without the example of drawing a tangent
to a curve, which it actually contained, and which was relied upon as giving Leibnitz a
knowledge of the new calculus. In support of this opinion, we find that what are called
the originals, said to have been received by Leibnitz, and Collins' draught of the papers
preserved in the Royal Society, contain merely an allusion to that method. These ori-
ginals have been printed in Leibnitz's Mathematical Works, published at Berlin in 1849,
but fac-similes hare not been given to enable us to judue of their genuineness. It is
diflacult to reconcile with these statements that of Newton himself, who declares that the
originals of the letters in question were sent to Leibnitz in Paris to hereturtied, and that
these originals were in the archives of the Royal Society. Leibnitz may have retained
imperfect copies of these originals, which must have contained the method of tangents.
If it be true that the original letters of Newton were sent to Leibnitz, we have nothing
to do with the copies either at Hanover or the Royal Society.

With regard to the seven " study exercises by Leibnitz, on the use of both the differ-
ential and integral calculus," as Professor De Morgan calls them, dated November 11,
21, 22, 1675, June 26, July, November 1676, which were published by Gerhardt in
1848, we cannot, without seeing the originals or proper facsimiles of the hand-writing,
receive them as evidence. Gerhardt admits that some person had been turning the 5 of
1675 into a 3 (from an obvious motive) ; and when we recollect how Leibnitz altered
grave documents to give him a priority to Bernoulli, as we shall presently see, we are
entitled to pause before we decide on any writings that have passed through his hands.
But even if we admit these documents to be genuine, the allegation of Newton's friends
that copies of his papers were in circulation before 1675, requires to be considered in the
controversy. We recommend to the reader the careful study of Mr. Edleston's statement
in the Correspondence of Sir Isaac Neictoti, p. xlvii., and of the very interesting paper
by Professor De Morgan, on the Companion to the Almanac for 1852, p. 8.

To these observations we may add, that Keill published in the Journal Litt&raire for
May and June 1713, vol. i. p. 215, the extract from the letter of December 10, 1672, as
the chief document upon which the report of the committee of the Royal Society was
founded, and at the same time distinctly stated that this letter teas sent to Leibnitz. Now
Leibnitz, as we know, read this letter, and never contradicted the allegation of Keill. If
the paper actually sent to him had been merely an abridgment of that letter, from
which the example was omitted, he would undoubtedly have come forward, and proved
by the production of what he did receive, and what we know he possessed, that the prin-
cipal argument used against him had no foundation.

Three years afterwards, in 1716, when Newton had challenged him to the discussion,
he had another opportunity which he did not use, of disowning the reception of the
letter.

1 See Appendix, No. XIII.

1684. LIFE OF SIR ISAAC NEWTON. 361

method of drawing tangents, with an example, had been sent to
Leibnitz in Jime 1676, and that on his return from France
through England to Germany, he had consulted Newton's let-
ters in the hands of Collins, and had not long after this fallen
upon a similar method. We have not succeeded in finding a
copy of the scholium, as it was published in the first edition of
the Principia,^ or any traces of the grounds upon which he
omitted the historical details in the original draughts of it.

It would be interesting to know why these contemplated
additions to the scholium were not adopted, and a single para-
graph from the letter of December 10, 1672, substituted for
the original scholium. In the letters of Pemberton to Newton,
in 1724 and 1725, I have found no reference to this change
upon the scholium.

It appears, therefore, that Newton had resolved to overlook
the aggressive movement of Leibnitz in 1684 ; and on another
occasion, when he believed his rights to be invaded, he exer-
cised the same forbearance.^ Circumstances, however, now
occurred which induced his friends to come forward in his

1 On a separate folio sheet I have found the following form of the scholium. The
words ih italics are not in the printed scholium, in which there i^ the word eandem here
omitted. " In literis quae mibi cum geometra periti-ssimo G. Q. Leibnitio annis abhinc
decern intercedebant, cum significarem me compotem esse method! determinandi maxi-
mas et minimas, ducendi tangentes, qiiadrandi Jiguras curvilineas, et similia peragendi
qu£e in terminis surdis seque ac in rationalibus procederet, methodumque exemplis illus-
trarem, sedficndamentum ejus literis transpo.'-itis banc sententiam involventibus [Data
sequatione quotcunque fluentes quantitates involvente, fluxiones invenire, et yice versa]
celarem : rescripsit vir clarissimua, anno proximo, se quoque in ejusmodi methodum in-
cidisse, et methodum suam communicavit a mea vix abludentem, prasterquam in ver-
borum et notarum formulis. Utriusque fundamentura continetur in hoc Lemmate."
This copy does not contiiin the few words added in the second edition of the Principia.

2 In the Acta Eruditorum for January and February 1689, Leibnitz published two
papers, one " On the Motion of Projectiles in a resisting Medium," and the other,
" On the Causes of the Celestial Motions." Newton regarded the proposiiions in these
papers, and in a third, De Lineis Opticis, as plagiarisms from the Principia, Leibnitz, as
he said, " pretending that he had found them all before that book came abroad," and
" to make the principal proposition his own, adapting to it an erroneous demonstration,
and thereby discovering that he did not yet understand how to work in second diflFer-
ences." — See Raphson's Fluxions, p. 117 ; and Recensio Commercii Epistolici; Newtoni
Opera, torn, iv p. 481, No. Ixxii,

362 LIFE OF SIR ISAAC NEWTON. CHAP. XIV.

cause. Having learned, as we have seen, that Newton's "no-
tions of Fluxions passed there by the name of Leibnitz's Dif-
ferential Calculus," Dr. Wallis stopped the printing of the
Preface to the first volume of his Works, in order to claim for
Newton the invention of Fluxions, as contained in the letters
of June and October 1676, which had been sent to Leibnitz.
In intimating to Newton what he had done, he said, " You
are not so kind to your reputation (and that of the nation) as
you might be, when you let things of worth lie by you so long,
till others carry away the reputation which is due to you." ^

Early in the year 1691, the celebrated James Bernoulli
"spoke contemptuously" of the Differential Calculus, maintain-
ing that it differed from that of Barrow only in notation, and
in an abridgment of the operation -^ but it nevertheless " grew
into reputation," and made great progress after the Marquis de
r Hospital had published, in 1696, his excellent work on the
Analysis of Infinitesimals. The claims of the two rival geo-
meters increased in value with the stake for which they con-
tended, and an event soon occurred which placed them in open
combat. Hitherto neither Newton nor Leibnitz had claimed to

1 See Appendix, No. XIV. " At the request of Dr. Wallis," says Newton, " I sent to
him in two letter.s, dated 27th August and 17th September 1692, the first proposition of
the Book of Quadratures, copied almost verbatim from the book, and also the method of
extracting fluents out of equations involving fluxions, mentioned in my letter of 21th
October 16r6, and copied from an older paper, and an explication of the method of
fluxions direct and inverse, comprehended in the sentence, Data equafione, &c. &c , and
the Doctor printed them all the same year (viz. anno 1692), in the second volume of his
works, pp. 391-396. This volume being then in the press, and coming abroad the next
year, two years before the first volume was printed oflF, and this is the first time that the
use of letters with pricks, and a rule for finding second, third, and fourth fluxions were
published, though they were long before in manuscript When I considered only first
fluxions, I seldom used letters with a prick ; but when I considered also second, third,
and fourth fluxions, &c., I distinguished them by letters with one, two, or more pricks ;
and for fluents I put the fluxions either included within a square (as in the aforesaid
analysis), or with a square prefixed as in some other papers, or with an oblique line upon
it. And these notations by pricks and oblique line'^, are the most compendious yet used,
but were not known to the Marquis de 1 Hospital when he recommended the difi'erential
notation, nor are necessary to the method." — A Supplement to the Remarks, p. 4.

2 Acta Eruditorum, Jan. 1691, p. 14.

1696. LIFE OF SIR ISAAC NEWTON. 363

himself the merit of being the sole inventor of the new calculus.
Newton was acknowledged even by his rival as the first inventor,
and in his scholium he was supposed to have allowed Leibnitz
in return the merit of a second inventor. Newton, however,
had always believed, without publicly avowing it, that Leibnitz
had derived his calculus from the communications made to him
by Oldenburg ; and Leibnitz, though he had repeatedly declared
that he and Newton had borrowed nothing from each other, was
yet inclined to consider his rival as a plagiarist.

This celebrated controversy, rendered interesting by the tran-
scendent talents of its promoters, and instructive by the moral
frailties with which it was stained, will form the subject of the
following chapter.

APPENDIX.

No. I.

{Referred to in page ^().)

LETTER EROM MR. NEWTON TO FRANCIS ASTON, ESQ., A YOUNG FRIEND AVHO
WAS ON THE EVE OF SETTING OUT UPON HIS TRAVELS.

Mr. Aston was elected a Fellow of the Royal Society in 1678. He was
an active member, and was frequently in tlie Council. He was chosen one
of the Secretaries on the 30th November 1681, and held that office till the
9th December 1685. He had been re-elected on the 30th of November, but,
at a meeting of the Council on the 9th December, " he threw up," says Mr.
Weld,i " the Secretaryship in so sudden and violent a manner, that the
Council resolved not to run the risk of being similarly treated on any
future occasion, and determined on having an officer more immediately
under their command." Halley's letter (dated March 27, 1686, and giving
an account of this affair to Mr. William Molyneux) will better explain the
circumstances of the case : —

" The history of ovir affairs," says Halley, " is briefly this. On St. An-
drew's day last, being our anniversary day of election, Mr. Pepys Avas
continued President, Mr. Aston, Secretary, and Tancred Robinson chosen
in the room of Mr. Musgrave. Every body seemed satisfied, and no dis-
content appeared anywhere, when, on a sudden, Mr. Aston, as I suppose,
willing to gain better terms of reward from the Society than formerly, on
December 9th, in Council, declared that he would not serve them as Secre-
tary ; and therefore desired them to provide some other to supply that
office ; and that after such a passionate manner, that I fear he has lost
several of his friends by it. The Council, resolved not to be so served for
the future, thought it expedient to have only honorary secretaries, and a
clerk or amanuensis, upon whom the whole burthen of the business should
lie, and to give him a fixed salary, so as to make it worth his while, and
he to be accountable to the secretaries for the performance of his office ;
and, on January 27th last, they chose me for their under officer, with a
promise of a salary of fifty pounds per annum at least."*

Mr. Aston does not seem to have taken oftence at these proceedings of the

1 History of the Royal Society, vol. i. pp. 302, 303.

2 Notwithstanding Mr. Aston's conduct, the Council ordered that he ba presented
■wi:h a gratuity of £60.

3G() LIFE OF SIR ISAAC NEWTON. APPENDIX

Council. He conmiunicated to the Society some observations on certain
unknown ancient characters, which were published in the Philosophical
Transactions for 1692 ; and, previous to his death, which seems to have
taken place in 1715, he bequeathed to the Royal Society a small estate,
still in their possession, at Mablesthorpe, in Lincolnshire, consisting of 55
acres, 2 roods, and 2 perches. He likewise left to the Society a consider-
able number of books and some personal property, which, after paying off
certain debts, amounted to £445. ^

On the 27th February 1684-5, Newton addressed to Mr. Aston a letter,
in which he states, that the attempt made by himself and Mr. Charles
Montague to establish a Philosophical Society at Cambridge, had failed.

The following letter was written when Newlon was only twenty-six years
of age. We have not been able to find any account of the information
which Mr. Aston communicated to his friend, either during his travels or
after his return : —

" Trikitt Collegb, Cambeidgb, May 18, 1669.

Sir, — Since in your letter you give mee so much liberty of spending my
judgment about what may be to your advantage in travelling, I shall do
it more freely than perhaps otherwise would have been decent. First,
then, I will lay down some general rules, most of which, I believe, you
have considered already ; but if any of them be new to you, they may ex-
cuse the rest ; if none at all, yet is my punishment more in writing than
your's in reading.

" When you come into any fresh company, 1. Observe their humoui-s.
2. Suit your own carriage thereto, by which insinuation you will make
their converse more free and open. 3. Let your discourse be more in
querys and doubtings than peremptory assertions or disputings, it being
the designe of travellers to learne, not to teach. Besides, it -will persuade
your acquaintance that you have the greater esteem of them, and soe make
them more ready to communicate what they know to you ; whereas no-
thing sooner occasions disrespect and quarrels than peremptorinesse. You
will find little or no advantage in seeming wiser, or much more ignorant
than your company, 4. Seldom discommend any thing though never so
bad, or doe it but moderately, lest you bee unexpectedly forced to an un-
hansom retraction. It is safer to commend any thing more than it deserves,
than to discommend a thing soe much as it deserves ; for commendations
meet not soe often with oppositions, or, at least, are not usually soe ill
resented by men that think otherwise, as discommendations ; and you will
insinuate into men's favour by nothing sooner than seeming to approve
and commend what they like ; but beware of doing it by a comparison.
5. If you bee affronted, it is better, in a forraine country, to pass it by in
silence, and with a jest, though with some dishonour, than to endeavour
revenge ; for, in the first case, your credit's ne'er the worse when you re-
turn into England, or come into other company that have not heard of the
quarrell. But, in the second case, you may beare the marks of the quarrell
while you live, if you outlive it at all. But, if you find yourself unavoid-
ably engaged, 'tis best, I think, if you can command your passion and
language, to keep them pretty eavenly at some certain moderate pitch, not
miich hightning them to exasperate your adversary, or provoke his friends,

1 Welds History oj Lhe Royal Society, voL i. p. 428.

NO. I. LIFE OF SIR ISAAC NEAVTON. 367

nor letting them grow over much dejected to make him insult. In a word,
if you can keep reason above passion, that and watchfullnesse will be your
best defendants. To which purpose you may consider, that, though such
excuses as this, — He provok't mee so much I could not forbear, — may pass
among friends, yet amongst strangers they are insignificant, and only
argue a traveller's weaknesse.

" To these I may add some general heads for inquirys or observations,
such as at present I can think on. As, 1. To observe the policy s, wealth,
and state affairs of nations, so far as a solitary traveller may conveniently
doe. 2. Their impositions upon all sorts of people, trades, or commoditys,
that are remarkable. 3. Their laws and customs, how far they differ from
ours. 4, Their trades and arts, wherein they excell or come short of us in
England. 5. Such fortifications as you shall meet with, their fashion,
strength, and advantages for defence, and other such military affairs as are
considerable, 6. The power and respect belonging to their degrees of
nobility or magistracy. 7. It will not be time mispent to make a cata-
logue of the names and excellencys of those men that are most wise,
learned, or esteemed in any nation. 8. Observe the mechanisme and man-
ner of guiding ships. 9. Observe the products of nature in several places,
especially in mines, with the circumstances of mining and of extracting
metals or minerals out of their oare, and of refining them ; and if you meet
with any transmutations out of their own species into another (as out
of iron into copper, out of any metall into quicksilver, out of one salt into
another, or into an insipid body, &c.), those, above all, will be worth
your noting, being the most luciferous, and many times lucriferous ex-
periments too in philosophy. 10. The prices of diet and other things.
11. And the staple commoditys of places.

" These generals (such as at present I could think of), if they will serve
for nothing else, yet they may assist you in drawing up a modell to regu-
late your travels by.

" As for particulars, these that follow are all that I can now think of, viz..
Whether at Schemnitium, in Hungary (where there are mines of gold, cop-
per, iron, vitriol, antimony, &c.), they change iron into copper by dissolv-
ing it in a vitriolate water, which they find in cavitys of rocks in the mines,
and then melting the slimy solution in a strong fire, which in the cooling
proves copper. The like is said to be done in other places, which I cannot
now remember ; perhaps, too, it may done in Italy. For about twenty or
thirty years agone there was a certain vitrioll came from thence (called
Eoman vitrioll), but of a nobler virtue than that which is now called by
that name ; which vitrioll is not now to be gotten, because, perhaps, they
make a greater gain by some such trick as turning iron into copper with it,
than by selling it. 2. Whether, in Hungary, Sclavonia, Bohemia, near the
town Eila, or at the mountains of Bohemia near Silesia, there be rivers
whose waters are impregnated with gold ; perhaps, the gold being dissolved
by some corrosive waters like aqtca regis, and the solution carried along with
the streame, that runs through the mines. And whether the practise of lay-
ing mercury in the rivers, till it be tinged with gold, and then straining the
mercury through leather, that the gold may stay behind, be a secret yet,
or openly practised. 3. There is newly contrived, in Holland, a mill to-
grind glasses plane withall, and I think polishing them too ; perhaps it will
be worth the while to see it. 4. There is in Holland one Borry, who

368 LIFE OF SIR ISAAC NEWTON. APPENDIX

some years since was imprisoned by the Pope, to have extorted from him
secrets (as I am told) of great worth, both as to medicine and profit, but he
escaped into Holland, where they have granted him a guard. I think he
usually goes cloathed in green. Pray inquire what you can of him, and
whether his ingenuity be any profit to the Dutch. You may inform your-
self whether the Dutch have any tricks to keep their ships from being all
worm-eaten in their voyages to the Indies. "Whether pendulum clocks do
any service in finding out the longitude, &c.

"I am very weary, and shall not stay to part with a long compliment,
only I wish you a good journey, and God be with you.

"Is. Newton.

" Pray let us hear from you in your travels. I have given your two
books to Dr. Arrowsmith."

No. II.

{Referred to in page 118.)

As Newton's Hypothesis "touching his Theory of Light and Colours,"
which he communicated to the Royal Society on the 9th December 1675,
and which he afterwards illustrated and extended in his celebrated letter
to Robert Boyle in 1679, is very little known, and must ever be referred to
in the Histoiy of Optical Discovery, we have reprinted these two interesting
documents : —

AN HYPOTHESIS* EXPLAINING THE PROPERTIES OF LIGHT DISCOURSED
OF IN MY SEVERAL PAPERS.

" Sir, — In my answ^er to Mr. Hook, you may remember I had occasion
to say something of hypotheses, where I gave a reason why all allowable
hypotheses in their genuine constitution should be conformable to my
theories, and said of Mr. Hook's hyiDothesis, that I took the most free and
natural application of it to phaenomena to be this : — ' That the agitated
parts of bodies, according to their several sizes, figure, and motions, do
excite vibrations in the ajther of various depths or bignesses, which being
promiscuously propagated through that medium to our eyes, effect in us a
sensation of light of a white colour ; but if by any means those of unequal
bignesses be separated from one another, the largest beget a sensation of a
red colour, the least or shortest of a deep violet, and the intermediate ones
of intermediate colours, much after the manner that bodies, according to
their several sizes, shapes, and motions excite- vibrations in the air of
various bignesses, which, according to those bignesses, make several tones
in sound, kc. I was glad to understand, as I apprehended from Mr.
Hook's discourse at my last being at one of your assemblies, that he had
changed his former notion of all colours being compounded of only two

1 In a letter to Oldenburg, dated January 25, 1675-76.

NO. II. LIFE OF SIR ISAAC NEWTON. 369

original ones, made by the two sides of an oblique pulse, and accommodated
his hypothesis to this my suggestion of colours, like sounds, being various,
according to the various bigness of the pulses. For this I take to be a
more plausible hypothesis than any other described by former authors ;
because I see not how the colours of thin transparent plates, or skins, can
be handsomely explained without having recourse to setherial pulses. But
yet I like another hypothesis better, which I had occasion to hint some-
thing of in the same letter in these words :— ' The hypothesis of light's
being a body, had I propounded it, has a much greater affinity with the
objector's own hypothesis than he seems to be aware of, the vibrations of
the aether being as useful and necessary in this as in his. For assuming
the rays of light to be small bodies emitted every way from shining sub-
stances, those, when they impinge on any refracting or reflecting super-
ficies, must as necessarily excite vibrations in the aether as stones do in water
when thrown into it. And supposing these vibrations to be of several
depths or thicknesses, accordingly as they are excited by the said cor-
puscular rays of various sizes and velocities, of what use they will be for
explicating the manner of reflexion and refraction, the production of heat
by the sunbeams, the emission of light from^ burning, putrifying, or other
substances whose parts are vehemently agitated, the phaenomena of thin
transparent plates and bubbles, and of all natural bodies, the manner of
vision, and the difference of colours, as also their harmony and discord, I
shall leave to their consideration who may think it worth their endeavour
to apply this hypothesis to the solution of phsenomena.' Were I to assume
an hypothesis, it should be this, if propounded more generally so as not to
determine what light is, further than that it is something or other capable
of exciting vibrations in the aether ; for thus it will become so general and
comprehensive of other hypotheses as to leave little room for new ones to
be invented ; and therefore because I have observed the heads of some
great virtuosos to run much upon hypotheses, as if my discourses wanted
an hypothesis to explain them by, and found that some, when I could not
make them take my meaning when I spake of the nature of light and
colours abstractedly, have readily apprehended it when I illustrated my
discourse by an hypothesis ; for this reason I have here thought fit to send
you a description of the circumstances of this hypothesis, as much tending
to the illustration of the papers I herewith send you ; and though I shall
not assume either this or any other hypothesis, not thinking it necessary
to concern myself whether the properties of light discovered by me be ex-
plained by this, or Mr. Hook's, or any other hypothesis capable of explain-
ing them ; yet while I am describing this, 1 shall sometimes, to avoid
circumlocution and to represent it more conveniently, speak of it as if I
assumed it and propounded it to be believed. This I thought fit to ex-
press, that no man may confound this with my other discourses, or measure
the certainty of one by the other, or think me obliged to answer objections
against this script ; for I desire to decline being involved in such trouble-
some, insignificant disputes.

" But to proceed to the hypothesis : — 1. It is to be supposed therein,
that there is an aetherial medium, much of the same constitution with air,
but far rarer, subtiler, and more strongly elastic. Of the existence of this
medium, the motion of a pendulum in a glass exhausted of air almost as
(luickly as in the open air is no inconsiderable argument. But it is not to
VOL. L 2 A

870 LIFE OF SIR ISAAC NEWTON, APPENDIX

be supposed that this medinm is one uniform matter, but composed partly
of the main phlegmatic body of aether, partly of other various getherial
spirits, much after the manner that air is compounded of the phlegmatic
body of air intermixed with various vapours and exhalations. For the
electric and magnetic effluvia, and the gravitating principle, seem to argiie
such variety. Perhaps the Avhole frame of nature may be nothing but
various contextures of some certain ietherial spirits or vapours, condensed
as it were by precipitation, much after the manner tliat vapours are con-
densed into water, or exhalations into grosser substances, though not so
easily condensable ; and after condensation wrought into various" forms, at
first by the immediate hand of the Creator, and ever since by the power of
nature, which, by virtue of the command, increase and multiply, became
a complete imitator of the copy set her by the Protoplast. Thus perhaps
may all things be originated from aether.

" At least the electric effluvia seem to instruct us that there is something
of an tetherial nature condensed in bodies. I have sometimes laid upon a
table a round piece of glass about two inches broad, set in a brass ring, so
that the glass might be about one-eighth or one-sixth of an inch from the
table, and the air between them inclosed on all sides by the ring, after the
manner as if I had whelmed a little sieve upon the table. And then rub-
bing a pretty while the glass briskly with some rough and raking stuff, till
some very little fragments of very thin paper laid on the table under the
glass began to be attracted and move nimbly too and fro ; after I had done
i*ubbing the glass, the papei's would continue a pretty while in various mo-
tions, sometimes leaping up to the glass and resting there a while, then
leaping down and resting there, then leaping iip, and perhaps down and up
again, and this sometimes in lines seeming perpendicular to the table,
sometimes in oblique ones ; sometimes also they would leap iip in one arch
and down in another divers times together, without sensible resting be-
tween ; sometimes skip in a bow from one part of the glass to another
without touching the table, and sometimes hang by a corner and turn often
about very nimbly, as if they had been carried about in the midst of a
whirlwind, and be otherwise variously moved, — every paper with a divers
motion. And upon sliding my finger on the upper side of the glass, though
neither the glass nor the enclosed air below were moved thereby, yet Avould
the papers as they hang under the glass receive some new motion, inclining
this way or that way, accordingly as I moved my finger. Now whence all
these irregular motions should spring I cannot imagine, unless from some
kind of subtile matter lying condensed in the glass, and rarefied by
rubbing, as water is rarefied into vapour by heat, and in that rarefaction
diftused through the space round the glass to a great distance, and made
to move and circiilate variously, and accordingly to actuate the papers, till
it returns into the glass again, and be recondensed there. And as this
condensed matter by rarefaction into an tetherial wind (for by its easy
penetrating and circulating through glass I esteem it a^therial) may cause
these odd motions, and by condensing again may cause electrical attraction
with its returning to the glass to succeed in the place of what is there con-
tinually recondensed ; so may the gravitating attraction of the earth be
caused by the continual condensation of some other such like .Ttherial
spirit, not of the main body of phlegmatic aether, l)ut of something very
tliinly and subtilely diff"used through it, perhaps of an unctuous, or gummy

NO. II. LIFE OF SIR ISAAC NEWTON". 371

tenacious and springy nature ; and bearing mucli the same relation to
sether whicli the vital aerial spirit requisite for the conservation of flame
and vital motions does to air. For if such an aetherial spirit may be con-
densed in fermenting or burning bodies, or otherwise coagulated in the
pores of the earth and water into some kind of humid active matter for the
continual uses of nature (adhei'ing to the sides of those pores after the
manner that vapours condense on the sides of a vessel), the vast body of
the earth, which may be everywhere to the very centre in perpetual work-
ing, may continually condense so much of this spirit as to cause it from
above to descend with greater celerity for a supply : in which descent it
may bear down with it the bodies it pervades with force proportional to
the superficies of all their parts it acts upon, nature making a circulation
by the slow ascent of as much matter out of the bowels of the earth in an
aerial form, Avhich for a time constitutes the atmosphere, but being con-
tinually buoyed up by the new air, exhalations, and vapours rising under-
neath, at length {some part of the vapours which return in rain excepted)
vanishes again into the aitherial spaces, and there perhaps in time relents
and is attenuated into its first principle. For nature is a perpetual circula-
tory worker, generating fluids out of solids, and solids out of fluids, fixed
things out of volatile, and volatile out of fixed, subtile out of gross, and
gross out of subtile, some things to ascend and make the upper teri'estrial
juices, rivers, and the atmosphere, and by consequence others to descend
for a requital to the former. And as the earth, so perhaps may the sun
imbibe this spirit copiously, to conserve his shining, and keep the planets
from receding further from him ; and they that will may also suppose that
this spirit affords or carries with it thither the solary fuel and material
principle of light, and that the vast getherial spaces between us and the
stars are for a sufficient repository for this food of the sim and planets.
But this of the constitution of a;therial natures by the bye.

" In the second place, it is to be supposed that the aether is a vibrating
medium like air, only the vibrations far more swift and minute ; those of
air made by a man's ordinary voice, succeeding one another at more than
half a i^oot or a foot distance, but those of aether at a less distance than the
hundred-thousandth part of an inch. And as in air the vibrations are
some larger tlian others, but yet all equally swift (for in a ring of bells the
sound of every tone is heard at two or three miles' distance in the same
order that the bells are struck), so I suppose the a^therial vibrations differ
in bigness, but not in swiftness. Now these vibrations, besides their use in
reflection and refraction, may be supposed the chief means by which the
jjarts of fermenting or putrifying substances, fluid liquors, or melted, burn-
ing, or' other hot bodies, continue in motion, are shaken asunder like a
ship by Avaves, and dissipated into vapours, exhalations, or smoke, and
light loosed or excited in those bodies, and consequently by which a body
becomes a burning coal, and smoke flame ; and I suppose flame is nothing
but the particles of smoke turned by the access of light and heat to burn-
ing coals, little and innumerable.

" Thirdly, the air can pervade the bores of small glass pipes, but yet not
so easily as if they were wider, and therefore stands at a greater degree of
rarity than in the free aerial spaces, and at so much greater a degree of
rarity as the pipe is smaller, as is known by the rising of water in such
pipes to a much greater height than the sxirface of the stagnating water

372 LIFE OF SIE ISAAC NEWTON.

APPENDIX

into which they are dipped. So I suppose aether, though it pervades the
pores of crystal, glass, water, and other natural bodies, yet it stands at a
greater degree of rarity in those pores than in the free setherial spaces, and
at so much a greater degree of rarity as the pores of the body are smaller.
Whence it may be that spirit of wine, for instance, though a lighter body,
yet having subtler parts, and consequently smaller pores than water, is the
more strongly refracting liquor. This also may be the principal cause of
the cohesion of the parts of solids and fluids, of the springiness of glass
and other bodies whose parts slide not one upon another in bending, and
of the standing of the mercury in the Torricellian experiment, sometimes
to the top of the glass, though a much greater height than twenty-nine
inches. For the denser aether which siirrounds these bodies must crowd
and press their parts together, much after the manner that air surrounding
two marbles presses them together if there be little or no air between
them. Yea, and that puzzling problem, hy wlmt means the muscles are
contracted and dilated to cause animal motion, may receirie greater light
fro'm, hence than from any other means men have hitherto been thinking on.
For if there be any power in man to condense and dilate at will the aether
that pervades the muscle, that condensation or dilatation must vary the
compression of the muscle made by the ambient aether, and cause it to
swell or shrink, accordingly ; for though common water will scarce shrink
by compression and swell by relaxation, yet (so far as my observation
reaches) spirit of wine and oil will ; and Mr. Boyle's experiment of a tad-
pole shrinking very much by hard compressing the water in which it swam,
is an argument that animal juices do the same : and as for their various
pression by the ambient aether, it is plain that that must be more or less,
accordingly as there is more or less aether within to sustain and counter-
poise the pressure of that without. If both aethers were equally dense,
the muscle would be at liberty as if pressed by neither : if there were no
aether within, the ambient would compress it with the whole force of its
spring. If the aether within were twioe as much dilated as that without,
so as to have but half as much springiness, the ambient would liave half
the force of its springiness counterpoised thereby, and exercise but the
other half upon the muscle ; and so in all other cases the ambient com-
presses the muscle by the excess of the force of its springiness abo¥e that
of the springiness of the included. To vary the compression of the muscle
therefore, and so to swell and shrink it, there needs nothing Uut to change
the consistence of the included aether ; and a very little change may suffice,
if the spring of aether be supposed very strong, as I take it to be many de-
grees stronger than that of air.

" Now for the changing the consistence of the aether, some may be
ready to grant that the soul may have an immediate power over the whole
ajther in any part of the body, to swell or shrink it at will ; but then how
depends the muscular motion on the nerves ? Others therefore may be
more apt to think it done by some certain aetherial spirits included within
the dura rruiter, which the soul may have power to contract or dilate at
will in any muscle, and so cause it to flow thither through the nerves ; but
still there is a difficulty why this force of the soul upon it does not take
off the power of springiness, whereby it should sustain more or less the
force of the outward aether. A third supposition may be, that the soul has
a power to inspire any muscle with this spirit, by impelling it thither

KO. II. LIFE OF SIR ISAAC NEWTON. 373

through the nerves ; but this too h.as its difficulties ; for it requires a for-
cible intruding the spring of the aether in the muscles by pressure exerted
from the parts of the brain ; and it is hard to conceive how so great force
can be exercised amidst so tender matter as the brain is ; and besides, why-
does not this aetherial spirit, being subtile enough, and urged with so great
force, go away through the dtira mater and skins of the muscle, or at least
so much of the other gether go out to make way for this which is crowded
in ? To take away these difficulties is a digression, but seeing the subject
is a deserving one, I shall not stick to tell you how I think it may be done.

*' First, then, I suppose there is such a spirit ; that is, that the animal
spirits are neither like the liquor, vapour, or gas, of spirits of wine ; but
of an Eetherial nature, subtile enough to pervade the animal juices as freely
as the electric, or perhaps magnetic, effluvia do glass. And to know how
the coats of the brain, nerves, and muscles, may become a convenient
vessel to hold so subtile a spirit, you may consider how liquors and spirits
are disposed to pervade, or not pervade, things on other accounts than their
subtilty ; water and oil pervade wood and stone, which qiiicksilver does
not ; and quicksilver, metals, which water and oil do not ; water and acid
spirits pervade salts, which oil and spirit of wine do not ; and oil and
spirit of wine pervade sulpliur, which water and acid spirits do not ; so
some fluids (as oil and water), though their .parts are in freedom enough
to mix with one another, yet by some secret principle of unsociaUeness
they keep asunder ; and some that are sociable may become unsociable by
adding a third thing to one of them, as water to spirit of wine by dissolv-
ing salt of tartar in it. The like unsociableness may be in astherial natures,
as perhaps between the aethers in the vortices of the sun and planets ; and
the reason why air stands rarer in the bores of small glass pipes, and
aether in the pores of bodies, may be, not want of subtilty, but sociable-
ness ; and on this ground, if the aetherial vital spirit in a man be very
sociable to the marrow and juices, and unsociable to the coats of the brain,
nerves, and muscles, or to anything lodged in the pores of those coats, it
may be contained thereby, notwithstanding its subtilty ; especially if we
suppose no great violence done to it to squeeze it ou.t, and that it may not
be altogether so subtile as the main body of aether, though subtile enough
to pervade readily the animal juices, and that as any of it is spent, it is
continually supplied by new spirit from the heart.

'' In the next place, for knowing how this spirit may be used for animal
motion, you may consider how some things uiisociable are made sociable
by the mediation of a third. Water, which will not dissolve copper, will
do it if the copper be melted with sulphur. Aquafortis, which will not
pervade gold, will do it by addition of a little sal-ammoniac or spirit of
salt. Lead will not mix in melting with copper ; but if a little tin, or
antimony, be added, they mix readily, and part again of their own accord,
if the antimony be wasted by throwing saltpetre, or otherwise. And so
lead melted with silver quickly pervades and liquifies the silver in a much
less heat than is required to melt the silver alone ; but if they be kept in
the test till that little substance that reconciled them be wasted or altered,
they part again of their own accord. And in like maniier the aetherial
animal spirit in a man may be a mediator between the common aether, and
the muscular juices, to make them mix more freely ; and so by sending a
little of this spirit into any muscle, though so little as to caxise no sensible

374 LIFE OF SIE ISAAC NEWTON".

APPENDIX

tension of the muscle by its own force, yet by rendering the juices more
sociable to the common external aether, it may cause that aither to pervade
the muscle of its own accord in a moment more freely and more copiously
than it would otherwise do, and to recede again as freely, so soon as this
mediator of sociableness is retracted ; whence, according to what I said
above, will proceed the swelling or shrinking of the muscle, and conse-
quently the animal motion depending thereon.

"Thus may therefore the soul, by determining this getherial animal
spirit or wind into this or that nerve, perhaps with as much ease as air is
moved in open spaces, cause all the motions we see in animals ; for the
making Avhich motions strong, it is not necessary that we should suppose
the aether within the muscle very much condensed, or rarefied, by this
means, but only that its spring is so very great that a little alteration of
its density shall cause a great alteration in the pressure. And what is
said of muscular motion may be applied to the motion of the heart, only
with this diiference ; that the spirit is not sent thither as into other
muscles, but continually generated there by the fermentation of the juices
with which its flesh is replenished, and as it is generated, let out by starts
into the brain, through some convenient dnctm, to perform those motions
in other muscles by inspiration, which it did in the heart by its generation.
For I see not why the ferment in the heart may not raise as subtile a spirit
out of its juices, to cause those motions, as rubbing does out of a glass to
cause electric attraction, or burning out of fuel to penetrate glass, as Mr.
Boyle has shown, and calcine by corrosion metals melted therein. '

*' Hitherto I have been contemplating the nature of aether and aetherial
substances by their effects and uses, and now I come to join therewith the
consideration of light.

"In the fourth place, therefore, I suppose light is neither aether, nor its
vibrating motion, but something of a different kind propagated from lucid
bodies. Tliey that will may suppose it an aggregate of various peripatetic
qualities. Others may suppose it multitudes of unimaginable small and
swift corpuscles of various sizes springing from shining bodies at great dis-
tances one after another, but yet without any sensible interval of time, and
continually urged forward by a principle of motion, which in the beginning
accelerates them, till the resistance of the aetherial medium equal the force
of that principle, much after the manner that bodies let fall in water are
Accelerated till the resistance of the .water equals the force of gravity. God,
who gave animals motion beyond our understanding, is, without doubt, able
to implant other principles of motions in bodies which we may understand as
little. Some would readily grant this may be a spiritual one ; yet a me-
chanical one might be shown, did not I think it better to pass it by. But
they that like not this, may suppose light any other corporeal emanation,
or an impulse or motion of any other medium or aatherial spirit diffused
through the main body of aether, or what else they imagine proper for this
purpose. To avoid dispute, and make this hypothesis general, let every
man here take his fancy ; only whatever light be, I would suppose it con-
sists of successive rays differing from one another in contingent circum-
stances, as bigness, force, or vigour, like as the sands on the shore, the

1 Boyle's Assays of the strange subtilty, &c., of effluTinins, &c., togeher with a dis-
covery of the perviousness of glass to ponderable parts of flame.

NO. n. LIFE OF SIR ISAAC NEWTON. 375

waves of the sea, the faces of men, and all other natural things of the same
kind differ, it being almost impossible for any sort of things to be found
without some contingent variety. And further, I would suppose it diverse
from the vibrations of the aether, because (besides that were it those vibra-
tions, it ought always to verge copiously in crooked lines into the dark or
quiescent medium, destroying all shadows, and to comply readily with any
crooked pores or passages as sounds do) I see not how any superficies (as
the side of a glass prism on which the rays within are incident at an angle
of about forty degrees) can be totally opake. For the vibrations beating
against the refracting confine of the rarer and denser aether must needs
make that pliant superficies undulate, and those undulations will stir up
and propagate vibrations on the other side. And further, how light, inci-
dent on very thin skins or plates of any transparent body, should for many
successive thicknesses of the plate in arithmetical progression, be alter-
nately reflected and transmitted, as I find it is, puzzles me as much. For
though the arithmetical progression of those thicknesses, which refiect and
transmit the rays alternately, argues that it depends upon the number of
vibrations between the two superficies of the plate, whether the ray shall
be reflected or transmitted, yet I cannot see how the number should vary
the case, be it greater or less, whole or broken, unless light be supposed
something else than these vibrations. Something^ indeed I could fancy
towards helping the two last difficulties, but nothing which I see not in-
sufficient.

" Fifthly, it is to be supposed that light and aether mutually act upon one
another, aether in refracting light, and light in warming aether, and that
the densest aether acts most strongly. When a ray therefore moves through
aether of uneven density, I suppose it most pressed, urged, or acted upon
by the medium on that side towards the denser aether, and receives a con-
tinual impulse or ply from that side to recede towards the rarer, and so is
accelerated if it move that way, or retarded if the contrary. On this
ground, if a ray move obliquely through such an unevenly dense medium
(that is, obliquely to those imaginary superflcies which run through the
equally dense parts of the medium, and may be called the refracting super-
ficies), it must be incurved, as it is found to be by observation in water,'
whose lower parts were made gradually more salt, and so more dense than
the upper. And this may be the ground of all refraction and reflexion.
For as the rarer air within a small glass pipe, and the denser without, are
not distinguished by a mere mathematical superficies, but have air between
them at the orifice of the pipe running through all intermediate degrees of
density, so I suppose the refracting superficies of aether between unequally
dense mediums to be not a mathematical one, but of some breadth, the
aether therein at the orifices of the pores of the solid body being of all in-
termediate degrees of density between the rarer and the denser aetherial
mediums ; and the refraction I conceive to proceed from the continual
incurvation of the ray all the while it is passing the physical superficies.
Now if the motion of the ray be supposed in this passage to be increased
or diminished in a certain jiroportion, according to the difference of the
densities of the aetherial mediums, and the addition or detraction of the
motion be reckoned in the perpendicular from the refracting superficies, as

1 Mr. Ilook'a Micrcgraphia where he speaks of the irflexion of rays.

376

LIFE OF SIR ISAAC NEWTON.

it ought to be, the sines of incidence and refraction f^'ill be proportional
according to what Descartes has demonstrated.

"The ray, therefore, in passing out of the rarer medium into the denser,
inclines continually more and more towards parallelism Avith the refracting
superficies ; and if the different densities of the mediums be not so great,
nor the incidence of the ray so oblique as to make it parallel to that super-
ficies before it gets through, then it goes through and is refracted ; but if
through the aforesaid causes the ray becomes parallel to that superficies
before it can get through, then it must turn back and be reflected. Thus,
for instance, it may be observed in a triangular glass prism o E F, that the

rays an that tend out of the glass
into air, do, by inclining them more
to the refracting superficies, emerge
more and more obliquely till they be
infinitely oblique, that is, in a man-
ner parallel to the superficies, which
happens when the angle of incidence
is about 40° ; and then if they be a
little more inclined, are all reflected,
as at A V \, becoming, I suppose,
jj parallel to the superficies before they
can get through it.
" Let A B c D represent the rarer medium, E F H o the denser, c D F E the
space between them or refracting physical superficies, in which the aither

z«\

X^^^^^^^'^'

--M

is of all intermediate degrees of density, from the rarest .ather at C D to the
densest at E F ; a m % L a ray, A m its incident part, m n its incurvation by
the refracting superficies, and n L its emergent part. Now, if the ray a m
be so much incurved as to become at its emergence n, as nearly as may be,
parallel to c D, it is plain that if that ray had been incident a little more
obliquely, it must have become parallel to c d before it had arrived at e f.

NO. II. LIFE OF SIE ISAAC NEWTON. 377

the further side of the refracting superficies, and so could have got no
nearer to E F, but must have turned baclc by further incurvation, and been
refiected as it is represented at a /x ?/ X : and the like would have happened
if the density of the sether had further increased from E F to p Q, so that
p Q H G might be a denser medium than E F G H was supposed ; for then the
ray in passing from m to n, being so much incurved as at n to become
parallel to c D or p Q, it's impossible it should ever get nearer to p q, but
must at n begin by further incurvation' to turn back, and so be reflected.
And because if a refracted ray (as wl) be made, incident, the incident (Am)
shall become the refracted ; and therefore if the ray a ^ »/, after it is arrived
at V, where I suppose it parallel to the refracting superficies, should be re-
flected perpendicularly back, it would return back in the line of incidence
V fi. A.; therefore going forward, it must go forward in such another line
vir\, both cases being alike, and so be reflected at an angle equal to that
of incidence.

" This maybe the cause and manner of reflexion, when light tends from
the rarer tow'ards the denser aether ; but to know how it should be reflected
when it tends from the denser towards the rarer, you are farther to con-
sider, how fluids near their superficies are less pliant and yielding than in
their more inward parts, and if formed into thin plates or shells, they be-
come much more stiff and tenacious than otherwise. Thus things which
readily fall in water, if let fall upon a bubble of water, they do not easily
break through it, but are apt to slide down by the sides of it, if they be
not too big and heavy. So if two well-polished convex glasses, ground on
very large spheres, be laid one upon the other, the air between them easily
recedes till they almost touch, but then begins to resist so m.uch that the
weight of the upper glass is too little to bring them together, so as to make
the black (mentioned in the papers I sent you) appear in the midst of the
rings of colours. And if the glasses be plain, though no broader than a
twopence, a man with his whole strength is not able to press all the air oiit
from between them, so as to make them fully touch. You may observe
also that insects will walk upon water without wetting their feet, and the
water bearing them up ; also motes falling upon water will often lie long
upon it without being wetted. And so I suppose aether in the confine of
two mediums is less pliant and yielding than in other places, and so much
the less pliant by how much the mediums differ more in density ; so that
in passing out of denser aether into rarer, when there remains but a very
little of the denser aether to be passed through, a ray finds more than
ordinary difficulty to get through, and so great difficulty where the mediums
are of a very differing density as to be reflected by incurvation after the
manner described above, the parts of aether on the side where they are less
pliant and yielding, acting upon the ray much after the manner that they
would do were they denser there than on the other side ; for the resistance
of the medium ought to have the same eff'ect on the ray from whatsoever
cause it arises. And this I suppose may be the cause of the reflexion of
quicksilver and other metalline bodies. It must also concur to increase the
reflective virtue of the superficies when rays tend out of the rarer medium
into the denser ; and in that case therefore the reflexion having a double
cause ought to be stronger than in the aether, as it is apparently. But in
refraction this rigid tenacity or unpliableness of the superficies need not be

378 LIFE OF SIE ISAAC XEWTON. APPENDIX

considered, because so much as tlie ray is thereby bent in passing to the
most tenacious and rigid part of the superficies, so much is it thereby un-
bent again in passing on from thence through the next parts gradually less
tenacious.

" Thus may rays be refracted by some superficies, and reflected by others,
be the medium they tend into denser or rarer. But it remains further to
be explained, how rays alike incident on the same superficies (suppose of
crystal, glass, or water) may be, at the same time, some i*efracted, others
reflected ; and for explaining this, I suppose that the rays Avhen they im-
pinge on the rigid resisting setherial superficies, as they are acted upon by
it, so they react upon it, and cause vibrations in it, as stones thrown into
water do in its surface ; and that these vibrations are propagated every
way into both the rarer and denser mediums, as the vibrations of air which
cause sound are from a stroke, but yet continue strongest where they be-
gan, and alternately contract and dilate the fether in that physical super-
ficies. For it's plain by the heat which light produces in bodies that it is
able to put their parts in motion, and much more to heat and put in mo-
tion the more tender iiether ; and it's more probable that it communicates
motion to the gross parts of bodies by the mediation of fether than immedi-
ately ; as, for instance, in the inward parts of quicksilver, tin, silver, and
other very opake bodies, by generating vibrations that run throiigh them,
than by striking the outward parts only without entering the body. The
shock of every single ray may generate many thousand vibrations, and by
sending them all over the body, move all the parts, and that perhaps with
more motion than it could move one single part by an immediate stroke ;
for the vilirations, by shaking each particle backAvard and forward, may
every time increase its motion, as a ringer does a bell by often pulling it,
and so at length move the particles to a very great degree of agitation,
which neither the simple shock of a ray, nor any other motion in the
{ether, besides a vibrating one, could do. Thus in air shut up in a vessel,
the motion of its parts caused by heat, how violent soever, is unable to
move the bodies hung in it with either a trembling or progressive motion ;
but if air be put into a vibrating motion by beating a drum. or two, it
shakes glass windows, the whole body of a man, and other massy things,
especially those of a congruous tone ; yea, I have observed it manifestly
shake under my feet a cellared free-stone floor of a large hall ; so as I be-
lieve the immediate stroke of five hundred dr\im-sticks could not have
done, iinless perhaps quickly succeeding one another at equal intervals of
time. iEtherial vibrations are therefore the best means by which such a
subtile agent as light can shake the gross particles of solid bodies to heat
them. And so supposing that light impinging on a refracting or reflecting
jetherial superficies puts it into a vibrating motion, that physical super-
ficies being by the perpetual appulse of rays always kept in a vibrating
motion, and the Dgther therein continually expanded and compressed by
turns ; if a ray of light impinge upon it while it is much compressed, I
suppose it is then too dense and stiff to let the ray pass through, and so
reflects it ; but the rays that impinge on it at other times, when it is
either expanded by the interval of two vibrations, or not too much com-
pressed and condensed, go through, and are refracted.

" These may be the causes of refractions and reflexions in all cases, but

NO. II.

LIFE OF SIR ISAAC NEWTON. 379

for understanding how they come to be so regular, it's further to be con-
sidered, that, as in a heap of sand, although the surface be rugged, yet if
water be poured on it to fill its pores, the water, so soon as its pores are
filled, will evenly overspread the surface, and so much the more evenly as
the sand is finer ; so, although the surface of all bodies, even the most
polished, be rugged, as I conceive, yet when that ruggedness is not too
gross and coarse, the refracting getherial superficies may evenly overspread
it. In polishing glass or metal, it is not to be imagined that sand, putty,
or other fretting powders should wear the surface so regularly as to make
the front of every particle exactly plane, and all those planes look the
same way, as they ought to do in well-polished bodies, were reflexion per-
formed by their parts ; but, that those fretting powders should wear the
bodies first to a coarse ruggedness, such as is sensible, and then to a finer
and finer ruggedness, till it be so fine that the aetherial superficies evenly
overspreads it, and so makes the body put on the appearance of a polish,
is a very natural and intelligible supposition. So in fluids it is not well to
be conceived that the surfaces of their parts should be all plain, and the planes
of the superficial parts always kept looking all the same way, notwith-
standing that they are in perpetual motion, and yet Avithotit these two
suppositions, the superficies of fluids could not be so regularly reflexive as
they are, were the reflexion done by the parts themselves, and not by an
aetherial superficies evenly overspreading the fluid.

" Further, considering the regular motion of light, it might be suspected
whether the various vibrations of the fluid through which it passes may
not much disturb it ; but that suspicion I suppose will vanish by consider-
ing, that if at any time the foremost part of an oblique wave begin to turn
it awry, the hindermost part by a contrary action must soon set it straight
again.

"Lastly, because without doubt there are in every transparent body
pores of various sizes, and I said that sether stands at the greatest rarity
in the smallest pores, hence the aether in every pore should be of a differing
rarity, and so light be refracted in its passage out of every pore into the
next, which would cause a great confusion, and spoil the body's transpar-
ency ; but, considering that the aether in all dense bodies is agitated by
continual vibrations, and these vibrations cannot be performed without
forcing the parts of aether forward and backward from one pore to another
by a kind of tremor, so that the aether which one moment is in a great pore
is the next moment forced into a less; and, on the contrary, this must
evenly spread the aether into all the pores not exceeding some certain big-
ness, suppose the breadth of a vibration, and so make it of an even density
throughout the transparent body, agreeable to the middle sort of pores.
But where the pores exceed a certain bigness, I suppose the aether suits its
density to the bigness of the pore or to the medium within it, and so, being
of a divers density from the aether that surrounds it, refracts, or reflects
light in its superficies, and so makes the body where many such interstices
are, appear opake.

" Thus much of refraction, reflexion, transparency, and opacity ; — and
now to explain colours. I suppose that as bodies of various sizes, densi-
ties, or tensions, do by percussion or other action, excite sounds of various
tones, and consequently vibrations in the air of various bignesses ; so, when

380 LIFE OF SIR ISAAC NEWTON. API>ENDIX

the rays of light, by impinging on the stiff refracting superficies, excite
vibrations in the sether, those rays, whatever they be, as they happen to
differ in magnitude, strength, or vigour, excite vibrations of various big-
nesses ; the biggest, strongest, or most potent rays, the largest vibrations,
and others shorter, according to their bigness, strength, or power ; and
therefore the ends of the capillamenta of the optic nerve, which front or
face tlie retina, being such refracting superficies, when the rays impinge
upon them, they must there excite these vibrations ; which vibrations (like
those of sound in a trumpet) will run along the aqueous pores or crystalline
pith of the capillamenta, through the optic nerves into the sensorium
(which light itself cannot do), and there, I suppose, affect the sense with
various colours, according to their bigness and mixture : the biggest with
the strongest colours, reds and yellows ; the least with the weakest, blues
and violets ; the middle with green, and a confusion of all, with white ;
much after the manner that in the sense of hearing nature makes use of
aerial vibrations of several bignesses, to generate sounds of divers tones ;
for the analogy of nature is to be observed. And further, as the hannony
and discord of sounds proceed from the proportions of the aerial vibrations,
so may the harmony of some colours, as of a golden and blue, and the dis-
cord of other, as of red and blue, proceed from the proportions of the
aitherial. And possibly colour may be distinguished into its principal de-
grees : red, orange, yellow, green, blue, indigo, and deep violet, — on the
same ground that sound within an eighth is graduated into tones. For,
some years past, the prismatic colours, being in a well -darkened room, cast
perpendicularly upon a paper about two-and-twenty foot distant from the
prism, I desired a friend to draw with a pencil lines across the image or
pillar of coloiirs, where every one of the seven aforenamed colours was
most full and brisk, and also where he judged the truest confines of them
to be, whilst I held the paper so that the said image might fall within a
certain compass marked on it. And this I did, partly because my own
eyes are not veiy critical in distinguishing colours, partly because another
to whom I had not comnumicated my thoughts about this matter could
have nothing but his eyes to determine his fancy in making those marks.
This observation we repeated divers times, both in the same and divers
days, to see how the marks on several papers woxild agree ; and comparing
the observations, though the just confines of the colours are hard to be as-
signed, because they passed into one another by insensible gradation, yet
the differences of the observations were but little, especially towards the
red end ; and taking means between those differences that were, the length
of the image (reckoned not by the distance of the verges of the semicircular
ends, but by the distance of the centres of those semicircles, or length of
the straight sides, as it oiight to be) was divided in about the same propor-
tion that a string is between the end and the middle to sound the tones in
an eighth. You will understand me best by viewing the annexed figure,
in which A B and c D represent the straight sides about ten inches long,
A p c and B T D the semicircular ends, x and Y the centres of those semi-
circles, X z the length of a musical string double to x Y, and divided between
X and Y so as to sound the tones expressed at the side (that is, x H the half,
X G and G I the third part, Y K the fifth part, Y M the eighth part, and G E
the ninth part of x y) ; and the intervals between these divisions express

LIFE OF SIR ISAAC NEWTOTs^.

381

the spaces which the colovirs written there took up, every colour being
most briskly specific in the middle of those spaces. Now for the cause of

S ^

£ G

gKi|M

these and such like colours made by refraction, the biggest or strongest
rays must penetrate the refracting superficies more freely and easier than
the weaker, and so be less turned awry by it, that is less refracted ; which
is as much as to say, the rays which make red are least refrangible, those
which which make blue, or violet, most refrangible, and others otherwise
refrangible according to their colour. Whence if the rays which come pro-
miscuously from the sun be refracted by a prism, as in the aforesaid experi-
ment, those of several sorts being variously refracted, must ga to several
places on an opposite paper or wall, and so parted, exhibit every one their
own colours, which they could not do while blended together. And because
refraction only severs them, and changes not the bigness or strength of the
ray, thence it is, that after they are once well-severed, refraction cannot
make any further changes in their colour. On this ground may all the
phgenomena of refractions be understood."

Letter from Newton to Robert Boyle.

"Honoured Sir, — I have so long deferred to send you my thoughts
about the physical qualities we speak of, that did I not esteem myself
obliged by promise, I think I should be ashamed to send them at all. The
truth is, my notions about things of this kind are so indigested, that I am
not well satisfied myself in them ; and what I am not satisfied in, I can
scarce esteem fit to be communicated to others ; especially in natural philo-
sophy, where there is no end of fancying. But because I am indebted to
you, and yesterday met with a friend, Mr. Mauly verer, who told me he was
going to London, and intended to give you the trouble of a visit, I could
not forbear to take the opportunity of conveying this to you by him.

" It being only an explication of qualities which you desire of me, I shall
set down my apprehensions in the form of suppositions as follows. And
first, I siippose that there is diffused through all places an aetherial sub
stance, capable of contraction and dilatation, strongly elastic, and, in a
word, much like air in all respects, but far more subtile.

"2. I suppose this aether pervades all gross bodies, but yet so as to stand
rarer in their pores than in free spaces, and so much the rarer, as their
pores are less ; and this I suppose (with others) to be the cause why light
incident on those bodies is refracted towards the perpendicular ; why two
well-polished metals cohere in a receiver exhausted of air ; why ^ stands

382

LIFE OF SIE ISAAC NEWTON.

sometimes up to the top of a glass pipe, though much higher than thirty
inches ; and one of the main causes why the parts of all bodies cohere ;
also the cause of filtration, and of the rising of water in small glass pipes
above the surface of the stagnating water they are dipped into ; for I sus-
pect the aither may stand rarer, not only in the insensible pores of bodies,
but even in the very sensible cavities of those pipes ; and the same prin-
ciple may cause menstruums to pervade with violence the pores of the
bodies they dissolve, the surrounding aether, as well as the atmosphere,
pressing them together.

" 3. 1 suppose the rarer aether within bodies, and the denser without them,
not to be terminated in a mathematical superficies, but to grow gradually
into one another ; the external aether beginning to grow rarer, anil the in-
ternal to grow denser, at some little distance from the superficies of the
body, and running tlu'ough all intermediate degrees of density in the in-
termediate spaces ; and this may be the cause why light, in Grimaldo's
experiment, passing by the edge of a knife, or other opake body, is turned
aside, and as it were refracted, and by that refraction makes several colours.
Let A B c D be a dense body, whether opake or transparent, E F G H the
outside of the uniform aether, which is within it, I K L M the inside of the
uniform aether, which is without it ; and conceive the aether, which is be-
tween EF GH and I K LM, to run through all intermediate degrees of density

Fig. 1.

between that of the two uniform aethers on either side. This being sup-
posed, the rays of the sun SB, s K, which pass by the edge of this body
between B and K, ought in their passage through the unequally dense
sether there, to receive a ply from the denser aether, Avhich is on that side
towards K, and that the more by how much they pass nearer to the bodj^
and thereby to be scattered through the space p Q R s T, as by experience
they are found to be. Now the space between the limits E F G H and
I K L M, I shall call the space of the aether's graduated rarity.

" 4. When two bodies moving towards one another come near together, I
suppose the aether between them to grow rarer than before, and the spaces

LIFE OF SIR ISAAC NEWTON.

383

of its graduated rarity to extend further from tlie superficies of the bodies
towards one another ; and this, hj reason that the aether cannot move and
play up and down so freely in the straight passage between the bodies, as
it could before they came so near together : thus, if the space of the aether's
graduated rarity reach from the body a B c D F E only to the distance
G H L M R s, when no other body is near it, yet may it reach further, as to
I K, when another body N o P Q approaches ; and as the other body ap-
proaches more and more, I suppose the aether between them will grow
rarer and rarer. These suppositions I have so described, as if I thought
the spaces of graduated aether had precise limits, as is expressed at I K L M

Fig. 2.

in the first figure, and G M R s in the second ; for thus I thought I could
better express myself. But really I do not think they have such precise
limits, but rather decay insensibly, and, in so decaying, extend to a much
greater distance than can easily be believed or need be svipposed.

" 5. Now, from the fourth supposition it follows, that when two bodies
approaching one another come so near together as to make the sether be-
tween them begin to rarefy, they will begin to have a reluctance from
being brought nearer together, and an endeavour to recede from one
another ; which reluctance and endeavom* will increase as they come
nearer together, because thereby they cause the interjacent aether to rarefy
more and more. But at length, when they come so near together that the
excess of pressure of the external aether which surrounds the bodies, above
that of the rarefied aether, which is between them, is so great as to over-
come the reluctance which the bodies have fi-om being brought together ;
then will that excess of pressure drive them with violence together, and
make them adhere strongly to one another, as was said in the second sup-
position. For instance, in the second figure, when the bodies E D and N p
are so near together that the spaces of the aether's graduated rarity begin
to reach to one another, and meet in the line i K, the a'ther between them
will have suff'ered much rarefaction, which rarefaction requires much
force, that is, much pressing of the bodies together ; and the endeavour

384 LIFE OF SIK ISAAC NEWTON. APPENDIX

which the aether between them has to return to its former natural state of
condensation, will cause the bodies to have an endeavour of receding from
one another. But, on the other hand, to counterpoise this endeavour,
there will not yet be any excess of density of the aether which surrounds
the bodies, above that of the aether which is between them at the line I K.
But if the bodies come nearer together, so as to make the aether in the
mid-way line i K grow rarer than the surrounding aether, there will arise
from the excess of density of the surrounding aether a compressure of the
bodies towards one another, which, when by the nearer approach of the
bodies it become so great as to overcome the aforesaid endeavour the bodies
have to recede from one another, they will then go towards one another
and adhere together. And, on the contrary, if any power force them
asunder to that distance, where the endeavour to recede begins to over-
come the endeavour to accede, they will again leap from one another.
Now hence I conceive it is chiefly that a fly walks on water without wet-
ting her feet, and consequently without touching the water ; that two
polished pieces of glass are not without pressure brought to contact, no,
not though the one be plain, the other a little convex ; that the particles
of dust cannot by pressing be made to cohere, as they would do, if they
did but fully touch ; that the particles of tinging substances and salts
dissolved in water do not of their own account concrete and fall to the
1)ottom, but difi"use themselves all over the liquor, and expand still more
if you add more liquor to them. Also, that the particles of vapours, ex-
halations, and air do stand at a distance from one another, and endeavour
to recede as far from one another as the pressure of the incumbent atmos-
phere will let . them ; for I conceive the confused mass of vapours, air,
and exhalations which we call the atmosphere, to be nothing else but the
particles of all sorts of bodies, of which the earth consists, separated from
one another, and kept at a distance, by the said principle.

" From these principles the action of menstruums upon bodies may be
thus explained : suppose any tinging body, as cochineal or logwood be put
into water ; so soon as the water sinks into its pores and wets on all sides
any particle which adheres to the body only by the principle in the
second supposition, it takes off", or at least much diminishes, the efficacy
of that principle to hold the particle to the body, because it makes the
asther on all sides the particle to be of a more uniform density than before.
And then the particle being shaken off" by any little motion, floats in the
water, and with many such others makes a tincture ; which tincture will
be of some lively colour, if the particles be all of the same size and density ;
otherwise of a dirty one. For the colours of all natural bodies whatever
seem to depend on nothing but the various sizes and densities of their
particles, as I think you have seen described by me more at large in
another paper. If the particles be very small (as are those of salts,
vitriols, and gums), they are transparent ; and as they are supposed bigger
and bigger, they put on these colours in order, black, white, yellow, red ;
violet, blue, pale green, yellow, orange, red ; purple, blue, green, yellow,
orange, red, &c., as it is discerned by the colours, which appear at the
several thicknesses of very thin plates of transparent bodies. Whence, to
know the causes of the changes of colours, which are often made by the
mixtures of several liquors, it is to be considered how the particles of
any tincture may have their size or density altered by the infusion of

NO. II. LIFE OF SIR ISAAC NEWTON. , 385

another liq\ior. When any metal is put into common water tlie water
cannot enter into its pores, to act on it and dissolve it. Not that
water consists of too gross parts for this purpose, but because it is un-
sociable to metal. For there is a certain secret principle in nature, by
which liquors are sociable to some things and unsociable to others ; thus
water will not mix with oil, but readily with spirit of wine, or with salts ;
it sinks also into Avood, which quicksilver will not ; but quicksilver sinks
into metals, which, as I said, water will not. So aquafortis dissolves ]),
not ; aqua regis 0, not ]), &c. But a liquor, which is of itself un-
sociable to a body, may, by the mixture of a convenient mediator, be made
sociable ; so molten lead, which alone will not mix with copper, or with
regulus of Mars, by the addition of tin is made to mix with either. And
water, by the mediation of saline spirits, will mix with metal. Now when
any metal is put in water impregnated with such spirits, as into aquafortis,
aqua regis, spirit of vitriol, or the like, the particles of the spirits, as
they, in floating in the water, strike on the metal, will by their sociable-
ness enter into its pores and gather round its outside particles, and by
advantage of the continual tremor the particles of the metals are in, hitch
themselves in by degrees between those particles and the body, and loosen
them from it ; and the water entering into the pores together with the
saline spirits, the particles of the metal will be thereby
still more loosed, so as by that motion the solution puts
them into, to be easily shaken off, and made to float in the
water : the saline particles still encompassing the me-
tallic ones as a coat or shell does a kernel, after the man-
ner expressed in the annexed figure, in which figure I
have made the particles round, though they may be cubical,
or of any other shape. ^^'^- ^■

" If into a solution of metal thus made be poured a liquor abounding
with particles, to which the former saline particles are more sociable than
to the particles of the metal (suppose with particles of salt of tartar), then
so soon as they strike on one another in the liquor, the saline particles
will adhere to those more firmly than to the metalline ones, and by degrees
be wrought off from those to enclose these. Suppose a
a metalline particle, inclosed with saline ones of spirit of
nitre, E a particle of salt of tartar, contiguous to two of
the particles of spirit of nitre, b and c ; and suppose
the particle E is impelled by any motion towards d, so as
to roll about the particle c till it touch the particle d, the
particle b adhering more firmly to E than to a, will be
forced off from A ; and by the same means the particle e,
as it rolls about A, will tear off the rest of the saline par-
ticles from A one after another, till it has got them all,
or almost all, about itself. And when the metallic par-
ticles are thus divested of the nitrous ones, which, as a
mediator between them and the water, held them floating ^^^ ^'

in it, the alcalizate ones, crowding for the room the metallic ones took up
before, will press these towards one another, and make them come more
easily together : so that by the motion they continually have in the water,
they shall be made to strike on one another ; and then, by means of the
principle in the second supposition, they will cohere and grow into clus-
VOL. I. 2 B

386 LIFE OF SIR ISAAC NEWTON. APPENDIX

ters, and fall down by their weight to the bottom, which is called pre-
cipitation. In the solution of metals, when a particle is loosing from the
body, so soon as it gets to that distance from it, where the principle of
receding described in the fourth and fifth supposition begins to overcome
the principle of acceding, described in the second supposition, the receding
of the particle will be thereby accelerated ; so that the particle shall, as it
were, with violence leap from the body, and putting the liquor into a brisk
agitation, beget and promote that heat we often find to be caused in solu-
tions of metals. And if any particle happen to leap off" thus from the
body, before it is surrounded with water, or to leap off with that smart-
ness as to get loose from the water, the water, by the principle in the
fourth and fifth suppositions, will be kept oft" from the particle, and stand
round about it, like a spherically hollow arch, not being able . to come to
a full contact with it any more ; and several of these particles afterwards
gathering into a cluster, so as by the same principle to stand at a distance
from one another, without any water between them, will compose a bub-
ble. Whence I suppose it is, that in brisk solutions there usually happens
an ebullition. This is one way of transmuting gross compact substance
into aerial ones. Another way is by heat ; for as fast as the motion of
heat can shake off" the particles of water from the surface of it, those par-
ticles, by the said principle, will float up and down in the air, at a distance
both from one another, and from the particles of air, and make that sub-
stance we call vapour. Thus I suppose it is, when the particles of a body
are very small (as I suppose those of water are), so that the action of heat
alone may be sufficient to shake them asunder. But if the particles be
much larger, they then require the greater force of dissolving menstruums
to separate them, unless by any means the particles can be first broken
into smaller ones. For the most fixed bodies, even gold itself, some have
said, will become volatile, only by breaking their parts smaller. Thus
may the volatility and fixedness of bodies depend on the diff'erent sizes of
their parts. And on the same difference of size may depend the more or
less permanency of aerial substances, in their state of rarefaction. To
understand this, let us suppose a B c D to
be a large piece of any metal, E F G H the
limit of the interior uniform aether, and K
a part of the metal at the superficies a b.
If this part or particle K be so little that it
reaches not to the limit E F, it is plain that
the aether at its centre must be less rare
than if the particle were greater ; for
were it greater, its centre would be further
from the superficies A B, that is, in a place
where the gether (by supposition) is rarer ;
ri«- 5. the less the particle K therefore, the denser

the sether at its centre ; because its centre comes nearer to the edge A B,
where the aether is denser than within the limit E F g h. And if the par-
ticle were divided from the body, and removed to a distance from it, where
the fether is still denser, the sether within it must proportionally grow
denser. If you consider this, you may apprehend how, by diminishing the
particle, the rarity of the «ther within it will be diminished, till between
the density of the aether without, and the density of the aether within it,

NO. II. LIFE OF SIR ISAAC NEWTON. 387

there be little difference ; that is, till the cause be almost taken away,
which should keep this and other such particles at a distance from one
another. For that cause explained in the fourth and fifth suppositions, was
the excess of density of the external aether above that of the internal.
This may be the reason then why the small particles of vapours easily
come together, and are reduced back into water, unless the heat, which
keeps them in agitation, be so great as to dissipate them as fast as they
come together ; but the grosser particles of exhalations raised by fermenta-
tion keep their aerial form more obstinately, because the aether within them
is rarer.

" Nor does the size only, but the density of the particles also, conduce
to the permanency of aerial substances ; for the excess of density of the
aether without such particles above that of the aether within them is still
greater ; which has made me sometimes think that the true permanent air
may be of a metallic original ; the particles of no substances being more
dense than those of metals. This, I think, is also favoured by experience,
for I remember I once read in the Philosophical Transactions, how M.
Huygens at Paris, found that the air made by dissolving salt of tartar
would in two or three days' time condense and fall down again, but the
air made by dissolving a metal continued without condensing or relenting
in the least. If you consider then, how by the continual fermentations
made in the bowels of the earth there are aerial substances raised out of
all kinds of bodies, all which together make the atmosphere, and that of
all these the metallic are the most permanent, you will not perhaps think
it absurd, that the most permanent part of the atmosphere, which is the
true air, should be constituted of these, especially since they are the
heaviest of all other, and so must subside to the lower parts of the atmos-
phere and float upon the surface of the earth, and buoy up the lighter ex-
halations and vapours to float in greatest plenty above them. Thus, I say,
it ought to be with the metallic exhalations raised in the bowels of the
earth by the action of acid menstruums, and thus it is with the true per-
manent air ; for this, as in reason it ought to be esteemed the most pon-
derous part of the atmosphere, because the lowest, so it betrays its
ponderosity by making vapours ascend readily in it, by sustaining mists
and clouds of snow, and by buoying up gross and ponderous smoke. The
air also is the most gross unactive part of the atmosphere, affording living
things no nourishment, if deprived of the more tender exhalations and
spirits that float in it ; and what more unactive and remote from nourish-
ment than metallic bodies ?

" I shall set down one conjecture more, which came into my mind now
as I was writing this letter ; it is about the cause of gravity. For this end
I will suppose aether to consist of parts differing from one another in stbb-
tilty by indefinite degrees ; that in the pores of bodies there is less of the
grosser aether, in proportion to the finer, than in open spaces ; and con-
sequently, that in the great body of the earth there is much less of the
grosser aether, in proportion to the finer, than in the regions of the air ;
and that yet the grosser aether in the air affects the upper regions of the
earth ; and the finer aether in the earth the lower regions of the air, in such
a manner, that from the top of the air to the surface of the earth, and
again from the surface of the earth to the centre thereof, the aether is in-
sensibly finer and finer. Imagine now any body suspended in the air, or

388 LIFE OF SIR ISAAC NEWTON. APPENDIX

lying on the earth, and the gether being by the hypothesis grosser in the
pores, which are in the upper parts of the body, than in those which are in
its lower parts, and that grosser aether being less apt to be lodged in those
pores than the finer aether below, it will endeavour to get out and give
way to the finer aether below, which cannot be, without the bodies descend-
ing to make room above for it to go out into.

" From this supposed gradual subtilty of the parts of aether some things
above might be further illustrated and made more intelligible ; but by
what has been said, you will easily discern whether in these conjectures k
there be any degree of probability, which is all I am at. For my own
part, I have so little fancy to things of this nature, that had not your en-
couragement moved me to it, I should never, I think, have thus far set pen
to paper about them. What is amiss, therefore, I hope you will the more
easily pardon in

" Your most humble servant and honourer,

" Isaac Newton.

" Cambeidgk, Feb. 28, 1678-9."

No. III.

{Referred to in page 190.)

The following is an accurate copy of the large drawing of a sheep's eye,
as mentioned in the text, and of the manuscript which accompanied it.

" 1. Ellipsis A X T T talis est ut parallel, (ad medium inter vitrum et
aquam medium refractos projiciat in z).

2. s z est fere ^ a s.

3. Retinas superficies piano duplo magis quam superficies
utravis crystallini.

4. Crystallini superficies anterior ^osteriore plenius est.

5. Convexitatis corneae et araneae fere commune centrum est ... .

6. Centrum anterioris araneae istis aliquanto inferior habetur. 2 r z est
i a B.

A T : X Y : : 25 : 18 (: : 7 : 5 proxime.)

e R : TT ^ : : 83 : 101 (: : 23 : 28 : : 9 : 11 pr.)

PR: f^: : 9 : 8.

ar: ^7r::13: 12.^

A T : E B.

AE : EB.

A B : A B.

B S : A R.

I commune centrum curvaturae tunicarum ad A, B, et R.'

I A : I R : : 13 : 21.

IB :ir: :19 : 36 (: : 1 : 2 fere.)

fp: te.

1 This is obviously a mistake.

LIFE OF SIR ISAAC NEWTON.

389

The dimensions of this figure, taken from a sheep's eye, are as fol-
loweth : —

By Experiment.

AS =

975.

/.5 =

1025.

AB =

52.

RS =

60.

e5 =

16.

a7 =

686.

A^ =

196.

FO =

429.

VW =

530.

HO =

248.

The angle ¥ v o about 160 degrees.

vow is a circle whose radius is G o = 265 ; and i a = 350, i B = 298,
r R = 565, and i f = 307, are the radii of spheres so much concave or con-
vex as the surfaces of the homy tunic a a 7, w b 0, of the retina ^ R tt,

390 LIFE OF SIR ISAAC NEWTON. APPENDIX

and of the exterior aranea v f w, at their vertices a, b, r, f. Lastly,
A a tr = 968 = arcui a 7 r.

By Deditction.

A T = 1350 = 2 a Q, and X Y = 972.

E R = 816 = 2mR, and Ai S = 993.

E p = 481 = 2 F K, and t& = 542.

AndAZ = 1143. The said lines at, xt, ee, &c., being the right and

transverse axes of the ellipses AaxTY7, e^rtt, and F f p w, and z the

exterior focus of a a t 7.

I was prevented by an accident from taking the distance of the crystal-
line humour from the homy tunic, which I would gladly have done to
have had the conformity of all the parts one to another in one and the
same eye ; but by all circumstances 'tis near the truth' to make a H = 340,
or A F = 159. I have made the same centre i to both the horny and network
tunic, they happening to be very near together. But I am apt to suspect
that it is somewhat too remote from the cornea by reason of the difficulty
of measuring the least convexity of the cornea, or the greatest convexity of
the retina. Perhaps it may not be amiss to make I a = 344, I R = 571, and
the point h (since it is so near it) coincident with i."

No. IV.

(Referred to in page 192.)

LETTER FROM NEWTON TO DR. WILLIAM BRIGGS.^

" For his Hon^ ffriend D' W™ Briggs.

" Though I am of all men grown y* most shy of setting pen to paper
about any thing that may lead into disputes yet yo'' friendship overcomes
me so far as y* I shall set down my suspicions about yo' Theory, yet on
this condition, that if I can write but plain enough to make you under-
stand me, I may leave all to yo"" use w**>out pressing it further on. For I
designe not to confute or convince you but only to present & submit my
thoughts to yo' consideration & judgment.

*' First then it seems not necessary that the bending of ye nei-ves in y«
Thalamus opticus should cause a differing tension of ye fibres, ffor those
weh have ye further way about, will be apt by nature to grow the longer.
If ye arm of a tree be grown bent it follows not that the fibres on y* elbow
are more stretcht then those on the concave side, but that they are longer.
And if a straight arm of a tree be bent by force for some time, the fibres
on y« elbow w«h were at first on ye stretch will by degrees grow longer &
1 Edlestou's Correspondence, &c., p. 265,

NO. IV. LIFE OF SIR ISAAC NEWTON. 391

longer till at length the arm stand of it's self in ye bended figure it was at
first by force put into, that is till y^ fibres on y^ elbow be grown as much
longer then ye rest as they go further about, & so have but the same degree
of tension w*^^ them. The observation is ordinary in twisted Codling
hedges, fruit trees nailed up against a wall &c. And ye younger & more
tender a tree is the sooner will it stand bent. How mifch more therefore
ought it to be so in that most tender substance of ye Optick nerves wei'
grew bent from ye very beginning? And whether if those nerves were
carefully cut out of ye brain & outward coat & put into brine made as
neare as could be of the same specific gravity -w*-^ ye nerves, they would
unbend or exactly keep the same bent they had in ye brain may be worth
considering, ffor though ye strength of a single fibre upon the stretch be
inconsiderably little, yet all together ought to have as much strength to
unbend y« nerve, as would suffice by outward application of ye hand to
bend a straight nerve of ye same thickness, the dura Mater being taken oft".

" Mr Sheldrake further suggests wittily that an object whether the axis
opticus be directed above it, under it, or directly towards it, appears in all
cases alike as to figure & colour excepting that in ye S'^ case tis distincter,
w* proceeds not from ye frame of ye nerves but from ye distinctness of ye
picture made in ye Retina in that case. But in ye first case where ye vision
is made by ye fibres above & second where tis made by those below, the
object appearing alike : he thinks it argues that the fibres above & below
are of ye same constitution & tension, or at least if they be of a differing
tension, that that tension has no effect on ye mode of vision, but I under-
stand you are already made acquainted w^^ his thoughts.

" It may be further considered that the cause of an objects appearing
one to both eyes is not its appearing of ye same colour form & bigness to
both, but in ye same situation or place. Distort one eye & you will see ye
coincident images of ye object divide from one another & one of them re-
move from ye other upwards downwards or sideways to a greater or less
distance according as ye distortion is ; & when the eyes are let return to
their natural posture the two images advance towards one another till they
become coincident & by that coincidence appear but one. If we would
then know why they appear but one, we must e[n]quire why they appear
in one & ye same place & if we would know ye cause of that we must
enquire why in other cases they appear in divers places variously situate
& distant one from another, ffor that w*^*^ can make their distance greater
or less can make it none at all. Consider whats the cause of their being
in ye same altitude when one is directly to ye right hand ye other to ye left
& what of their being in ye same coast or point of ye compas, when one is
directly over ye other : these two causes joyned will make them in ye same
altitude & coast at once that is in ye same place. The cause of situations
is therefore to be enquired into. Now for finding out this ye analogy will
stand between ye situations of sounds & the situations of visible things, if
we will compare these two senses. But the situations of sounds depend
not on their tones. I can judge from whence an echo or other sound comes
tho I see not ye sounding body, & this judgment depends not at all on ye
tone. I judge it not from east because acute, from west because grave :
but be ye tone what it will I judge it from hence or thence by some other
principle. And by that principle I am apt to think a blind man may dis-
tinguish unisons one from another when ye one is on his right hand ye

392 LIFE OF SIR ISAAC NEWTON. APPENDIX

other on his left. And were our ears as good & accurate at distinguishing
ye coasts of audibles as our eyes are at distinguishing y« coasts of visibles
I conceive we should judge no two sounds the same for being unisons
unless they came so exactly from y* same coast as not to vary from one
another a sensible point in situation to any side. Suppose then you had
to do with one of so accurate an ear in distinguishing y^ situation of
sounds, how would you deale with him ? Would you tell him that you
heard all unisons as but one sound ? He would tell you he had a better
ear than so. He accounted no sounds ye same wci» differed in situation : &
if yoixr eyes were no better at ye situation of things then your ears, you
would perhaps think all objects ye same, v,'^^ were of ye same colour. But
for his part he found y* ye like tension of strings & other sounding bodies
did not make sounds one, but only of ye same tone : & therefore not
allowing the supposition that it does make them one, the inference from
thence that ye like tension of ye optick fibres made ye object to ye two
eyes appeare one, he did not think himself obliged to admit. As he found
y* tones depended on those tensions so perhaps might colours, but the
situation of audibles depended not on those tensions, & therefore if the
two senses hold analogy with one another, that of visibles does not, & con-
sequently the union of visibles as well as audibles which depends on the
agreement of situation as well as of colour or tone must have some other
cause.

" But to leave this imaginary disputant, let us now consider what may
be ye cause of ye various situations of things to ye eyes. If when we look
wth one eye it may be asked why objects appear thus & thus situated one
to another the answer would be because they are really so situated among
themselves & make their coloured pictures in ye Retina so situated one to
another as they are & those pictures transmit motional pictures into ye sen-
sorium in ye same situation & by the situation of those motional pictures
one to another the soul judges of ye situation of things withou.t. In like
manner when we look with two eyes distorted so as to see ye same object
double if it be asked why those objects appeare in this or that situation &
distance one from another, the answer should be because through ye two
eyes are transmitted into ye sensorium two motional pictures by whose
situation & distance then from one another the soule judges she sees two
things so situate & distant. And if this be true then the reason why when
the distortion ceases & ye eyes return to their natural posture the doubled
object grows a single one is that the two motional pictures in ye sensorium
come together & become coincident.

"But you will say, how is this coincidence made ? I answer, what if I
know not ? Perhaps in ye sensorium, after some such way as ye Cartesians
would have beleived or by some other way. Perhaps by ye mixing of ye
marrow of ye nerves in their juncture before they enter the brain, the fibres
on ye right side of each eye going to ye right side of ye head those on ye
left side to ye left. If you mention ye experim* of ye nerve shrunck all
ye way on one side ye head, that might be either by some unkind juyce
abounding more on one side ye head y^ on ye other, or by ye shrinking of
ye coate of ye nerve whose fibres & vessels for nourishment perhaps do not
cross in ye juncture as ye fibres of ye marrow may do. And its more pro-
bable y*^ ye stubborn coate being vitiated or wanting due nourishment
shrank and made ye tender marrow yeild to its capacity, than that ye ten-

NO. IV. LIFE OF SIR ISAAC NEWTON. 393

der marrow by shrinking should make ye coate yeild. I know not whether
you would have y^ succus niitriciiis run along y® marrow. If you would,
'tis an opinion not yet proved & so not fit to ground an argument on. If
you say yt in ye Camselion & ffishes ye nerves only touch one another with-
out mixture & sometimes do not so much as touch ; 'Tis true, but makes
altogether against you. flfishes looke one way with one eye ye other way
with ye other : the Chamoelion looks up w'^* one eye, down w'*» t'other, to
ye right hand w'^ this, to ye left w*'^ y', twisting his eyes sevei'ally this way
or that way as he pleases. And in these Animals which do not look ye
same way w''^ both eyes what wonder if ye nerves do not joyn ? To make
them joyn would have been to no purpose & nature does nothing in vain.
But then whilst in these animals where tis not necessary they are not
joyned, in all others we^ look ye same way w^^ both eyes, so far as I can
yet learn, they are joyned. Consider therefore for what reason they are
joyned in ye one & not in the other, ffor God in ye frame of animals has
done nothing w^^out reason.

" There is one thing more comes into my mind to object. Let ye circle
2) / represent the Ketina, or if you will
the end of ye optick nerve cut cross. A
the end of a fibre above of most ten-
sion, C ye end of one below of least ten-
sion. JJ & G ye ends of fibres above on
either hand almost of as much tension as
A, F k J the ends of others below almost
of as little tension as C. E ye end of a fibre
of less tension then A or G k of more then
C or. /. And between AkC, GkJ there
will [be] fibres of equal tension \f^^ E be-
cause between them there are in a con-
tinual series fibres of all degrees of tension
between ye most tended at ^ & 6r & least
tended at C k J. And by the same argu-
ment that 3 fibres E, B k H of like ten-
sion are noted let the whole line of fibres of the same Degree of tension
running from E to H be noted. Do you now say y* ye reason why an ob-
ject seen w'li two eyes appears but one is that ye fibres in ye two eyes by
wei» 'tis seen are unisons ? then all objects seen by unison fibres must for
ye same reason appear in one & ye same place that is all ye objects seen by
the line of fibres E B H running from one side of the eye to ye other. ff"or
instance two stars one to ye right hand seen by ye fibres about H, the other
to ye left seen by ye fibres about E ought to appear but one starr, & so of
other objects. ff"or if consonance unite objects seen w'^ the fibres of two
eyes much more will it unite those seen w*''» those of ye same eye. And yet
we find it much otherwise. What soever it is that causes the two images
of an object seen with both eyes to appear in ye same place so as to seem
but one can make them upon distorting ye eyes separate one from ye other
& go as readily & as far asunder to ye right hand & to ye left as upwards
& downwards.

" You have now ye summ of what I can think of worth objecting set
down in a tumultuary way as I could get time from my Sturbridge ffair
friends. If I have any where exprest myself in a more peremptoiy way

394 LIFE OF SIR ISAAC NEWTON.

APPENDIX

then becomes y* weaknes of y® argument pray look on that as done not in
earnestness but for ye mode of discoursing. Whether any thing be so ma-
terial as yt it may prove any way useful to you I cannot tell. But pray
accept of it as written for that end. flFor having laid Philosophical specula-
tions aside nothing but ye gratification of a friend would easily invite me to
so large a scribble about things of this nature.

" S-- I am

" Yo' humble Servant

" Trin. Coll. Cambr. Sept. 12th. i682. Is. Newton."'

No. V.

{Referred to in page 195.)

[This letter is prefixed to the Latin version of Briggs' Theory of Vision,
Lond. 1685, which was made at Newton's request, and must have been
intended as a recommendation of that work as well as of his Ophihalmo-
graphia.']

" Isaacus Newtonus Doctori Gulielmo Briggio.

" Vir Clarissime,
" Hisce tuis Tractatibus* duas magni nominis scientias uno opere pro-
moves, Anatomiam dico & Opticam. Organi enim (in quo utraque versatur)
artificio summo constructi diligenter perscrutaris mysteria. In hujus dis-
sectione peritiam & dexteritatem tuam non exiguo olim mihi oblectamento
fuisse recordor. Musculis motoi'iis secundum situm suum naturalem ele-
ganter a te expansis, ca^terisque partibus coram expositis, sic ut singularum
usus & ministeria non tam intelligere liceret quam cernere, eflfeceret dudum
ut ex cultro tuo nihil non accuratum sperarem. Nee spem fallebat eximius
ille Tractatus Anatomicus, quem postmodum edidisti. Jam praxeos hujus
OLKpi^eiav pergis ingeniosissima Theoria instruere & exornare. Et quis The-
oriis condendis aptior extiterit, quam qui phsenomenis accurate observandis
navarit operam ? Nervos opticos ex capillamentis varii tensis constare sup-
ponis, eaque magis esse tensa qute per iter longius porriguntur ; ex diversS,
autem tensione fieri ut objectorum partes singulge non coincidant & confun-
dantur inter se, sed pro situ suo naturali diversis in locis appareant ; &
capillamentis amborum oculorum aequali tensione factis concordibiis, gemi-
nas objectorum species uniri. Sic ex tensione chordarum, qua soni vel
variantur vel concordant in MusicS,, colligere videris quid fieri debet in
Optica. Simplex etenim est Natura, & eodem operandi tenore in immensa

1 From the original in the British Museum, Add. MSS. 4237, fol. 34.

2 i.e., Ophthahnographia, Cantab. 1676 (2d edit. Lond. 1687), and his Theory of
Vision.

NO. VI. LIFE OF SIR ISAAC NEWTON. 395

effectuum varietate sibi ipsa constare solet. Quanto vero magis in sensuum
cognatorum causis ? Et quamvis aliam etiam horum sensuum analogiam
suspicari possim, ingeniosam tamen esse quam tute excogitasti, certe nemo
non lubenter fatebitur. Nee inutilem censeo Dissertationem ultimam qua
diluis objectiones. Inde Lector attentus & plenius intelliget Hypothesin
totam, & in qusestiones incidet vel tuis Meditationibus illnstratas, vel novis
experimentis & disquisitionibus posthac dirimendas. Id quod in usum
cedet juventuti Academicae, & provectiores ad ulteriores in Philosophia
progressus manuducet. Pergas itaque, vir ornatissime, scientias hasce
praeclaris inventis, uti facis, excolere ; doceasque difficultates causarum
naturaliam tarn facile solertia vinci posse, quam solent conatibus vulgari-
bus difficulter cedere.

" Vale.'-
" Dabam Cantabrigice 7 Kal. Mail.
1685.'-"

No. VI.

{Referred to in page 197.)

Newton's Fifteenth Query. '

Abe not the species of objects seen with both eyes united where the
optic nerves meet before they come into the brain, the fibres on the right
side of both nerves uniting there, and, after union, going thence into the
brain in the nerve which is on the right side of the heart ; and the fibres on
the left side of both nerves uniting in the same place, and, after union,
going into the brain in the nerve which is on the left side of the head, and
these two nerves meeting in the brain, in such a manner that their fibres
make but one entire species or picture, half of which on the right side of
the sensorium, comes from the right side of both eyes through the right
side of both optic nerves, to the place where the nerves meet, and from
thence on the right side of the head into the brain ; and the other half on
the left side of the sensorium comes in like manner from the left side of
both eyes. For the optic nerves of such animals as look the same way
with both eyes (as of men, dogs, sheep, oxen, &c.), meet before they come
into the brain, but the optic nerves of such animals as do not look the
same way with both eyes (as of fishes and of the chameleon) do not meet,
if I am rightly informed.

No. VII.

{Referred to in page 197.)

Although we have extracted a part of this document in the text, for the
sake of illustration, we shall give the whole of it as published by Mr.
Harris.

1 Optics, 3d edit. 1T21, pp. 320, 321.

396

LIFE OF SIE ISA.AC NEWTON.

Description of the Optic Nerves and their Juncture in the
Brain, by Sir Isaac Newton.*

" The tunic retina grows not from the sides of the optic nerve (as the
other two which rise one from the dura, tlie other from the pia mater), but
it grows from the middle of the nerve, sticking to it all over the extremity
of its marrow. Which marrow, if the nerve be any where cut cross-wise
betwixt the eye and the union of the nerves, appears full of small spots or
pimples, which are a little prominent, especially if the nerve be pressed, or
warmed at a candle ; and these shoot into the very eye, and may be seen
within side, where the retina grows to the nerve ; and they also continue
to the very juncture E F g H. But at the juncture they end on a sudden
into a more tender white pap, like the anterior part of the brain ; and so
the nerve continues after the juncture into the brain filled Avith a white
tender pap, in which can be seen no distinction of parts as betwixt the
said juncture and the eye.

"Now I conceive that every point in the retina of one eye, hath its cor-
respondent point in the other ; from which two very slender pipes filled
with a most limpid liquor do, without either interruption or any other un-
evenness or irregularity in their process, go along the optic nerves to the

1 The original of this drawing and description I found at Hurtzbourne Park in a
manuscript "book without one of its boards, p. 17.

NO. VII. LIFE OF SIR ISAAC NEWTON. 397

juncture E F G H, where they meet either betwixt G F or F H, and there unite
into one pipe as big as both of them ; and so continue in one, passing either
betwixt I L or M K, into the brain, where they are terminated perhaps at
the next meeting of the nerves betwixt the cerebrum and cerebellum, in the
same order that their extremities were situated in the retina's. And so
there are a vast multitude of these slender pipes which flow from the brain,
the one half through the right side nerve i L, till they come at the juncture
G p, where they are each divided into two branches, the one passing by G
and T to the right side of the right eye A B, the other half shooting through
the space E F, and so passing by x to the right side of the left eye a jS.
And in like manner the other half shooting through the left side nerve
M K, divide themselves at F h, and their branches passing by E v to the
right eye, and by H Y to the left, compose that half of the retina in both
eyes, which is towards the left side c D and y 5.

" Hence it appears, 1. Why the two images of both eyes make but one
image ahcdm the brain.

" 2. Why, when one eye is distorted, objects appear double ; for if the
image of any object be made upon a in the one eye, and j3 in the other,
that object shall have two images in the brain at a and h- Therefore the
pictures of any object ought to be made upon the corresponding points of
the two retinas ; if upon A in the right eye, then upon a in the left ; if
upon B, then also upon /3. And so shall the motions concur after they
have passed the juncture G H, and make one image at a or 6 more vivid
than one eye alone could do.

" 3. Why, though one thing may appear in two places by distorting the
eyes, yet two things cannot appear in one place. If the picture of one
thing fall upon A, and of another upon a, they may both proceed to p, but
no farther ; they cannot both be carried on the same pipes p a into the
brain ; that which is strongest or most helped by phantasy will there pre-
vail, and blot out the other.

" 4. Why, if one of the branches of the nerve beyond the juncture, as at
G F or F H, should be cut, that half of both eyes towards the wounded
nerve would be blind, the other half remaining perfect.

" 5. Why the juncture is almost as broad again betwixt G and H, as be-
tween E and F ; because all the tubuli of both eyes pass between G and H,
and but half of them betwixt E and F.

" 6. Why the nerve G i L F buts not directly upon the nerve x E H Y, but
deviates a little towards T v ; because its tubuli are to pass only into that
side of the nerve E H x Y towards E x. The like of F M K H.

" 7. Why the marrow of the nerve T v E G grows soft on a sudden, when
it comes at the juncture E F, and more suddenly on that side towards G
than towards E. And the like of the nerve E x y H : For it being necessary
that the nerve T v E G should be stretched and bended several ways by the
motion of the eye ; therefore the tubuli are involved or wrought up within
the substances of several tough skins, which, being folded up together,
compose the marrow of the nerve pretty solid and flexible, lest the tubuli
should be prejudiced by the several motions of the nerve. And those
small pimples or prominencies which appear in the nerve cut crosswise, I
conceive to be made by the foldings of those crasser skins. But the nerve
at the juncture E G F H, being well guarded from all violence and motion
by the bones into which it is closely adapted ; 'tis not necessary the said
membraneous substance should be continued any farther than E g ; there-

398 LIFE OF SIR ISAAC NEWTON. APPENDIX

fore the tubuli there ou a sudden unsheath themselves, that those on the
inner side of the nerves towards v E and x E may severally cross 'twixt E F,
and be united with their correspondents on the other sides yh and T G.
Now, because the inner tubuli must first cross, before they can concur with
the outmost tubuli of the opposite nerve ; hence it is, that the nerves grow
soft sooner on the inner side at E, than on the outer side at G and H.

" 8. Why the two nerves meet a second time in the brain : because the
two half images carried along i L and M K may be united in one compleat
image, in the sensory. Note, that the nerves at their meeting, are round
about disjoined from the rest of the brain ; nor are they so thick there, as
a little before their meeting. But by their external figure, they seem as if
the capillamenta concentered like the radii of a hemisphere to a point in
the lower part of the juncture. And 'tis probable that the visive faculty
is there : for else why do the nerves swell there to so great a bulk, as it
were preparing for their last office ? Why do they run directly cross from
either side the brain to meet there, if the design was to have the motions
conveyed by the shortest cut from the eye to the sensorium, before they
grew too weak. If they were to proceed farther, they might have gone a
shorter cut, and in a less channel. There is indeed a marrow shoots from
under them towards the cerebellum, to which they are united ; but the
greatest part of their substance, if not all of it, lies above this marrow,
and also shoots cross beyond it to the centre of the brain, where they meet.
Lastly, the substance here is most pure, the situation in the midst of the
brain, constituting the upper part of that small passage 'twixt all the ven-
tricles, where all superfluous humours have the greatest advantage to slide
away, that they may not incumber that precious organ.

" Light seldom strikes upon the parts of gross bodies (as may be seen in
its passing through them) ; its reflection and refraction is made by the di-
versity of aethers ; and therefore its efi"ect upon the retina can only be to
make this vibrate : which motion then must be either carried in the optic
nerves to the sensorium, or produce other motions that are carried thither.
Not the latter, for water is too gross for such subtile impressions ; and as
for animal spirits, tho' I tied a piece of the optic nerve at one end, and
Avarmed it in the middle, to see if any airy substance by that means would
disclose itself in bubbles at the other end, I could not spy the least bubble ;
a little moisture only, and the marrow itself squeezed out. And indeed
they that know how difficultly air enters small pores of bodies, have rea-
son to suspect that an airy body, tho' much finer than air, can pei-vade and
without violence (as it ought to do) the small pores of the brain and nerves,
I should say of water ; because those pores are filled with water : and if it
could, it would be too subtile to be imprisoned by the dura mater and
skull, and might pass for cether. However, what need of such spirits?
Much motion is ever lost by communication, especially betwixt bodies of
different constitutions. And therefore it can no way be conveyed to the
sensorium so entirely, as by the aether itself. Nay, granting me, but that
there are pipes filled with a pure transparent liquor passing from the eye
to the sensorium, and the vibrating motion of the aether will of necessity
run along thither. For nothing interrupts that motion but reflecting sur-
faces ; and therefore also that motion cannot stray through the reflecting
surfaces of the pipe, but must run along (like a sound in a trunk) entire to
the sensorium. And that vision thus made, is very conformable to the
sense of hearing, which is made by like vibrations. "

NO. VIII. LIFE OF SIR ISAAC NEWTON. 399

No. VIII.

{Referred to in page 269, as No. IX. )

The interesting correspondence between Halley and Newton, consisting
of fifteen letters, which, with the exception of one given in Chap. XVI.,
Vol. II., we give in this Appendix, forms an essential part of the History
of the Principia, and throws much light on the personal character of
Newton. The eight letters, Nos. 1, 3, 4, 5, 6, 8, 10, and 11, having been pre-
served in the archives of the Eoyal Society, were published in their entire
state by my late amiable and learned friend. Professor Rigaud of Oxford,
in the Appendix to his interesting volume, entitled Historical Essay on
the First Publication of the Principia. ^ The greater number of them had
been printed in a garbled and imperfect state by the authors of the articles
Halley, Hooke, and Newton, in the General Dictionary and in the Bio-
graphia Britannica, and therefore Mr. Rigaud had them carefully copied
from the guard-book of the Royal Society. At the end of each letter he
has mentioned the parts that have been omitted, and the changes that
have been made upon it in the diflerent works where it has been used.
We have adopted these important notes of Mr. Rigaud.

The other six letters, Nos. 2, 7, 9, 12, 13, and 14, which, with the one
already referred to, complete the correspondence, were found among the
Newtonian papers in the possession of the Earl of Portsmouth, and are
now printed for the first time.

1.— Halley to Newton.

" May 22, 1686.

" Sir,
'' Your incomparable treatise, entitled Philosophiae Naturalis Principia
Mathematica, was by Dr. Vincent presented to the Royal Society on the
28th past ; and they were so very sensible of the great honour you do them
by your dedication, that they immediately ordered you their most hearty
thanks, and that a council should be summoned to consider about the
printing thereof ; but by reason of the president's attendance upon the
King, and the absence of our vice-presidents, whom the good weather has
drawn out of town, there has not since been any authentic council to resolve
what to do in the matter : so that on Wednesday last the Society, in their
meeting, judging that so excellent a work ought not to have its publica-
tion any longer delayed, resolved to print it at their own charge in a large
quarto of a fair letter ; and that this their resolution should be signified to
you, and your opinion therein be desired, that so it might be gone about
with all speed. I am intrusted to look after the printing it, and will take
care that it shall be performed as well as possible ; only I would first have
your directions in what you shall think necessary for the embellishing
thereof, and particularly whether you think it not better that the schemes
1 Oxford, 1838.

400 LIFE OF SIR ISAAC NEWTON. APPENDIX

should be enlarged, which is the opinion of some here : but what you
signify as your desire shall be punctually observed.

"There is one thing more that I ought to inform you of, viz., 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 should make some mention of him in
the preface, which 'tis possible you may see reason to prefix. I must beg
your pardon, that 'tis I that send you this ungrateful account ; but I
thought it my duty to let you know it, that so you might act accordingly,
being in myself fully satisfied, that nothing but the greatest candour
imaginable is to be expected from a person, who has of all men the least
need to borrow reputation."

The following paragraph and conclusion of the letter, taken from the
original, did not exist in any of the previously printed copies of it.

"When I shall have received your directions, the printing shall be
pushed on with all expedition, which, therefore, I entreat you to send me
as soon as may be. You may please to direct to me, to be left with Mr.
Hunt at Gresham College, and your line will come to the hands of,

"Sir,
"Your most afiectionate humble servant,

"Edm. Halley."

" This letter was printed from the copy in the Letter Book of the Royal
Society (Supplement, vol. iv. p. 340), by Birch, in his History of the
Royal Society (vol. iv. p. 484). It is also printed in the Biographia
Britannica (vol. v, p. 322o)."

2.— Halley to Newton.

" London, June 7, 1686.
" Sir,
" I here send you a proof of the first sheet of your book, which we think
to print on this paper, and in this character ; if you have any objection, it
shall be attended to : and if you approve it, we will proceed ; and care
shall be taken that it shall not be published before the end of Michaelmas
term, since you desire it. I hope you Avill please to bestow the second
part, or what remains of this, upon us as soon as you shall have finished it,
for the application of this mathematical part to the system of the world, is
what will render it acceptable to all naturalists, as well as mathematicians ;
and must advance the sale of the book. Pray, please to revise this proof,
and send it me up with your answer. I have already corrected it, but can-
not say I have spied all the faults. When it has passed your eye, I doubt
not but it will be clear from errata. The printer begs your excuse of the
diphthongs, Avhich are of a character a little bigger, but he has some a cast-
ing of the just size. This sheet being a proof, is not so clear as it ought to
be ; but the letter is new, and I have seen a book of a very fair character.

NO. VIII. LIFE OF SIR ISAAC NEWTON. 401

which was the last thing printed from this set of letter ; so that I hope the
Edition may in that particular be to yonr satisfaction. — I am, Sir,
" Your most affectionate humble servant,

" E. Halley.

" Please to send by the coach, directed to me, to be left with Mr. Hunt,
at Gresham College.

^' To his honoured Friend,
Mr. Isaac Newton,
at his Chamber in Trinity College,

Cambridge."

3.— Newton to Halley.

''Sir,
" In order to let you know the case between Mr. Hooke and me, I gave
you an account of what passed between xis in our letters, so far as I could
remember ; for, 'tis long since they were writ, and I do not know that I
have seen them since. I am almost confident by circumstances, that Sir
Chr. Wren knew the duplicate proportion when I gave him a visit ; and
then Mr. Hooke (by his book Cometa written afterwards) will prove the
last of us three that knew it. I intended in this letter to let you under-
stand the case fully ; but it being a frivolous business, I shall content my-
self to give you the heads of it in short, viz., that I never extended the
duplicate proportion lower than to the superficies of the earth, and before
a certain demonstration I found the last year, have suspected it did not
reach accurately enough down so low ; and therefore in the doctrine of
projectiles never used it nor considered the motions of the heavens ; and
consequently Mr. Hooke could not from my letters, which were about
projectiles and the regions descending hence to the centre, conclude me
ignorant of the theory of the heavens. That what he told me of the dupli-
cate proportion was erroneous, namely, that it reached down from hence
to ,tlie centre of the earth. That it is not candid to require me now to
confess myself, in print, then ignorant of the duplicate proportion in the
heavens ; for no other reason, but because he had told it me in the case of
projectiles, and so upon mistaken grounds accused me of that ignorance.
That in my answer to his first letter I refused his correspondence, told him
I had laid philosophy aside, sent him only the experiment of projectiles
(rather shortly hinted than carefully described), in compliment to sweeten
my answer, expected to hear no further from him ; could scarce persuade
myself to answer his second letter ; did not answer his third, was upon
other things ; thought no further of philosophical matters than his letters
put me upon it, and therefore maybe allowed not to have had my thoughts
of that kind about me so well at that time. That by the same reason he
concludes me then ignorant of the rest of the duplicate proportion, he may
as well conclude me ignorant of the rest of that theory I had read before
in his book. That in one of my papers writ (I cannot say in what year,
but I am sure some time before I had any correspondence with Mr. Olden-
burg, and that's) above fifteen years ago, the proportion of the forces of
VOL. I. 2 c

402 LIFE OF SIR ISAAC NEWTON. APPENDIX

the planets from the sun, reciprocally duplicate of their distances from
him, is expressed, and the proportion of our gravity to the moon's conatus
recedendi a centro terrae is calculated, though not accurately enough.
That when Hugenius put out his Horol. Oscil. , a copy being presented to me,
in my letter of thanks to him, I gave those rules in the end thereof a par-
ticular commendation for their usefulness in Philosophy, and added out of
my aforesaid paper an instance of their usefulness, in comparing the forces
of the moon from the earth, and earth from the sun ; in determining a
problem about the moon's phase, and putting a limit to the sun's parallax,
which shows that I had then my eye ujion comparing the forces of the
planets arising from their circular motion, and understood it ; so that a
Avhile after, when Mr. Hooke propounded the problem solemnly, in the
end of his Attempt to prove the Motion of the Earth, if I had not known
the duplicate proportion before, I could not but have found it now. Be-
tween ten and eleven years ago, there Avas an hypothesis of mine registered
in your books, wherein I hinted a cause of gravity towards the earth, sun,
and planets, with the dependence of the celestial motions thereon ; in
which the proportion of the decrease of gravity from the superficies of the
planet (though for brevity's sake not there expressed) can be no other than
reciprocally duplicate of the distance from the centre. And I hope I shall
not be' urged to declare, in print, that I understood not the obvious mathe-
matical conditions of my own hypothesis. But gi'ant I received it after-
wards from Mr. Hooke, yet have I as great a right to it as to the ellipsis.
For as Kepler knew the orb to be not circular but oval, and guessed it to
be elliptical, so Mr. Hooke, without knowing what I have found out since
his letters to me, can know no more, but that the proportion was duplicate
quam proxime at great distances from the centre, and only guessed it to be
so accurately, and guessed amiss in extending that proportion down to the
very centre, whereas Kepler guessed right at the ellipsis. And so Mr.
Hooke foimd less of the proportion than Kepler of the ellipsis. There is so
strong an objection against the accurateness of this proportion, that with-
out my demonstrations, to which Mr. Hooke is yet a stranger, it cannot
be believed by a judicious philosopher to be any where accurate. And so,
in stating this business, I do pretend to have done as much for the propor-
tion as for the ellipsis, and to have as much right to the one from Mr.
Hooke and all men, as to the other from Kepler ; and therefore on this
account also he must at least moderate his pretences.

" The proof you sent me I like very well. I designed the whole to con-
sist of three books ; the second was linished last summer being short, and
only wants transcribing, and drawing the cuts fairly. Some new proposi-
tions I have since thought on, which I can as welf let alone. The third
wants the theory of comets. In autumn last I spent two months in cal-
culations to no purpose for want of a good method, which made me after-
wards return to the first book, and enlarge it with divers propositions,
some relating to comets, others to other things, found out last winter.
The tliird 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 am no sooner come near
her again, but she gives me warning. The two first books, without the
third, will not so well bear the title of Pliilosophite Naturalis Principia
Matheniatica ; and therefore I had altered it to this, De Motu Corporum

NO. VIII. LIFE OF SIR ISAAC NEWTON. 403

libri duo. But, upon second thoughts, I retain the former title. 'Twill
help the sale of the book, which I ought not to diminish now 'tis yours.
The articles are, with the largest, to be called by that name ; if you please
you may change the word to sections, though it be not material ; which is
all at present from

" your affectionate friend,

"and humble servant,

Is. Newton.
" CAMBaiDGE, June 20, 1686.

" Since my writing this letter, I am told by one, who had it from another
lately present at one of your meetings, how that Mr. Hooke should there
make a great stir, pretending that I had all from him, and desiring they
would see that he had justice done him. This carriage towards me is very
strange and undeserved ; so that I cannot forbear, in stating the point of
justice, to tell you further, that he has published Borell's hypothesis in
his own name ; and the asserting of this to himself, and completing it as
his own, seems to me the ground of all the stir he makes. Borell did
something in it, and wrote modestly. He has done nothing, and yet writ-
ten in such a way, as if he knew and had sufficiently hinted all but what
remained to be determined by the drudgery of calculations and observa-
tions, excusing himself from that labour by reason of his other business,
whereas he should rather have excused himself by reason of his inability.
For 'tis plain, by his words, he knew not how to go about it. Now is not
this very fine ? Mathematicians, that find out, settle, and do all the busi-
ness, must content themselves with being nothing but dry calculators and
drudges ; and another, that does nothing but pretend and grasp at all
things, must carry away all the invention, as well of those that were to
follow him, as of those that went before. Much after the same manner were
his letters writ to me, telling me that gravity, in descent from hence to the
centre of the earth, was reciprocally in a duplicate ratio of the altitude,
that the figure described by projectiles in this region would be an ellipsis,
and that all the motions of the heavens were thus to be accounted for ;
and this he did in such a way, as if he had found out all, and knew it most
certainly. And, upon this information, I must now acknowledge, in print,
I had all from him, and so did nothing myself but drudge in calculating,
demonstrating, and writing, upon the inventions of this great man. And
yet, after all, the first of those three things he told of me is false, and very
unphilosophical ; the second is as false ; and the third was more than he
knew, or could affirm me ignorant of by any thing that past between us in
our letters. Nor do I understand by what right he claims it as his own ;
for as Borell wrote, long before him, that by a tendency of the planets to-
wards the sun, like that of gravity or magnetism, the planets would move
in ellipses, so Bullialdus wrote that all force, respecting the sun as its
centre, and depending on matter, must be reciprocally in a duplicate ratio
of the distance from the centre, and used that very argument for it, by
which you, sir, in the last Transactions, have proved this ratio in gravity.
Now if Mr. Hooke, from this general proposition in Bullialdus, might leani
the proportion in gravity, why must this proportion here go for his inven-
tion ? My letter to Hugenius, which I mentioned above, was directed to
Mr. Oldenburg, who used to keep the originals. His papers came into

404 LIFE OF SIR ISAAC NEWTON. APPENDIX

Mr. Hooke's possession, Mr. Hooke, knowing my hand, might have the
curiosity to look into that letter, and thence take the notion of comparing
the forces of the planets arising from their circular motion ; and so what
he wrote to me afterwards, about the rate of gravity, might be nothing but
the fruit of my own garden. And it's more than I can affirm, that the
duplicate proportion was not expressed in that letter. However, he knew
it not (as I gather from his books) till five years after any mathematician
could have told it him. For when Hugenius had told how to find the force
in all cases of circular motion, he had told 'em how to do it in this as well
as in all others. And so the honour of doing it in this is due to Hugenius.
For another, five years after, to claim it as his own invention is as if some
mechanic, who had learned the art of surveying from a master, should after-
wards claim the surveying of this or that piece of ground for his own
invention, and keep a heavy quarter to be in print for't. But what, if this
surveyor be a bungler, and give an erroneous survey? Mr. Hooke has
erred in the invention he pretends to, and his error is the cause of all the
stir he makes. For his extending the duplicate proportion down to the
centre (which I do not) made him correct me, and tell me the rest of his
theory as a new thing to me, and now stand upon it, that I had all from
that his letter, notwithstanding that he had told it to all the world before,
and I had seen it in his printed books, all but the proportion. And why
should I record a man for an invention, who founds his claim upon an
error therein, and on that score gives me trouble ? He imagines he obliged
me by telling me his theory, but I thought myself disobliged by being,
\ipon his own mistake, corrected magisterially, and taught a theory, which
every body knew, and I had a truer notion of than himself. Should a man
who thinks himself knowing, and loves to show it in correcting and instruct-
ing others, come to you, when you are busy, and notwithstanding your
excuse press discourses upon you, and through his own mistakes correct
you, and multiply discourses ; and then make this use of it, to boast that
he taught you all he spake, and oblige you to acknowledge it, and cry out
injury and injustice if you do not ; I believe you would think him a man
of strange unsociable temper. Mr, Hooke's letters in several respects
abounded too much with that humour, which Hevelius and others com-
plain of; and therefore he may do well in time to consider, whether,
after this new provocation, I be much more bound (in doing him that
justice he claims) to make an honourable mention of him in print, especi-
ally since this is the third time that he has given me trouble in this kind.
For your further satisfaction in this business, I beg the favour you would
consult your books for a paper of mine entitled. An Hypothesis explaining
properties of Light, It was dated Dec, 7, 1675, and registered in your
book about January or February following. Not far from the beginning
there is a paragraph ending with these words : ' And as the earth, so per-
haps may the sun imbibe this spirit copiously to conserve his shining, and
keep the planets from receding further fi'om him ; and they that will may
also suppose that this spirit affords or carries thither the solary fuel and
material principle of light. And that the vast ethereal spaces betAveen us
and the stars are for a sufficient repository for this food of the sun and
planets. But this of the constitution of ethereal natures by the by.'

"In these and the foregoing words ^you have the common cause of
gravity towards the earth, sun, and all the planets, and that by this cause

:no. Vlir. LTFE OF SIR ISAAC NEWTON". 405

the planets are kept in their orbs about the stin. And this is all the philo-
sophy Mr. Hooke pretends I had from his letters some years after, the
duplicate proportion only excepted. The preceding words contain the
cause of the phsenomena of gravity, as we find it on the surface of the
earth, without any regard to the various distances from the centre. For at
first I designed to write of nothing more. Afterwards, as my manuscript
shews, I interlined the words above cited relating to the heavens ; and in
so short and transitory an interlined hint of things, the expression of the
proportion may well be excused. But if you consider the nature of the
hypothesis, you'll find that gravity decreases upwards, and can be no other
from the superficies of the planet than reciprocally duplicate of the dis-
tance from the centre, but downwards that proportion does not hold. This
Avas but an hypothesis, and so to be looked upon only as one of my
guesses, which I did not rely on ; but it sufficiently explains to you, why
in considering the descent of a body down to the centre, I used not the
duplicate proportion. In the small ascent and descent of projectiles above
the earth, the variation of gravity is so inconsiderable, that Mathematicians
neglect it. Hence the vulgar hypothesis with them is uniform gravity.
And why might not I, as a Mathematician, iise it frequently, without
thinking on the philosophy of the heavens, or believing it to be philoso-
phically true ?

"This letter, with the postscript belonging to it, was printed in the
General Dictionary by Bernard, Birch, and Lockman (vol. vii. p. 797).
The writers in the Biographia Britannica likewise adopted it; but have
separated the different parts, and printed one portion twice. They have
given the beginning (p. 401 to p. 402, line 37) in the life of Hooke (vol. iv.
p. 2659) ; the next part (p. 402) in the life of Newton (vol. v. p. 13225), and
the end (p. 403) is repeated in the life of Halley (vol. iv. p. 2504). The
postscript (p. 403 to p. 405) was added to the part annexed to the life of
Hooke (vol. iv. p. 2660)."

4.— Halley to Newton. ■ ''

<( Sir " London, 29 June, 1686.

" I am heartily sorry, that in this matter, wherein all mankind ought
to acknowledge their obligations to you, you should meet with any thing
that should give you disquiet ; or that any disgust should make you think
of desisting in your pretensions to a Lady, whose favours you have so
much reason to boast of. 'Tis not she, but your rivals, envying your
happiness, that endeavour to disturb your quiet enjoyment ; which when
you consider, I hope you will see cause to alter your resolution of supress-
ing your third book, there being nothing which you can have compiled
therein, which the learned world will not be concerned to have concealed.
Those gentlemen of the Society, to whom I have communicated it, are
very much troubled at it, and that this unlucky business should have
happened to give trouble, having a just sentiment of the author thereof.
According to your desire in your former, I waited upon Sir Christopher
Wren, to inquire of him, if he had the first notion of the reciprocal dupli-
cate proportion from Mr. Hooke. His answer was, that he himself very

406 LIFE OF SIR ISAAC NEWTON. APPENDIX

many years since had had his thoughts upon the making out the y»lanets'
motions by a composition of a descent towards the sun, and an impressed
motion ; but that at length he gave it over, not finding the means of doing
it. Since wliich time Mr. Hooke had frequently told him, that he had
done it, and attempted to make it out to him ; but that he never was
satisfied that his demonstrations were cogent. And this I know to be
true, that in January 1681, I having, from the considerations of the sesqui-
alter proportion of Kepler, concluded that the centripetal force decreased
in the proportion of the squares of the distances reciprocally, came on
Wednesday to town, where I met with Sir Christopher Wren and Mr.
Hooke, and falling in discourse about it, Mr. Hooke affirmed, that upon
that principle all the laws of the celestial motions were to be demonstrated,
and that he himself had done it. I declared the ill success of my own
attempts ; and Sir Christopher, to encourage the inquiry, said, that he
would give Mr. Hooke, or me, two months' time, to bring him a convinc-
ing demonstration thereof ; and besides the honour, he of us, that did it,
should have from him a present of a book of 40 shillings. Mr. Hooke
then said, that he had it, but he would conceal it for some time, that
others trying and failing might know how to value it, when he should
make it public. However 'I remember, that Sir Christopher was little
satisfied that he could do it ; and though Mr. Hooke then promised to
shew it him, I do not find, that in that particular he has been so good as
his word. The August following, when I did myself the honour to visit
you, I then learned the good news, that you had brought this demonstra-
tion to perfection : and you were pleased to promise me a copy thereof,
which the November following I received with a great deal of satisfaction
from 'Mr. Paget; and thereupon took another journey to Cambridge, on
purpose to confer with you about it, since which time it has been entered
upon the Eegister Books of the Society. As all this passed, Mr. Hooke
was acquainted with it, and according to the philosophically ambitious
temper he is of, he would, had he been master of a like demonstration, no
longer have concealed it, the reason, he told Sir Christopher and me, now
ceasing, But now he says, this is but one small part of an excellent
system of nature, which he has conceived, but has not yet completely
made out, so that he thinks not fit to publish one part without the other.
But I have plainly told him, that unless he produce another differing de-
monstration, and let the world judge of it, neither I nor any one else can
believe it. As to the manner of Mr. Hooke's claiming the discovery, I
fear it has been represented in worse coloiirs than it ought ; for he neither
made public application to the Society for justice, nor pretended you had
all from him. The truth is this : Sir John Hoskyns, his particular friend,
being in the chair, when Dr. Vincent presented your book, the Doctor gave
it its just encomium both as to the novelty and dignity of the subject. It
was replied by another gentleman, that you had carried the thing so far,
that there was no more to be added. To which the Vice-president replied,
that it was so much the more to be prized, for that it was both invented
and perfected at the same time. This gave Mr. Hooke off'ence, that Sir
John did not, at that time, make mention of what he had, as he said, dis-
covered to him ; upon which they two, who till then were the most in-
separable cronies, have since scarce seen one another, and are utterly
fallen out After the breaking up of that meeting, bein^ adjourned to

NO. VIII. LIFE OF SIR ISAAC NEWTON. 407

the coffee-house, Mr. Hooke did there endeavour to gain belief, that he
had some sucli thing by him, and that he gave you the first hint of this
invention. But I found, that they were all of opinion, that nothing thereof
appearing in print, nor on the books of the Society, you ought to be con-
sidered as the inventor. And if in truth he knew it before you, he ought
not to blame any but himself, for having taken no more care to secure a
discovery, which he puts so much value on. What application he has
made in private, I know not ; but I am sure that the Society have a very
great satisfaction, in the honour you do them, by the dedication of so
worthy a treatise. Sir, I must now again beg you, not to let your resent-
ments run so high, as to deprive us of your third book, wherein the appli-
cation of your mathematical doctrine to the theory of comets and several
curious experiments, which, as I guess by what you write, ought to com-
pose it, will undoubtedly render it acceptable to those, who will call them-
selves Philosophers without Mathematics, which are much the greater
number. Now you approve of the character and paper, I will push on the
edition vigorously. I have sometimes had thoughts of having the cuts
neatly done in wood, so as to stand in the jjage with the demonstrations.
It will be more convenient, and not much more charge. If it please you
to have it so, I will try how well it can be done ; otherwise I will have
them in somewhat a larger size than those you have sent up. I am, Sir,
" Your most affectionate luimble servant,

"E. Halley.

" This letter was printed in the Gen, Die. (vol. vii. p. 799.) In the
Biographia Britannica the parts are separated, and some, as was done for
No. 3, are repeated. The beginning (p. 405 to p. 406) is annexed to the
life of Ne\vton ^ol. v. p. 3226), and the first part of it apper^rs also (to
p. 406) in the life of Halley (vol. iv. p. 2504). The middle (p. 406) will be
found in the life of Hooke (vol. iv. p. 2661) ; the end (p. 407) printed in
the life of Newton (vol. v. p. 3226), and the latter part also in the life of
Halley (vol. iv. p. 2504). The words (p. 406), 'As all this passed, Mr,
Hooke was acquainted with it, and' — are wholly omitted."

5.— Newton to Halley.

" July 14, 1686.

" Sir,
" I have considered your proposal about wooden cuts, and believe it will
be much convenienter for the reader, and may be sufficiently handsome,
but I leave it to your determination. If you go this way, then I desire you
would divide the first figure into these two :^ I crowded them into one to
save the trouble of altering the numbers in the schemes you have. I am
very sensible of the great kindness of the gentlemen of your Society to me,
far beyond what I could ever expect or deserve, and know how to distin-
guish between their favour and another's humour. Now I understand he
was in some respects misrepresented to me, I wish I had spared the post-
script to my last. This is true, that his letters occasioned my finding the
method of determining figures, which when I had tried in the ellipsis, I
threw the calculations by, being upon other studies ; and so it rested for
1 The figures here are unnecessary.

408 LIFE OF SIE ISAAC NEWTON. appendix

about five years, till upon your request I sought for that paper ; and not
finding it, did it again, and reduced it into the propositions shewed you by
Mr. Paget : but for the duplicate proportion I can aftirm that I gathered
it from Kepler's theorem about twenty years ago. And so Sir Christopher
Wren's examining the ellipsis over against the fociis shews, that he knew it
many years ago, before he left off his enquiry after the figure by an im-
pressed motion and a descent compounded together. There was another
thing in Mr. Hooke's letters, which he will think I had from him. He told
me, that my proposed experiment about the, descent of falling bodies was
not the only way to prove the motion of the earth ; and so added the ex-
periment of your pendulum clock at St. Helena as an argument of gravity's
being lessened at the equator by the diurnal motion. The experiment was
new to me, but not the notion ; for in that very paper, which I told you
was vn-it some time above fifteen years ago, and to the best of my memory
was writ eighteen or nineteen years ago, I calculated the force of ascent at
the equator, arising from the earth's diurnal motion, in order to know what
would be the diminution of gravity thereby. But yet to do this business
right, is a thing of far greater difficulty than I was aware of. A third
thing there was in his letters, which was new to me, and I shall acknow-
ledge it, if I make use of it. 'Twas the deflexion of falling bodies to the
south-east in our latitude. And now having sincerely told you the case
between Mr. Hooke and me, I hope I shall be free for the future from the
prejudice of his letters. I have considered how best to composeUhe pre-
sent dispute, and I think it may be done by the inclosed scholium to the
fourth proposition. In turning over some old papers I met with another
demonstration of that proposition, which I have added at the end of this
scholium. Which is all at present from

" your affectionate friend,

" and humble servant,

" Is. Newton.

" This letter was printed in the Gen. Die. (vol. vii. p. 800) ; but the first
fourteen lines and the diagrams belonging to them are omitted. .It was re-
printed in the Biographia Britannica (life of Hooke, vol. iv. p. 2661), where
the last sentence ('In turning over,' &c. p. 41) is omitted, as well as the
beginning, which was left out in the General Dictionary."

6.— Newton to H alley.

" Sir,
'* Yesterday I unexpectedly struck upon a copy of the letter, I tola you
of, to Hugenius. 'Tis in the hand of one Mr. John Wickins, who was then
my chamber-fellow, and is now parson of Stoke Edith near Monmouth
[Hereford], and so is authentic. It begins thus, being directed to Mr.
Oldenburg.

" ' Sir,
" ' I receiv'd your letters, with M. Hugens's kind present, which I have
viewed with great satisfaction, finding it full of very subtile and useful

NO. VIII. LIFE OF SIE 'ISAAC NEWTON. 409

speculations very worthy of the author. I am glad, that we are to expect
another discourse of the Vis Centrifuga, which speculation may prove of
good use in Natural Philosophy and Astronomy, as well as Mechanics.
Thus, for instance, if the reason, why the same side of the*moon is ever
towards the earth, be the greater conatus of the other side to recede from
it, it will follow (upon supposition of the earth's motion about the sun),
that the greatest distance of the sun from the earth is to the greatest dis-
tance of the moon from the earth, not greater than 10000 to 56 ; and
therefore the parallax of the sun not less than toVoo of the parallax
of the moon ; because were the sun's distance less in proportion to that of
the moon, she would have a greater conatus from the sun than from the
earth. I thought also some time that the moon's libration might depend
upon her conatus from the sun and earth compared together, till I appre-
hended a better cause.'

'' Thus far this letter concerning the Vis Centrifuga. The rest of it, for
the most part concerning colours, is printed in the Phil. Trans, of July 21,
1673, No. 96. Now from these words it's evident, that I was at that time
versed in the theory of the force arising from circular motion, and had an
eye upon the forces of the planets, knowing how to compare them by the
proportions of their periodical revolutions and distances from the centre
they move about : an instance of which you have here in the comparison
of the forces of the moon arising from her menstrual motion about the
earth, and annual about the sun. So then in this theory I am plainly be-
fore Mr. Hooke. For he about a year after, in his Attempt to prove the
Motion of the Earth, declared expressly, that the degrees, by which gravity
decreased, he had not then experimentally verified ; that is, he knew not
how to gather it from phenomena ; and therefore he there recommends
it to the prosecution of others.

" Now, though I do not find the duplicate proportion expressed in this
letter (as I hoped it might), yet if you compare this passage of it here
transcribed, with that hypothesis of mine, registered by Mr. Oldenburg in
your book, you will see that I then understood it. For I there suppose
that the descending spirit acts upon bodies here on the superficies of the
earth with force proportional to the superficies of their parts ; which can-
not be, unless the diminution of its velocity in acting upon the first parts
of any body it meets with, be recompensed by the increase of its density
arising from that retardation. Whether this be true is not material. It
suffices, that 'twas the hypothesis. Now if this spirit descend from above
with uniform velocity, its density, and consequently its force, will be re-
ciprocally proportional to the square of its distance from the centre. But
if it descend with accelerated motion, its density will everywhere diminish
as much as its velocity increases ; and so its force (according to the hypo-
thesis) will be the same as before, that is, still reciprocally as the square of
its distance from the centre.

" In short, as these things compared together shew, that I was before Mr.
Hooke in what he pretends to have been my master, so I learned nothing
by his letters but this, that bodies fall not only to the east, but also in our
latitude to the south. In the rest his correcting and informing me was to
be complain'd of. And tho' his correcting my spiral occasioned my finding
the theorem, by which I afterwards examined the ellipsis ; yet am I not
beholden to him for any light into the business, but only for the diversion

410 LIFE OF SIR ISAAC NEWTON.

APPENDIX

he gave me from my other studies to think on these things, and for his dog-
maticalness in writing, as if he had found the motion in the ellipsis, which
inclined me to try it, after I saw by what method it was to be done. Sir,
I am,

" your affectionate friend,

" and humble servant,
: *' Is. Newton.

" Jvly 27, ie86.

" This letter was printed in the Gen. Diet. (vol. vii. p. 800), and reprinted
in the Biographia Britannica (life of Hooke, vol. iv. p. 2661). The original
letter to Oldenburg, from which an extract is given here by Newton, is in
the guard-book (No. 1), and the date of it is there preserved, 'June 23, 73.'
It likewise contains a passage, in addition to what Newton has quoted, and
which is omitted in the copy that is printed in the Phil. Transactions (vol.
viii. p. 6087). It does not indeed bear upon the present subject, but still
the completion of the letter may be some apology for inserting it in this
place. It is as follows :

" In the demonstration of the 8th proposition de descensu gravium, there
seems to be an illegitimate supposition, namely, that the flexures at B and
c do not hinder the motion of the descending body. For in reality they
will hinder it, so that a body which descends from a shall not acquire so
great velocity, when arrived at d, as one which descends from E. If this
supposition be made because a body descending by a curve line meets with
no such opposition, and this proposition is laid down in order to the con-
templation of motion in curve lines, then it should have been shewn that
though rectilinear flexures do hinder, yet the infinitely little flexures
which are in curves, though infinite in number, do not at all hinder the
motion.

" The rectifying curve lines by that way which Mr. Hugens calls evolu-
tion, I have been sometimes considering also, and here met with a way of
resolving it, which seems more ready and free from the trouble of calcula-
tion than that of M. Hugens. If he please, I will send it him. The pro-
blem also is capable of oeing improved by being propounded thus more
generally.

" ' Curvas invenire quotascunque, quarum longitudines cum propositse
alicujus curvae longitudine, vel cum area ejus ad datam lineam applicata,
comparari possunt.' "

7.— H ALLEY TO Newton.

" London, October 14, 1686.
" Sir,
" By reason you are desirous that your book should not be public before
Hilary Term, the impression has not been expedited as it might have been ;
but I hope that it is the more correct for proceeding so slow. I have sent
you by the coach which goes from hence to-morrow morning, all the sheets
that are done, desiring you would be pleased to mark all the errata you
shall find, that so if there be any material one, the re^j^er may be adver-

NO. VIII. LIFE OF SIR ISAAC NEWTON. 4 1 ]

tised thereof, but this at your leisure. At present I more immediately
want to be informed concerning your geometrical effection of the problem
XXIII, as much as relates to the 63d figure, for upon trial (there being no
demonstration annexed) there seems to be some mistake committed: where-
fore I intreat you would please to send me, revised by yourself, those few
lines that relate thereto, and, if it be not too much trouble, be prevailed
upon to subjoin something of the Demon.stration. In your transmutation
of figures according to the 22d lemma, which you use in the two following
problems, to me it seems that the manner of transmuting a trapezium into
a parallelogram needs some further explanation ; I have printed it as you
sent it, but I pray you please a little farther to describe by an example the
manner of doing it, for I am not perfectly master of it ; a short hint will
suffice. Pray, defer the answer hereto as little as may stand with your
convenience, for we^ are now within a sheet of the 2-3d problem, and shall
want your amendments, if there be occasion for them. If there be any
service I can do you here in town, pray command. Sir,

" Your most affectionate humble servant,

" Edm. H alley.

" To his honoured Friend,
Mr. Isaac Newton,

at Trinity Colledg, CambridgiI,
These."

8.— Newton to H alley.

" Sir,
"In the scholium you write of, the words ' vel hyperbolge' in the 3d line
are to be struck out, and in the 5th and 6th lines the words ' quae sit ad
Gk' should be ' qu£e sit ad ^ GK.' I send you inclosed the beginning of this
scholium with the 63d figure as I would have them printed. I thank you
heartily for giving me notice that it was amiss. The ground of the trans-
mutation of a trapezium into a parallelogram I lay down^ pag. 87, in these
words : ' Nam rectse quasvis convergentes transmutantur in parallelas, ad-
hibendo pro radio ordinato primo AO lineam quamvis rectam, quae per con-
cursum convergentium transit : id adeo c[uia concursus ille hoc pacto abit
in infinitum, lineae autem parallelse sunt quae ad punctum infinite distans
tendunt.' In the figure, pag. 86, conceive the curve hgi to be produced
both ways till it meet and intersect itself any where in the radius ordinatus
primus AO : and when the point G moving up and down in the curve hi
arrives at that intersection point, I say the point g moving in like manner
up and down in the curve h i will become infinitely distant. For the point
G falling upon the line OA, the point D will fall upon the point a, and the
line OD upon the line o A ; and so becoming parallel to as their intersection
point d will become infinitely distant, and consequently the line d g will
become infinitely distant, and so will its point g. Q. E. D. So then if any
two lines of the primary figure H G i D intersect in the radius ordinatus pri-
mus AO, their intersection in the new figure h gi d shall become infinitely
distant ; and, therefore, if the two intersecting lines be right ones, they
shall become parallel. For right lines, which lead to a point infinitely dis-

412 LIFE OF SIR ISAAC NEWTON.

APPENDIX

tant, do not intersect one another and diverge, but are parallel. Therefore,
if in the primary figure there be any trapezium, whose opposite sides con-
verge to points in the radius ordinatus primus o a, those sides in the new
figure shall become parallel, and so the trapezium be converted into a
parallelogram.

" The printed sheets I intend to look over. Mr, Paget, in his stay here,
has noted these errata, of which the 3d is a fault in the copy.

''P. 6, 1. 27, velocitate ; p. 8, 1. 19, tur Sunt. ; p. 14, 1. 30, reciproce ut
DO ; p. 18, 1. 1, recta. I wish the printer be careful to mend all you note.
Sir, I am very sensible of the great trouble you are at in this business, and
the great care you take about it. Pray take your own time. And if you
meet with any thing else, which you think need either correcting or further
explaining, be pleased to signify it to

" your humble and obliged servant,

" Is. Newton.

"Trin. Coll.
Oclob. 18, 1686.

*' My thanks for your note of De la Hire."

9.— Halle Y to Newton.

" London. Feb. 24 [1686-7].

" Honoured Sir,
** I return you most hearty thanks for the copy you sent me of the sheet
which was lost by the printer's negligence ; I will now do nothing else till
the whole be finished, which I hope may be soon after Easter ; and to re-
deem the time I have lost, 1 will employ another press to go on with the
second part, which 1 am glad to understand you have perfected, and if you
please to send it up to me, as soon as I have it I will set the printer to
work on it, and will not be wanting to do my part to let it appear to the
world to your satisfaction. 1 am sorry the Society should be represented
to you so unsteady as to fall so frequently into variance,' but there is no
such thing ; and I am bold to say, that I serve them to their satisfaction,
though six out of thirty-eight last general election did their endeavour to
have put me by.^ Dr. Wallis his papers I will send you ; the result is
much the same with yours, and he had the hint from an account 1 gave him
of what you had demonstrated, I will send it you with some more sheets
this next week ; it is as yours founded on the hypothesis of the opposition
being proportionate to the celerity which you say you find reason to dis-
pute. Your demonstration of the parallax of the sun from the inequalities
of the moon's motions, is what the Society has commanded me to request
of you, it being the best means of determining the dimensions of the pla-
netary system, which all other ways are deficient in ; and they entreat you
not to desist when you are come so near the solution of so noble a problem.
This done, there remains nothing more to be enquired in this matter, and

1 Mr. Weld, in his History of the Royal Society, does not mention any " variances" as
taking place at this time.

2 Halley was at this time Clerk and Assistant Secretary, and continued so till 1688.

NO. VIII. LIFE OF SIR ISAAC NEWTON. 413

you will do yourself the honour of perfecting scientifically what all past
ages have but blindly groped after. I have your two propositions^you sent
me some time since, and shall insert them in their proper place.
" I am, Sir, to the utmost of my power,

" Your most affectionate humble servant,

" Edm. H alley.
" To his Honoured Friend,
Mr. Isaac Newton,

in Tkinty Colledg, Cambridg,
These."

10.— Newton to Halley.

" Sir,

" I have sent you the sheet you want. The second book I made ready
for you in autumn, having wrote to you in sulnmer that it should come out
with the first, and be ready against the time you might need it, and guess-
ing by the rate of the press in summer you might need it about November
or December. But not hearing from you, and being told (though not truly)
that, upon some differences in the Royal Society, you had left your secre-
tary's place, I desired my intimate friend Mr. C. Montague' to enquire of
Mr. Paget how things were, and send me word. He writes, that Dr.
Wallis has sent up some things about projectiles pretty like those of mine
in the papers Mr. Paget first shewed you, and that 'twas ordered I should
be consulted whether I intend to print mine. I have inserted them into
the beginning of the second book with divers others of that kipd : which
therefore, if you desire to see, you may command the book when you please,
though otherwise I should choose to let it lie by me till you are ready for
it. I think I have the solution of your problem about the sun's parallax,
but through other occasions shall scarce have time to think further on
these things : and besides, I want something of observation, for if my
notion be right, the sun draws the moon in the quadratures, so that there
needs an equation of about 4 or 4| minutes to be subducted from her mo-
tion in the first quarter and added in the last. I hope you received a
letter with two corollaries I sent you in autumn. I have eleven sheets
already, that is, to M. When you have seven more printed off I desire you
would send them. I thank you for putting forward the press again, being
very sensible of the great trouble I give you amidst so much business of
your own and the Royal Society's. In this, as well as in divers other
things, you will much oblige

" your affectionate friend,

" and humble servant,

" Is. Newton.

" Tein. Coll. Cambridge,
Feb. 28, 1686. [1686-7.]"

1 .ifterwards the Earl of Halifax.

414 LIFE OF SIR ISAAC NEWTON.

11.— Newton to H alley.

" Sir,
" You'll receive the 2nd book on Thursday night or Friday by the coach.
I have directed it to be left with Mr. Hunt at Gresham Coll. Pray let me
beg the favour of a line or two to know of the receipt. I am obliged to
you for pushing on the edition, because of people's expectation, tho' other-
wise I could be as well satisfied to let it rest a year or two longer. 'Tis a
double favour, that you are pleased to double your pains about it. Dr.
Wallis's papers may be long, and I would not give you the trouble of tran-
scribing them all. The heads may suffice. The resistance, in swift mo-
tions, is in a duplicate proportion to the celerity. The deduction of the
sun's parallax from the moon's variation, I cannot promise now to consider.
When astronomers have examined whether there be such an inequality of
her motion in the quadratures, as I mentioned in my last, and determined
the quantity thereof, I may take some occasion perhaps to tell them the
reason. No more at present from

" your most affectionate humble servant,

"Is. Newton.
" Cambridge.
March 1, 8d-7."

12.— Halley to Newton.

" London, March 7, 168C-7.

" Honoured Sir,
" I received yours, and according to it your Second Book, which this
week I will put to the press, having agreed with one that promises me to
get it done in seven weeks, it making much about twenty sheets. The
First Book will be about thirty, which will ]>e finished much about the
same time. This week you shall have the eighteenth sheet according to
your directions. You mention in this Second your Third Book De Syste-
inate Mundi, which from such firm principles, as in the preceding you
have laid down, cannot choose but give universal satisfaction, if this be
likewise ready, and not too long to get printed at the same time, and you
think fit to send it ; I will endeavour by a third hand, to get it all done
together, being resolved to engage in no other business till such time as all
is done, desiring hereby to clear myself from all imputations of negligence
in a business wherein I am much rejoiced to be any ways concerned in
handing to the world that that all future ages will admire, and as being,
" Sir, your most obedient servant,

"Edm. Halley,
" To Mr. Isaac Newton,

at Trinity Colledg Cambridg."

No answer to this letter, or any of the subsequent letters, has been pre-
served.

NO. VIII. LIFE OF SIR ISAAC NEWTON. 415

13.— Halley to Newton.

" March 14, 1686-7.
" Sir,
" I have now sent you the eighteenth sheet of your book, but could not
be as good as my word, by reason of the extraordinary trouble of the last
sheet, which was the reason it could not be finished time enough to send
it you the last week. I have not been wanting to endeavour the clearing
it of errata, but am sensible that, notwithstanding all my care, some have
crept in ; but I hope none of consequence. Pray, please to examine it
yourself, and note what mistakes are committed, that so they may be
noted at the end ; and if they be very material, the sheet shall be done
over again, as I was forced to do the sheet D ; and half the sheet P must
be done, for the figure is turned upside down by the negligence of the
printer, in p. 112. I hope, in a fortnight more, to send you as many more
sheets, and very suddenly to have the first part finished — being,
" Sir, your most humble servant,

Edm. Halley. '<
" To Mr, Isaac Newton,

at Trinity Coll.,

Cambrldge.

These present—
With a small parcel."

14.— Halley to Newton.

" London, April 5, 1687.
" Honoured Sir,
"I received not the last part of your divine treatise till yesterday,
though it came to town that day se'ennight, having had occasion to be out
of town the last week. The first part will be finished within the three
weeks, and, considering the shortness of the third over the second, the
same press that did the first will get it done so soon as the second can be
finished by another press ; but I find some difficulty to match the letter
justly. Your method of determining the orb of a comet deserves to be
practised upon more of them, as far as may ascertain whether any of those
that have passed in former times may have returned again ; for their nodes
and perihelia being fixed, will prove it sufficiently, and, by their periods,
the transverse diameters will Idc given, which possibly may render the
problem more easy. If you can remove the fault in the comet's latitudes,
'twill be better ; but as it is, the numbers you have laid down do make
out the verity of the hypothesis past dispute. I do not find that you have
touched that notable appearance of comets' tails, and their opposition to
the sun, which seems rather to argue an efflux from the sun than a gravita-
tion towards him. I doubt not but this may follow from your principles
with the like ease as all the other phenomena ; but a proposition or two
concerning these will add much to the beauty and perfection of your theory
of comets. I find I shall not get the whole completed before Trinity
Term, when I hope to have it published, when the world will not be more

4 ] 6 LIFE OF SIR ISAAC NEWTON. APPENDIX

instructed by the demonstrative doctrine thereof, than it will pride itself
to have a subject capable of penetrating so far into the abstrusest secrets
of nature, and exalting human reason to so sublime a pitch by this utmost
effort of the mind. But least my affection should make me transgress, I
remain,

" Your most obedient servant,

Edm. Halley.
" To Mr. Isaac Newton,

to he left with Mr. Parish Rector oj

Coulsterworth, in Lincolnshire.

These—"

No. IX.

{Referred to in page 272, as No. XI.)

The following is a copy of the verses written by Halley, and prefixed to
the First Edition of the Principia. In imitation of Professor Rigaud, the
original verses are printed in the larger type. The alterations made by
Bentley, in the second edition of 1713, are in a smaller type, and the parts
between brackets are the alterations adopted in the third edition, published
by Pemberton in 1726.

HALLEY's verses PREFIXED TO THE PRINCIPIA.

viri praestantissimi

D, ISAACi Newtoni

opus hocce

mathematico-physicum

Sfeculi gentisque nostrae decus egregium.

En tibi norma Poll, et divse libramina Molis,

[en] [et]

Computus atque Jovis ; quas, dum primordia renim
Conderet, omnipotens sibi ipse

Pangeret, omniparens Leges violare Creator
Dixerit, [atque operum quae fundamenta locarit.]
Noluit, aeternique operis fundamina fixit.
Intima panduntiir victi penetralia coeli,
circumrotet.
Nee latet extremos quae Vis circumrotat Orbes.
Sol solio residens ad se jubet omnia prono
Tendere descensu, nee recto tramite currus
Sidereos patitur vastum per inane moveri ;
Sed rapit immotis, se centro, singula Gyris.

NO. IX. LIFE OF SIR ISAAC NEWTON. 417

Hinc qua

Jam patet horrificis quae sit via flexa Cometis ;
Jam non miramur barbati Pliamomena Astri. ^
Discimus hinc tandem qua causa argentea Phoebe

eat, et
Passibus baud sequis graditur ; cur subdita nulli
Hactenus Astronomo numerorum fraena recuset :

remeent progrediantur

Cur remeant Nodi, curque Auges progrediuntur.
Discimus et quantis refluum vaga Cynthia Pontum

impellai ; [fessis dum]
Viribus impellit, dum fractis fluctibus Ulvam
Deserit, ac Nautis suspectas nudat arenas ;
Alternisve ruens spumantia pulsat.

Alternis vicibus suprema ad littora pulsans.
Quai toties animos veterum torsere Sophorum,

hodie
Qugeque Scholas frustra rauco certamine vexant
Obvia conspicimus nubem pellente Mathesi.
Jam dubios nulla caligine praegravat error, ^

Quae superas
Queis Superum penetrare domos atque ardua Coeli
Mewtoni auspiciis, jam dat contingere Templa.
Scaudere sublimis Genii concessit acumen.
Surgite Mortales, terrenas mittite curas ;
cognoscite
Atque hinc coeligense vires dignoscite Mentis,
A pecudum vita longe lateque remotae.

primus
Qui scriptis jussit Tabulis compescere Caedes,
Furta et Adulteria, et perjurse crimina Fraudis ;
Quive vagis populis circumdare moenibus Urbes
Autor erat ; Cererisve beavit munere gentes ;
Vel qui curarum lenimen pressit ab Uva ;
Vel qui Niliaca monstravit arundine pictos
Consociare sonos, oculisque exponere Voces ;
Humanam sortem minus extulit ; utpote pauca
In commune ferens miserae solatia

[^tantu7n solamina]
Eespiciens miserae solummodo commoda vitse.
Jam vero Superis convivae admittimur, alti

diae
Jura poll tractare licet, jamque abdita coecae

Naturae, et
Claustra patent Terrae, rerumque^ immobilis ordo,

prseteritis latuere incognita saeclis.
Et quae praeteriti latuerunt saecula mundi.
justis
Talia monstrantem mecum celebrate Camcenis,

Vbis line was entirely omitted in 1713, and restored in 1726.

2 This line also was omitted in 1713, and restored in 1726.

3 que— omitted in 1713, restored in 1726. The parts in italics are alterations, made in
the third, though not in the second edition.

VOL. L 2d

418 LIFE OF SIR ISAAC NEWTON.

[o calicolum yaudentes]
Vos qui coelesti gaudetis nectare vesci,
Newtonum clausi reserantem scrinia Veri

carum
Newtonum Musis charum, cui pectore puro
Phoebus adest, totoque incessit Numine mentem :
Nee fas est propius Mortali attingere Divos.

Edm. Halley.

It does not appear on what aiithority those changes were introduced into
the third edition, which did not exist in the two first. It is quite certain
that they were made without the authority either of Halley or Newton. It
is probable, from the following anecdote, which we found in Conduitt's
manuscripts, that Pemberton was the author of them.

" Bentley," says Conduitt, " altered Halley's verses when he printed the
Principia. Halley told me that Sir Isaac Newton made him hope that in
Pemberton's edition his verses would be printed from his o^vn copy, but
complained they were not, for he made it—

^ternique operis fundamcnta fixit.
And it is printed,

Operumque fundamenta locaTit.

And when I said that perhaps Sir Isaac Newton did not care for having
anything appear before his book, that seemed to favour the idea that the
world was eternal ; — ' Yes,' said he, ' that is what Pemberton would fix
upon me, but ceternum is only atiternum, and I meant no more.' " — Con-
duitt's MSS.

No. X.

{Referred to in page 278, as No. XII.)

It is either a great privilege or a great misfortune to be the associate of dis-
tinguished individuals. The light of the halo which surrounds them falls
brightest on their companions, but though it generally illustrates and adorns,
it sometimes displays failings and imperfections of character, and transmits
them to posterity. We have already seen how unfortunate for the memory
of Mr. Paget was his connexion with Newton and Flamsteed. We shall
now see the reverse in the case of Cotes, who, though justly distinguished
by his own talents and acquirements, has yet derived a considerable por-
tion of his reputation from being the friend of Ne\\i:on, and an editor of
the Principia. It is probable, indeed, from the fact that Bentley was the
proprietor of the second edition of the Principia, and a Avorshipper of
Mammon, that Fame Avas the only reward which fell to the lot of Cotes.

Roger Cotes was born at Burbage, in Leicestershire, on the 10th July
1682. His father, who Avas rector of the parish, placed him at Leices-

NO. X. LIFE OF SIR ISAAC NEWTON. 419

ter school, where, at the age of twelve, he displayed a great taste for
mathematics. At the house of his uncle, the Rev. John Smith, and with
his assistance, he made great progress in mathematics, and at St. Paul's
School in London, he made equal progress in classical learning.

From St. Paul's School he went to Trinity College, Cambridge, where he
was entered pensioner on the 6th April 1699. He was elected scholar in
May 1701, took his degree of B. A. in 1703, and was sworn minor Fellow of
the College, on the 3d of October 1705. On the 6th October 1707, he was
appointed the first Plumian Professor of Astronomy and Experimental
Philosophy. In 1713 he took orders, and in the same year undertook to
superintend the second edition of the Principia.

In 1714 he published in the Philosophical Transactions a paper, entitled
Logometria, the first part of the treatise on tlie same subject, which forms
the principal part of his posthumous work, entitled Harmonia Mensiira-
rum, edited in 1722 by his cousin. Dr. Robert Smith. In 1716, he com-
municated to the Society an account of the great fiery meteor seen on the
6th March of that year, but it is obvious from his description of it that it
was only an Aurora Borealis.

In a few weeks after he wrote this communication to the Society, he was
seized with fever, and, after a relapse, accompanied with violent diarrhoea
and constant delirium, he died on the 5th June 1716, amid the deep regrets
of the University and the scientific world. When Newton received the sad
intelligence of the loss of his friend, he made the memorable observation,
'' If Mr. Cotes had lived we might have known something."

A short time before his death, when he was only in his thirty-second
year, he demonstrated the beautiful optical theorem, that "the magnitude
of the image of an object seen through any number of lenses is to that of
the object itself, as the distance of the image from the eye is to the appar-
ent distance of the object." '

In 1722, there appeared the Epistola ad Amicum de Cotesii Tnveniis, ad-
dressed to Mr. James Wilson, by Henry Pemberton, and an Appendix,
bearing the date of May 1722. Beside some tracts in Latin, which have
not been published, he left behind him a course of lectures on Hydro-
statics and Pneumatics, which was published by Dr. Smith in 1738. In
Mr. Edleston's Correspondence, he has published twenty-four letters from
Cotes to his friends, from one of which it appears that he had anticipated
S'Gravesende in the invention of the Heliostate.^

Cotes was interred in the chapel of Trinity College, and the following
and much admired inscription on his monument, was written by Dr.
Bentley.

H. S. E.
ROGERUS ROBERTI FILIUS COTES,

Hujus Collegii S. Trinitatis Socius,

Et Astronomiae et Experimentalis

Philosophise Professor Plumianus ;

1 See Smith's Optics, vol. i p. 191, cor. 19 ; and vol. ii., Remarks, p. 76.

3 Mr. Edleston refers to the Register of the Royal Society for evidence, that Hooke
and Halley had previously invented the Heliostate. The first publication, however, of
the invention, is due to the Dutch philosopher. — See S'Gravesende's Physices Ekm.
Math. vol. ii. p. 715, § 2660, Tab. 84, 85. Edit. 1742.

420 LIFE OF SIR ISAAC NEWTON. APPENDIX

Qui immatiira morte prsereptus,

Pauca quidem ingenii sui

Pignora reliquit,

Sed egregia, sed admiranda,

Ex intimis Matheseos penetralibus

Felici solertia turn primum eruta ;

Post magnum ilium NeAvtonum,

Societatis hujus spes altera,

Et decus geraellum ;

Cui ad summam doctrinae laiidem

Omries morum virtutumque dotes

In cumulum accessenint ;

Eo magis spectabilis amabilisque,

Quod in formoso corpore

Gratiores venirent.

Natus Burbagii
In agro Leicestriensi

Jul. X. MDCLXXXII.

Obiit Jun. v. mdccxvi.

No. XI.

{Referred to in page 297, as No. XIII. )

The great interest excited by the Principia even among persons who
were not qtialified by their mathematical knowledge to comprehend it, led
some individuals of active and powerful minds to acquire as much geo-
metrical and analytical knowledge as would enable them to understand
and appreciate the leading truths which Newton had discovered. Dr.
Bentley, as we have already seen, was anxious to expound the discoveries
of Newton 1 in a popular form, and to adduce them as proofs of the wisdom
and benevolence of the Deity ; and having resolved to study the work
which contained them, he applied, through his friend, Mr. William Wot-
ton,2 to John Craige, an able Scotch mathematician, for a list of works

1 Dr. Monk is of opinion that Bentley had previously attended Newton's lectures.
" The true system of the universe," he says, " and the proper methods of philosophical
investigation, had not become public by the writings of Newton, but the light of the
Newtonian discoveries was partially revealed to Cambridge before the rest of the world
by the lectures of the philosopher himself, delivered in the character of the Lucasian
Professor. These Bentley had an opportunity of attending; and that he did not neglect
it, 1 am induced to believe, by his selection of the Newtonian discoveries as a prominent
subject of his Boyle's Lectures, and his familiarity with the train of reasoning by which
they are established." — Monk's Life of Bentley, pp. 6, 7.

2 William Wotton, the friend of Bentley and of Craige, was a very remarkable person ;
and Dr. Monk informs us that he was the only one of Bentley's contemporaries with

NO. XI. LIFE OF SIR ISAAC NEWTON. 421

which should be read in order to understand the Principia. Alarmed with
the long list of authors sent him by Craige on the 24th June 1691, Bentley
seems to have applied to Newton himself, from whom he received the fol-
lowing directions. Mr. Edleston thinks that the date of it is probably
about July 1691 :—

Directions given hy Newton to Berdley respecting the hooks necessary to
he read hefore studying the Principia. ^

" Next after Euclid's Elements the Elements of y« Conic sections are to
be understood. And for this end you may read either the first part of ye
Elementa Gurvarum of John De Witt, or De la Hire's late treatise of y®
conick sections, or D"" Barrow's Epitome of Apollonius.

" For Algebra read first Barth[ol]in's introduction, & then peruse such
Problems as you will find scattered up & down in ye Commentaries on
Cartes' s Geometry & other Algebraical [sic] writings of Francis Schooten.
I do not mean y* you should read over all those Commentaries, but only
ye solutions of such Problems as you will here & there meet with. You
may meet with De Witt's Elementa Curvarum & Bartholin's Introduction
bound up together w'^ Carte's Geometry & Schooten's Commentaries.

" For Astronomy read first ye short account of ye Copernican System in
the end of Gassendus's Astronomy & then so much of Mercator's Astro-
nomy as concerns ye same system & the new discoveries made in the
heavens by Telescopes in the Appendix.

" These are sufficient for understanding my book : but if you can pro-
cure Hugenius's Horologium Oscillatorium, the perusal of that will make
you much more ready.

''At ye first perusal of my Book it's enough if you understand ye Pro-
positions wtii some of ye Demonstrations w^h are easier than the rest. For
when you understand "ye easier they will afterwards give you light into ye
harder. When you have read ye first 60 pages, pass on to ye 3<J Book &
when you see the design of that you may turn back to such Propositions

whom he maintained a friendship in after life. " He was," adds Dr. Monk, " the ahle
antagonist of Sir W. Temple on the controversy ' On Ancient and Modern Learning.'
As their combined efforts on that occasion have associated together the names of Wotton
and Bentley, it is right to take some notice of the former, who, when he entered the
University, was a child, and presents the best authenticated instance of a juvenile pro-
digy that I have ever found upon record. It is certified by the testimony, not of one,
but many persons of sense and learning, that at six years of age he was able to read
and translate Latin, Greek, and Hebrew ; to which at sevcM be added some knowledge of
the Arabic and Syriac. On his admission at Catherine Hall, in his tenth year, the
master. Dr. Eachard, the antagonist of Hobbes, recorded 'Gulielnius Wotton, infra
decern annos, nee Hammondo nee Grotio secundus.' This surprising proficiency during
his academical career is testified by some of the best scholars of that day. . . . When
be proceeded Bachelor of Arts, he was acquainted with twelve languages, and, as there
was no precedent of granting that degree to a boy of thirteen. Dr. H. Gower, one of the
Caput, thought fit to put upon record a notice of his proficiency in every species of
literature, as a justification of the University." — Monk's Life of Bentley, pp. 7, 8; see
also Nichol's Literary Aneedotes, vol. iv. pp. 253-259.

' We have given this paper exactly as it is printed in Mr. Edleston's Correspondence,
&c., pp. 273, 274. It is copied from the original, presented, along with the original
M8S. of Newton's four celebrated letters to Bentley, by his grandson, Richard Cumber-
laud, to Trinity College.— Cumberland's Memoirs, vol. i. p. 94.

i22 LIFE OF SIR ISAAC NEWTON. APPENDIX

as you shall have a desire to know, or peruse the whole in order if you
think fit."
The following memorandum is written upon the MS. by Bentley :—

" Directions from Mr Newton by his own Hand."

Directions given by John Craigefor understanding ilie Principia.

The course of reading proposed by John Craige for understanding the
Principia is much more extensive than that of Newton. It is published in
Bentley's Correspondence/ in a very interesting letter addressed to William
Wotton, which, we have no doubt, will be gratifying to some of our
readers : —

" Windsor, 24 June, 1691.
• " Sir,

" I would have sent you this line before this, if I had thought you had
returned from Cambridge. You may tell your Friend that nothing less
than a thorough knowledge of all that is yet known in the most curious
parts of Mathematicks can make him capable to read Mr. Newton's book
with that advantage which I believe he proposes to himself. Upon this
account, then, it may justly seem a very undecent piece of vanity to under-
take to give a method for reading a book that involves so much in it, and
so far above my strength ; however, in compliance with your desire, I
shall give you that which appears to me to be the shortest and most proper
method for such an end.

" Next to Euclid's Elements, let him apply himself to the Conick Sec-
tions, for which he need only read De Witt's First Book De EleTmnti.s
Lineamm Curvarum ; but let him not meddle with the second, which
treats of the Loca OeometHca. After he has made himself Master of the
Conick Sections, he must read some good System of Algebra : I know none
better than Jo. Prestefs Elemens des Mathemati'jues, especially if he can
get the new edition : here it is absolutely necessary to be constantly exer-
cising himself in the resolving of Problems ; but let him forbear meddling
with any geometrical Problem, until he be entirely Master of all the pre-
cepts of common Algebra ; afterwards he may look over Wallis, De Beaun,
Fermott, Hudden, and pick out several things which he will scarcely meet
with in Prestet, or any one System. When this is done, the great diffi-
culty of the work is over : this is the foundation of all ; and, therefore, he
must not grudge to bestow more time and application upon it, than, per-
haps, he would willingly allow, if he knew how much of both are requisite.
I must not forget to desire him to have a care not to begin with Kersey's
Algebra, which is apt (by its pompous bulk and title) to deceive new begin-
ners, as sad experience has taught myself. I can assure him there was
never a duller book writ; and, as far as I can judge, there was never a
man who pretended to write of Algebra that understood the design of it
less than Mr. Kersey did : but, to do him justice, he treats the Arithmetical
part of Algebra (both as to rational and Surd Quantified) in a very plain,
full, and clear method. The prodigious loss of time which this unluck>"
book made me sustain (when I had no guide to direct me in my studies of
this kind), drew this severe character of Mr. Kersey from me ; and I doubt
1 See vol. ii. pp. 736-740 ; and vol. i. p. xxxii.

NO. XI. LIFE OF SIR ISAAC NEWTON. 423

not but this advertisement will be of some use to your friend. When he
is thus well instructed with the Elements both of Geometry and Algebra,
he must study the use of both, Avhich consists in these two things, viz.,
the inventing of Theorems and resolving of Geometrical Problems ; for
which end he must begin with Cartes his Geometry, reading only the first
and third book ; but let him forbear the second till such time as he per-
fectly understands the first and last, which is Cartes his own advice in one
of his Letters, and, indeed, the nature of the thing shows it should be so.
This will give him a vaster idea of Geometry and of the great use of
Algebra than is possible for me to express, or for one that has not read it
to imagine. In the next place, let him peruse diligently De Wittfs second
book, which treats of the Loca Gemnetrica; and immediately after that
read Cartes his second book, which treats of the same subject : and because
the method of Tangents is the chief part of this 2nd book, and, indeed, of
all his whole Geometry (as he himself confesses), let him read Slusius his
Method, which he'll find in the Philosophical Transactions; Dr. Barrow's
Method, which he'll find (if I remember right) at the end of his 10th Geo-
metrical Lecture; and Mr. Leibnitz his Method, which he'll find in the
Acta Eruditorum, which is the best of all ; for by these four (not to men-
tion several others of less note) various methods he will become master of
this famous Problem, which, of all others, is of the greatest use in the
solution of the hardest Problems in Geometry. Here it will be again
necessary to exercise his pen much in the solving of Geometrical, as before
in the solving of Arithmetical Problems ; which he may furnish himself
with out of any books that are by him, particularly out of Vieta, Reinal-
dini, Henderson, Schooten, Kersey, &c. ; but he must keep close to Cartes
his General Method, and make no other use (as yet) of those books, but
only to provide himself with good store of Problems.

" Another great Invention, which has extremely promoted Geometry in
our Age, is the Method of Indivisibles. Wherefore, in the next place, let
him read the famous Cavalerius on that subject, who is, if not the Inventor,
yet, at least, the great Restorer of that Method. After him must be read
Dr. Barrow's Geometrical Lectures, who has carried that Method further
than any, and who will inform him with more excellent and universal
Theorems than any book that has been written in this Age. When your
friend has gone so far, he needs not be much solicitous in what order he
read any book of pure Geometry or Algebra, but may take them promis-
cuously as they come to his hand ; for scarce any thing will occur which he
will not be alDle to overcome : but the books that I think will be most
worthy of his application are, Archimedes and Apollonius, his works of Dr.
Barrow's edition ; Slusius his Mesolabium ; Vieta ; Gregorius a Sancto
Vincentio ; Mr. J wanes Gregory's Works ; Hugenius his Horologium Oscil-
latorium ; La Hire his Conick Sections ; and Tschirnhaus his Medicina
Mentis : but in this last, as also in Archimed and Hugenius, he must pass
over all that is not pure Geometry or Algebra.

" Then he must advance to those parts that are of a more compounded
nature, and which have a more immediate Relation to Mr. Newton's book.
First, then, he must read with a great deal of care Galileus his Works De
Motit ; in reading of which he will find vast help from Dr. Barrow's five
first Lectures. Then he must read Torricelli's book De Motu, who canies on
Galileus his design. He will find also much to the same purpose in Gas-

424 LIFE OF SIR ISAAC NEWTON. APPENDIX

sendus, Hugenius, and Mersenniis ; after them he must read Mariot, who
treats ofHhe Laws of Motion; then let him read what Sir Christopher
Wren and Dr. Wallis hath printed in the Philosophical Transactions con-
cerning the said Laws ; after this it will not be amiss to read Dr. Wallis
his Mechanicks, but he may pass over all that part De Calculo Centn gra-
vitatis. There are several things in Mr. Hobbes De Motu which will be of
some use to him : and indeed, without a good understanding of what these
Authors have already written concerning Motion, it is simply impossible to
understand this unparalleled book of Mr. Newton's, which treats of nothing
else but Motion, but in such a manner as tends to the perfecting of Philo-
sophy, and particularly that part of it which relates to the motion of the
Stars and Planets. Therefore, in the next place, your friend must make
himself perfect in Astronomy, in studying of which let him begin with
Tacqiiet ; for though he follows -a false Hypothesis, yet none has treated
this matter in so clear and full a method. But here I suppose yoxir friend
to be skilled in Trigonometry (both plane and spherical, for which ^Vorw?oo(^
first, and Ward afterwards, are to be read), and the use of the Sphere.
When he has done with Tacquet, let hjm get Kepler, Bulliald, Seth Ward,
Mercator and Gassendv^, and Copemictts, who ought to have been first
mentioned : by the help of these he will have a perfect understanding of
the state of Astronomy as it was before Mr. Newton published his book ;
which he might safely now begin with, were it not for some collateral
things which he brings in from the Opticks, Hydrostaticks, &c. For the
Opticks he must read Cartes, Ja. Gregory, Dr. Barrow, Honoratus Fabri,
and Tacquet ; and till he hath read these, he must pass over Avhat Cartes
speaks of his Ovals in the 2d book of his Geometry. For Hydrostaticks,
he must read Architned and Borelli, and something which he'll find in Dr.
Wallis his Mechanicks. And because much of Master Newton's book
refers to the Quadratures of Figures, he must read what has been written
on this subject by Dr. Wallis and Mr. David Gregory.

" Here, yoM see, is a vast deal to be done, even enoixgh to discourage a
man whose inclinations have not a great bias this way ; but he that seri-
ously considers the real pleasure and advantage that arises from this, and
(if I be not mistaken) only from this kind of study, will not be disheartened
either by the tediousness or difficulty that attends it ; but my business was
not to persuade, but, as far as I am able, to instruct your friend in Avhat
Order he ought to proceed in this matter ; which I have done with all the
care and exactness that was possible. And if this shall chance to be of no
use to him, yet I shall not fail entirely in the end for which I writ it, which
was to show my readiness, at least, to serve you, for whose sake there is
nothing that I will refuse to do that lies within the compass of my power,
though it were even to the discovery of my own weakness and ignorance,
which, perhaps, I have sufficiently done already ; and, therefore, shall add
no more, but that I am and ever shall be,

" Your most real friend and humble .servant,

"Jo. Craige.

" For Mr. William Wotton,

Chaplain to The Earle of Nottinghame,
at Cleveland-House,
London."

NO. XI. LIFE OF SIR ISAAC NEWTON. 425

The following note in Bentley's handwriting is written on the fourth
page or cover of Mr. Craige's letter : —

" Ex Newtono

Cartesii geometria in De la Hire Lectiones Conicse

Barthii Introductio in Algebra

Mercatoris Astronomia

Hugenii Horologium Oscillatorium."

The most complete and successful attempt to make the Principia acces-
sible to those who are " little skilled in mathematical science," has been
made by Lord Brougham, in his admirable analysis of that work, which
forms the greater part of the second volume of his edition of Paley's
Natural Theology.'^

"The reader of the Principia,'' says Lord Brougham, "if he be a toler-
ably good mathematician, can follow the whole chain of demonstration by
which the universality of gravitation is deduced from the fact, that it is a
power acting inversely, as the square of the distance to the centre of attrac-
tion. Satisfying himself of the law§ which regulate the motion of bodies in
trajectories around given centres, he can convince himself of the sublime
truths unfolded in that immortal work, and must yield his assent to this
position, that the moon is deflected from the tangent of her orbit round
the earth, by the same force by which the satellites of Jupiter are deflected
from the tangent of theirs, the very same force which makes a stone un-
supported fall to the ground. The reader of the Mecanique Celeste, if he be
a still more learned mathematician, and versed, in the modern improvements
of the calculus which Newton discovered, can follow the chain of demonstra-
tion by which the wonderful provision made for the stability of the universe,
is deduced from the fact, that the direction of all the planetary motions is
the same — the eccentricity of their orbits small, and the angle formed by
the plane of their orbits with the ecliptic acute. Satisfying himself of the
laws which regulate the mutual actions of these bodies, he can convince
himself of a truth yet more sublime than Newton's discovery, though flow-
ing from it, and must yield his assent to the marvellous position, that all
the irregularities occasioned in the system of the universe, by the mutual
attraction of its members, are periodical, and subject to an eternal law
which prevents them from ever exceeding a stated amount, and secures
through all time the balanced structiire of a universe composed of bodies
whose mighty bulk and prodigious swiftness of motion, mock the utmost
eiforts of the human imagination. All these truths are to the skilful
mathematician as thoroughly known, and their evidence is as clear, as the
simplest proposition of arithmetic is to common understandings. But how
few are those who thus know and comprehend them ! Of all the millions
that thoroughly believe these truths, certainly not a thousand individuals
are capable of following even any considerable portion of the demonstra-
tions upon which they rest ; and probably not a hundred now living have
ever gone through the whole steps of these demonstrations. "2

1 Dissertations on Subjects of Science, connected with Natural Theology/. By Henry
Lord Brougham, F.R.S., and Member of the National Institute of France. Vol. ii. pp.
243-480. Lond. 1839.

2 Ibid. vol. ii. pp. 172, 173.

426 LIFE OF SIR ISAAC NEWTON. APPENDIX

This analytical view of the Principia has since been published in a sepa-
rate form (1855) by Lord Brougham and Mr. Routh of St. Peter's College,
Cambridge. Mr. Routh has extended it to the second 'and third book.
The only addition made by Lord Brougham to the publication of 1839, is
an elaborate Appendix, chiefly upon central forces directed to more than
one centre, which it is greatly' to be lamented that Sir Isaac Newton did
not treat of

I have mentioned in'page 2/1, on the authority of Conduitt's MSS., the
time when different parts of the Principia were written. I have found, in
Sir Isaac's own handwriting, the following memorandum, which contains
some additional information of considerable interest : —

" In the tenth proposition of the second book, there was a mistake in the
first edition, by drawing the tangent of the arch gh from the wrong end of
the arch, which caiased an error in the conclusion ; but in the second edi-
tion I rectified the mistake. And there may have been some other mistakes
occasioned by the shortness of the time in which the book was written, and
by its being copied by an amanuensis who understood not what he copied ;
besides the press faults, for I wrote it in seventeen or eighteen months, be-
ginning in the end of December 1684, and sending it to the Royal Society
in May 1686, excepting that about ten or twelve of the propositions were
composed before, viz., the 1st and 11th in December 1679, the 6th, 7th, 8th,
9th, 10th, 12th, 13th, and 17th, Lib. I., and the 1st, 2d, 3d, and 4th, Lib. II..
in June and July 1684."

No. XII.

{Referred to in page 360, as No. XIII.)

After the publication of the second edition of the Principia, wlien an
erroneous interpretation had been given of the Scholium, Newton was very
anxious that the motive under which he wrote it, and the precise meaning
which he attached to it, should be understood. I have, therefore, given
in page 359 an explanation of his views, which is more full than that quoted
in the note from Raphson ; but I have found another MS. in which an ad-
ditional motive is stated. " And because," he says, " Mr. Leibnitz had
])ublished those elements (meaning those in the Lemma) a year and some
months before, without making any mention of the correspondence which
I had with him by means of Mr. Oldenburg ten years before that time, I
added a Scholium, not to give away the Lemma, but to put him in mind of
that correspondence, in order to his making a public acknoivledgment
thereof before he proceeded to claim that Lemma from vie."^
1 The words in Italics are an interlineation.

LIFE OF SIR ISAAC NEWTON. 42'

DRAUGHT COPIES OF THE SCHOLIUM TO THE LEMMA.
SCHOLIUM.

In Uteris qiice mihi cum Geometra peritissimo G. G. Leihnitio, anno 1676,
intercedebant, cum signijicarort me compotem esse methodi analyticse deter-
minandi Maximas et Minwms, ducendi Tangentes, quadrandi figuras
curvilineas, conferendi easdem inter se, et similia peragendi quae m ter-
minis surdis ceque ac in rationalibus procederent, et Tractatus quos de
hujusmodi rebus scripsisse, alternm quern Barrovius, anno 1669, ad Col-
linium niisit, et alterum anno 1671 in quo banc methodum prius expo-
sueram ; cumque fundamentum bujus methodi Uteris transpositis hanc
sententiam involventibus {Data Equatione quotcimque fluentes quantvtates
involvente Fluxiones invenire et vice versa), celarem, specimen vero ejusdem
in curvis quadrandis subjungerem et exemplis illustrarem ; et cum Col-
linius Epistolam, 10 Decern. 1672 datam, a me accepisset in qua metbodum
banc descripseram et exemplo Tangentium more Slusiano ducendarum
illustraveram, et bujus Epistolas exemplar mense Junio anno 1676 in
Galliam ad D. Leibnitium misisset, et vir clarissimus sub finem mensis
Octobris, in reditu suo e Gallia per Angliam in Germaniam, epistolas meas
in manu Collinii insuper consuluisset : incidit is tandem in methodum
similem sub diversis verborum et notarum formulis, et mense Junio
sequente specimen ejusdem in Tangentibus more Slusiano ducendis ad me
misit, et subjunxit se credere methodum meam, a sua non abludere pre-
sertim cum quadraturse curvarum per utramque methodum faciliores
redderentur. Methodi vero utriusque fundamentum continetur in hoc
Lemmate.

Almost the whole of the Scholium printed in i\i^Q first and second editions
of the Principia is put in Italics, in order to show the change upon it
which Sir Isaac had proposed for the third edition.

In the other two forms of the Scholium, written on the same sheet with" the
preceding, the first and second half of it are partly transposed ; and at the
end of one of them after in hoc Lemmate, are the words et hoec methodus
plenius exponitur in Tractatu.

It is singular that both Newton and Cotes should have permitted the
words annis abhinc decern to remain in the second edition, seeing that in
1713, thirty -seven years had elapsed. In the draughts, however, of the
Scholium under consideration, the more correct words anno 1676 are sub-
stituted.

I have found another draught of the Scholium, distinctly written, with-
out any important correction, which differs only from the printed one in
the first edition of the Principia in the following points : —

1. After ducendi tangentes the words quadrandi figuras curviUneas are
added.

2. After procederet, the words methodumque, exempUs iUustrarem are
added ; and

3. Before celarem, the word eandem is inserted.

428 LIFE OF SIR ISAAC NEWTON.

No. XIII.

{Referred to in page 362, cis No. XIV.)

John Wallis, D.D., the author of the following letter, was one of the
most distinguished mathematicians of the seventeenth century. He was
born at Ashford in Kent on the 23d November 1616. He studied at
Emanuel College, Cambridge, and was a Fellow of Qiieens'. In 1644 he
was chosen one of the Secretaries to the Westminster Assembly of Divines,
and in 1649 Savilian Professor of Geometry at Oxford. Between the years
1654 and 1662 he carried on a keen controversy with Hobbes. His princi-
pal work is his Arithmetica Infinitorum, published in 1655.' His works,
both theological and mathematical, were published by the curators of the
University of Oxford in 1699, in 3 vols, folio. He died at Oxford on the
28th October 1703, and was in the 82d year of his age when he wrote the
two following letters : —

1. — LETTER FROM WALLIS TO NEWTON.

" Oxford, April 30, 1695.
" Sir,
*' I thank you for your letter of April 21st by Mr. Conou. But I can by
no means admit your excuse for not publishing your Treatise of Light and
Colours. You say you dare not yet publish it. And why not yet ? Or if
not now, when then ? You add, lest it create you some trouble. What
trouble now more than at another time. Pray consider how many years
this hath layn upon your hands already, and while it lyes upon your hands
it will still be some trouble ; (for I know your thoughts must still be run-
ning upon it.) But when published that trouble will be over. You think,
perhaps, it may occasion some letters (of exceptions) to you, which you
shall be obliged to answer. What if so ? 'Twill be at your choice whether
to answer them or not. The treatise will answer for itself. But are you
troubled with no letters for not publishing it? I suppose your other
friends call upon you for it as well as I, and are as little satisfied with the
delay. Meanwhile you lose the reputation of it, and we the benefit, so
that you are neither just to yourself nor kind to the public. And perhaps
some' other may get scraps of the notion and publish it as his own ; and then
'twill be his, not yours, though he may perhaps never attain to the tenth
part of what you be already master of. Consider that 'tis now about thirty
years since you were master of these notions about Fhtxions and Infinite
Series ; but you have never published aught of it to this day (which is
worse than nonumque prematur in annum). 'Tis true I have endeavoured
to do you right in that point. But if I had published the same or like
notions without naming you, and the world possessed of another calculus
differentialis instead of your fluxions : how should this or the next age
know of your share therein ? And even what I have said is but playino; an
after game for you to recover (precariously ex postliminio) what you had
let slip in its due time. And even yet I see you make no great haste to
1 See this Volume, page 340.

NO, XIII. LIFE OF SIR ISAAC NEWTON. 429

publish these letters i which are to be my vouchers for what I say of it.
And even these letters at first were rather extorted from you than volun-
tary. You may say, perhaps, the last piece of this concerning colour is
not quite finished. It may be so (and perhaps never will), but pray let us
have what is ; and while that is printing, you may (if ever) perfect the
rest. But if, during the delay, you chance to die, or those papers chance
to take fire (as some others have done), 'tis all lost both as to you and as
to the public. It hath been an old complaint that an Englishman never
knows when a thing is well (but will still be overdoing), and thereby loseth,
or spoils many times what was well before. I own that modesty is a virtue,
but too much diffidence (especially as the world now goes) is a fault. And
if men will never publish aught till it be so perfect that nothing more can
be added to it, themselves and the public will both be losers. I hope, Sir,
you will forgive me this freedom (while I speak the sense of others as well
as my own), or else I know not how we shall forgive these delays. I could
say a great deal more, but if you think I have said too much already, pray
forgive this kindness of

" Your real friend and humble servant,

*' John Wallis.
" Dr. Gregory gives you his service."

2.— LETTER FROM WALLIS TO NEWTON.

The following letter, written more than two years afterwards, is partly
on the same subject, but is interesting from the message which it contains
from Leibnitz in the postscript of a letter to Wallis, dated May 28, 1697 : — *

" OxoNi^, Julii 1, 1697.
" Clarissime Vir,
" Accepi nuper a D. Leibnitio literas Hanoverae datas Mai 28, 1697. In
quibus cum nonnulla sint quse te quadamtenus spectant, liberem tibi suis
verbis exponere, viz. , ' Si qica esset occasio, D. Newtono, summi ingenii
viro (forte per amicum) salutem officiosissimam a me nunciandi, eumque meo
nomine precandi ne se ab edendis prceclaris meditationibus diverti pateretur,
heneficio hoc a te petere auderem. Item methodum Fluxionum profundissimi
Newtoni cognitam esse methodo mea differentiali non tamen animadverti,
postquam opus ejus ad lucem prodiit, sed etiam professus sum in A ctis
EniditoTum ; et alios quoque monui. Id enim candori meo convenire judi-
cam non minus quam ipsius merito. Itaque communi nomine designare soleo
Analyseos Injinitesimalis {quce latius quam Methodus Tetragonista patet)
interim ; quemadmodum et Vietiana et Cartesiana methodus, Analyseos
Speciosa nomine venit ; discrimina tamen nonnulla supersunt. Itafortasse
Newtoniana et mea differunt in nonnullis.' Hsec ea verbatim transcripsi
ex nobilissimi Leibnitii Uteris ut videas id ab exteris etiam desiderari,
quod ego non tantum petii sed obtestatus sum aliquoties, aliique mecum,
nee tamen hactenus obtinuimus ut quae apud te primis desideratissima

1 The letters on Fluxions in Walliss Works, vol. ii. pp. .391-396.

2 The letter of Leibnitz is dated 28<A March, though in the title prefixed to it by
Wallis, and in the following letter, the date is made 28th May.

430 LIFE OF SIR ISAAC NEWTON.

APP. NO. XIII.

ederentur. Qnippe cum hoc aut negas aut differs ; non tantum tuse fama-
sed et bono publico deesse videris. Duas illas Epistolas (longiusculas et
refertissimas) anno 1676 scriptas (unde ego Excerpta qusedam antehac edidi)
ciirabo ego (nisi me id vetes) subjungi volumini cuidam meo (jam aliqiiandiu
sub praelo) quamprimum per pra?li moras licebit. Tuam de Lumine et
Coloribus Hypothesin novam (cujus aliquot specimina jam ante multis
annis dederis) quara per annos (si recte conjicio) triginta apud te suppri-
mere dictum est, spero ut propediem edendam cures ; \\t quam ego insig-
aem Natural! Philosophise accessiouem jamdudum existimavi et publice
deberi : Quam et PhbIo tuisse diu paratam audio. ) Idem dixerim de pluri-
bus qute apud te latent, quorum ego non sum conscius. Heec interim rap-
tim monenda duxi.

" Tuus ad officia,

" J.;hannes Wallis. i
" I put it into this form, that if you think it proper you may desire Dr.
Sloan to insert it in the Transactions."^ I

The letter is addressed on the back,

" To Mr. Isaac Newton, Controller
of the Mint at The Tower,

London,"

The first paragraph of this message to Newton, in the preceding letter, is
given in Leibnitz's letter to Wallis, as printed in the third volume of hLs
works, and the following reason is assigned for withholding the rest of the
message -.—[Seqiiebantur paiica qxicc rem Mathematicam non spectant] —
Wallisii Oj^era, tom. iii. p. 680.

In Wallis's reply to Leibnitz, dated July 30, 1697, he says,—" Quje
Newtonurn sp^ctant, ad eum scripsi tuis verbis, simulque obtestatus sum
meo nomine ut imprimi curet qute sua siipprimit scripta. Quod et saepe
ante feceram, sed hactenus in cassum," — Ibid. p. 685.

1 This raemorandum is placed at the very foot of the page, apparently fur the pur-
pose of its being cut off.

END OF VOLUME FIRST.

KDINBURGH : T CONSTABLE, ' V

PRINTKR TO THE QUEEN, AXI) TO THE UNIVKKSITY. A. V.

PLEASE 00 NOT REMOVE
CARDS OR SLIPS FROM THIS POCKET

UNIVERSITY OF TORONTO LIBRARY

P&AScL