Infomotions, Inc.Essays on the life and work of Newton, by Augustus De Morgan, ed., with notes and appendices, by Philip E. B. Jourdain ... / De Morgan, Augustus, 1806-1871




Author: De Morgan, Augustus, 1806-1871
Title: Essays on the life and work of Newton, by Augustus De Morgan, ed., with notes and appendices, by Philip E. B. Jourdain ...
Publisher: Chicago, London : The Open court publishing company, 1914.
Tag(s): leibniz, gottfried wilhelm, freiherr von, 1646-1716; brewster, david, sir, 1781-1868. memoirs of the life of sir isaac newton; newton, isaac, sir, 1642-1727; newton; leibniz; commercium epistolicum; differential calculus; royal society; isaac newton; brews ter's; catherine barton
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GIFT OF 




Mathematics Dept 



ESSAYS ON THE LIFE 
AND WORK OF NEWTON 




SIR ISAAC NEWTON. 



LIFE AND WORK OF 
NEWTON 



BY 

AUGUSTUS DE MORGAN 

EDITED, WITH NOTES AND APPENDICES, BY 

PHILIP E. B. JOURDAIN 

M. A. (Cantab.) 



CHICAGO AND LONDON 
THE OPEN COURT PUBLISHING COMPANY 

1914 




Copyright in Great Britain under the Act of 191 1 



EDITOR'S PREFACE 

AUGUSTUS DE MORGAN'S biographical sketch en- 
titled ' ' Newton " appeared in The Cabinet Portrait 
Gallery of British Worthies^ in 1846, and is the 
first essay printed in the present volume. It was, 
as Mrs De Morgan 2 said, " after Baily's Life of 
Flamsteed* the first English work in which the 
weak side of Newton's character was made known. 
Justice to Leibniz, to Flamsteed, even to Whiston, 
called for this exposure ; and the belief that it was 
necessary did not lower the biographer's estimate 
of Newton's scientific greatness, and of the simplicity 
and purity of his moral character. Francis Baily's 
discovery of the correspondence between the Rev. 
John Flamsteed, the first Astronomer Royal, and 
Abraham Sharp, as well as between Newton, 
Halley, and Flamsteed, on the publication of Flam- 
steed's catalogue of stars, had thrown a new light 

1 Vol. xi, London, 1846, pp. 78-117. This series was edited by 
Charles Knight. A three-columned quarto edition in one volume, and 
giving no editorial credit, was published in London by Henry G. Bohn 
in 1853 under.the title Old England's Worthies : A Gallery of Portraits. 
Besides the small woodcut portraits, it contains twelve full-page 
" illuminated engravings." De Morgan's " Newton " occupies pp. 220- 
224 of this edition. 

* Memoir of Augustus De Morgan, London, 1882, p. 256. 

3 London, 1835. 

v 

609758 



vi EDITOR'S 

on the character of Newton. It appeared that the 
practical astronomer had been treated ungenerously 
by Newton, who failed to observe the conditions of 
publication agreed to by all parties ; and afterwards, 
when remonstrated with, omitted the name of 
Flamsteed in places where it had formerly stood in 
the earlier editions of the Principia. " 

" My husband," adds Mrs De Morgan, "entered 
into the enquiry with keen interest, and with a 
power of research possible only to one who was 
fully master of the history of mathematical dis- 
covery. " And it is not only mathematical discovery 
and controversy that De Morgan treats in the just, 
broad-minded, and high-minded way that is char- 
acteristic of him. He disclaimed any particular 
interest in those religious beliefs of Newton which 
he discussed so thoroughly ; still, " notwithstanding 
this disclaimer," says Mrs De Morgan, 1 "I believe 
my husband felt more interest in the question, from 
its own nature, than he was himself aware of. 
Whether I am mistaken in this may be surmised 
by those who have read his own letter to his mother 
in this volume. 2 He says, ' Whatever Newton's 
opinions were, they were the result of a love of 
truth, and of a cautious and deliberate search after 

1 Op. cit., p. 260. Cf. pp. 260-261, and XI. of the first essay 
printed below. 

2 This letter of De Morgan's to his mother, which is printed in the 
Memoir, is on pp. 139-144 and there is no mention of Newton in 
it. The passage, however, occurs towards the end of XI. of De 
Morgan's biography of Newton printed below. 



PREFACE vii 

it.' That Newton was a firm believer in Christianity 
as a revelation from God is very certain, but whether 
he held the opinions of the majority of Christians 
on the points which distinguish Trinitarians from 
Arians, Socinians, and Humanitarians, is the 
question of controversy." 

The second of De Morgan's Essays printed in 
this volume concerns the great controversy about 
the invention of the fluxional or infinitesimal calculus, 
in which Newton and Leibniz were the principals. 
The essay printed is from the Companion to the 
Almanac -, and is now extremely rare. It is of 
great interest and importance both on account of 
the fairness and vigour which De Morgan always 
showed in the defence of Leibniz against the im- 
putations of Newton and the Royal Society, and 
because it first introduced the English public to 
Gerhardt's important discovery of Leibniz's manu- 
scripts showing his gradual discovery of the calculus 
in 1673-1677. This essay also contains a summary 
of much of De Morgan's historical work on the con- 
troversy./ In January 1846, a paper by De Morgan, 
"On a point connected with the Dispute between 
Keill and Leibnitz about the Invention of Fluxions," 
was read to the Royal Society, and it was after- 
wards printed in the Philosophical Transactions^ 

1 Phil. Trans.) 1846, pp. 107-109. This paper was wrongly stated 
in Mrs De Morgan's Memoir (pp. 257, 402, 406) to be printed in the 
Transactions of the Cambridge Philosophical Society. On the subject 
of this paper, see the second appendix to the third essay. 



x EDITOR'S 

planatory, or critical nature have been added to all 
the essays, but all that is not De Morgan's is put 
in square brackets. Such notes have become 
necessary, and it is hoped that the present ones 
will reply to all the calls of necessity and will make 
the book both useful and complete. Very little 
has to be criticised in De Morgan's history or con- 
clusions. Like everything he wrote, these essays 
of his are marked by scrupulous care, sanity of 
judgment, and wide reading ; and one hardly knows 
which to admire most : the breadth or the height of 
his mind. 

Several minor structural alterations have been 
made : the first and third essays have been split 
into sections to facilitate reading and reference ; 
the names of Huygens and Leibniz have through- 
out had their spelling altered from " Huyghens " 
and ' ' Leibnitz " except in the titles of books and 
actual quotations. 1 Leibniz always signed himself 
as "Leibniz," but I have always cited the titles 
of books as they were printed, even though mis- 
spellings may have occurred there. This seems 
quite indispensable for convenience in reference. 

The frontispiece is from an engraving by E. 
Scriven of Vanderbank's portrait of Newton in the 
possession of the Royal Society of London. An 
engraving from this picture accompanied the original 

1 The spelling " Leibnitz " even in titles of books where " Leibniz" 
is written is one of the faults in Gray's Bibliography. 



PREFACE xi 

of De Morgan's biographical sketch ; but the present 
frontispiece is from a much finer engraving prefixed 
to the biography of Newton in the first volume of 
The Gallery of Portraits : with Memoirs. * 

PHILIP E. B. JOURDAIN. 

THE LODGE, 

GIRTON, CAMBRIDGE, 

ENGLAND. 

1 London, 1833, pp. 79-88. On the portraits of Newton, cf. Samuel 
Crompton, Proc. Lit. and Phil. Soc. of Manchester, vol. vi, 1866-7, 
pp. 1-7. 



CONTENTS 

TAGZ 

EDITOR'S PREFACE ...... v 

I. NEWTON (1846) ..... i 

II. A SHORT ACCOUNT OF SOME RECENT DISCOVERIES 
IN ENGLAND AND GERMANY RELATING TO 
THE CONTROVERSY ON THE INVENTION 
OF FLUXIONS (1852) . . . .65 

APPENDIX ON THE MANUSCRIPTS AND PUBLICA- 
TIONS OF NEWTON AND LEIBNIZ . . 102 

III. REVIEW OF BREWSTER'S MEMOES OF THE LIFE, 
WRITINGS, AND DISCOVERIES OF SIR ISAAC 
NEWTON (1855) . . . . .117 

APPENDIX I. DE MORGAN'S VIEW OF LEIBNIZ'S 
CHARACTER . . . . .183 

APPENDIX II. NOTE BY DE MORGAN ON THE 
CHARACTER OF NEWTON AND ON THE ACTIONS 
OF THE ROYAL SOCIETY, WRITTEN IN 1858 . 187 

INDEX ....... 194 



xiii 



I 

NEWTON 

(1846) 



NEWTON 

A BIOGRAPHY of Newton, intended for such a collec- 
tion as this, must necessarily be much condensed ; 
the account of his discoveries must be- little more 
than allusion, and a perfect list of his writings and 
their editions is out of the question. The only Life 
which exists on any considerable scale (as justly 
remarked by the author) is that by Sir David 
Brewster in the "Family Library" (No. 24): this 
will be our chief reference on matters of fact. 1 On 

1 [The fullest life of Newton that has appeared was published after 
this biography (1846) by De Morgan, and was also written by Sir 
David Brewster under the title Memoirs of the Life, Writings, and 
Discoveries of Sir Isaac Newton, 2 vols., Edinburgh, 1855. A second 
edition apparently unaltered, even as to the mistakes was issued at 
Edinburgh in 1860. De Morgan's famous but scarce review (1855) of 
this work is reprinted below as the third of these Essays. An ex- 
tremely valuable " Synoptical View of Newton's Life" was prefixed to 
J. Edleston's Correspondence of Sir Isaac Newton and Professor Cotes, 
. . . (London and Cambridge, 1850). The earlier biographies of 
Newton were as follows: J. B. Biot, "Newton," Biographic Univer- 



of Si 

Library," No. 24, 1831 (revised by W. T. Lynn in 1875) ; De Morgan, 
"Newton," Penny Cyclopedia, 1840; Fontenelle's Eloge de Monsieur 
le Chevalier Newton, 1728, translated into English in the same year; 
and Benjamin Martin in Biographia Philosophica, 1764. For bio- 
graphies of Newton, see also G. J. Gray, A Bibliography of the Works 
of Sir Isaac Newton, Cambridge, second edition, 1907 (the first was 
published in 1888), pp. 70-76. 

Various aspects of Newton's work have been dealt with in, for 

3 



4 NB iVTON 

those of opinion, particularly as to the social char- 
acter of Newton, we must differ in some degree 
from our guide, as well as from all those (no small 
number) whose well-founded veneration for the 
greatest of philosophical inquirers has led them to 
regard him as an exhibition of goodness all but 
perfect, and judgment unimpeachable. That we can 
follow them a long way will sufficiently appear in 
the course of this sketch. 

I 

Isaac Newton was born at Woolsthorpe, near 
Grantham, in Lincolnshire, on Christmas Day, 
1642 : l a weakly and diminutive infant, of whom it 
is related that, at his birth, he might have found 
room in a quart mug. He died on March the 2Oth, 
1727, after more than eighty-four years of more 
than average bodily health and vigour ; it is a proper 
pendant to the story of the quart mug to state that 
he never lost more than one of his second teeth. 
His father, Isaac Newton, though lord of the poor 

example, (i) Stephen Peter Rigaud, Historical Essay on the First 
Publication of Sir Isaac Newton's Principia, Oxford, 1838 ; (2) W. W. 
Rouse Ball, An Essay on Newton's " Principia," London and New 
York, 1893 ; (3) Ferdinand Rosenberger, Isaac Newton und seine 
physikalischen Principien^ . . . Leipsic, 1895. Besides these, there 
is notably the account and critique of Newton's principles of mechanics 
in Ernst Mach's Mechanik, translated into English by T. J. M'Cormack 
under the title The Science of Mechanics : A Critical and Historical 
Account of its Development, third edition, Chicago, 1907, pp. 201-245.] 
1 [Old style. The new year was then reckoned from March the 25th, 
so that what we now call, for example, January the 6th, 1672, was then 
January the 6th, 1671, and is sometimes written "January the 6th, 
1671/2." We will always write dates in the modern way.] 



NE WTON 5 

manor of Woolsthorpe, was in fact a small farmer, 
who died before the birth of his son. The manor, 
which had been in the family about a hundred 
years, was Newton's patrimony : it descended to 
the grandson of his father's brother. This heir sold 
it in 1732 to Edmund Tumor, to whose descendant 
the world is much indebted for a collection of facts 
connected with Newton's history. 1 A curious tradi- 
tion of a conversation of Newton with Gregory, in 
which the former affirmed himself to be descended 
from a Scotch family, his grandfather having come 
from East Lothian at the accession of James I., 
will be found in the appendix to Brewster's Life? 
with a careful attempt to see how far the presump- 
tion it affords can be supported by collateral evidence. 
But Newton himself (twenty years before the date 
of this conversation) gave his pedigree on oath into 
the Heralds' Office, stating that he had reason to 
believe that his great grandfather's father was John 
Newton, of West by, in Lincolnshire. 3 To bring all 
that relates to his family together, his mother, when 
he was three years old, married Barnabas Smith, 
rector of North Witham, by whom she had one son 
and two daughters (who gained by marriage the 



1 [Edmund Tumor, Collections for the History of the Town and Soke 
of Grant ham, containing authentic Memoirs of Sir /. Newton now first 
published, 1806. This book contains, among other things, Conduitt's 
sketch of Newton which was drawn up for the use of Fontenelle.] 

2 \Cf. Brewster's Memoirs, 1855, vol. ii, pp. 537-545.] 

3 [On Newton's pedigree (1705), see Tumor, op. cit., p. 169, and 
the reference to Brewster's Memoirs given in the fourth note.] 



6 NE WTON 

names of Pilkington and Barton). The children of 
these three, four nephews and four nieces of Newton 
by the half-blood, inherited his personal property, 
amounting to 32,000. One of these nieces, 
Catherine, who married a Colonel Barton, became a 
widow, and afterwards lived in Newton's house. 
After her second marriage (to Mr Conduitt, who 
succeeded Newton as master of the Mint), she and 
her husband resided with him until his death. 1 They 
are the authority for many anecdotes given by 
Fontenelle in the Eloge read to the Academy of 
Science. Mrs Conduitt's only daughter, Catherine, 
married Mr Wallop, afterwards Viscount Lymington 
by inheritance ; she transmitted a large collection 
of Newton's papers, also by inheritance, to the 
family of the Earl of Portsmouth. These " Ports- 
mouth Papers" still exist unpublished, 2 and there 
is also a mass of papers in the Library of Trinity 
College, Cambridge, which are well known. 3 

1 [It is a mistake that Catherine Barton, the daughter of Robert 
Barton and Hannah Smith, Newton's half-sister, was the widow of 
Colonel Barton. That this was so was stated in an anonymous Life of 
the Earl of Halifax published in 1715. Cf. Brewster, Memoirs^ 1855, 
vol. ii, p. 273.] 

2 [The scientific part of the " Portsmouth Papers" was presented by 
Lord Portsmouth to the University of Cambridge, and has now been 
classified and deposited in the University Library. A descriptive 
catalogue of it was published at Cambridge, in 1888, under the title 
A Catalogue of the Portsmouth collection of Books and Papers written 
by or belonging to Sir Isaac Newton, the Scientific Portion of which 
has been presented by the Earl of Portsmouth to the University of 
Cambridge. This catalogue was drawn up by the Syndicate appointed 
on November the 6th, 1872, and the Preface was signed by H. R. Luard, 
G. G. Stokes, J. C. Adams, and G. D. Liveing. Only small parts of 
the collection have as yet been published.] 

3 [The correspondence with Cotes and some other letters were 



NE WTON 7 

At his mother's second marriage, Newton passed 
under the care of his grandmother. After some 
education at day schools, he was placed, in his 
twelfth year, at the public school at Grantham. 
He distinguished himself here by a turn for 
mechanics and carpentering ; and among his early 
tastes was the love of writing verses, 1 and of draw- 
ing. 2 The dials which he made on the wall of his 
family house at Woolsthorpe have lasted to our day. 
They were lately carefully cut out by Mr Turner, 
and presented, framed in glass for preservation, to 
the Royal Society. 3 While at Grantham he formed 
a friendship, which afterwards became a more serious 
feeling, with a young lady named Storey, who lived 
with the family in which he boarded. Their 
marriage was prevented by their poverty, Miss 
Storey was afterwards twice married, and as Mrs 
Vincent, at the age of eighty-two, after Newton's 
death, gave many particulars concerning his early 
life. He continued her friend to the end of his 
life, and was her frequent benefactor : and he lived 

published by Edleston in the above-mentioned work. On other manu- 
scripts of Newton's, see W. W. Rouse Ball, op. cit., pp. 2-5, where 
" Snirburn Castle" is, as in G. J. Gray, op. cit., p. 75, misspelt 
" Sherborn Castle" a mistake that may give rise to a confusion of 
two different places, near Wallingford in Berkshire and in Dorset 
respectively.] 

1 [See Brewster, Memoirs, 1855, vol. i, pp. 12-13.] 

2 [According to Newton's own later confession, he was extremely 
inattentive to his studies and stood very low in the school ; but soon, 
owing to the excitation of a spirit of emulation, he exerted himself in 
the preparation of his lessons and finally rose to the highest place in 
the school (Brewster, Memoirs^ 1855, vol. i, pp. 7-8). On Newton's 
drawings, see ibid., p. 12.] 

:! [But cf. Brewster, Memoirs, 1855, vo ^ *> PP 11-12.] 



8 NE WTON 

and died a bachelor, though to say for her sake 
would perhaps be going beyond evidence ; particu- 
larly when the engrossing nature of his subsequent 
studies is considered. 1 



II 

When he was fourteen years old his stepfather 
died, and his mother, who then took up her residence 
at Woolsthorpe, recalled him from school to assist 
in the management of the farm. 2 As it was found, 
however, that he was constantly occupied with his 
books when he should have been otherwise engaged, 
his maternal uncle recommended that he should be 
sent to Cambridge. He was accordingly admitted, 
on June the 5th, 1660, a member of Trinity College, 
a foundation which his name has ever since not 
only supported, but invigorated. According to the 
college books, he was subsizar 3 in 1661, scholar in 

1 [CJ. Brewster, Memoirs, 1855, vol. i, pp. 13-14.] 

2 [On Newton's early scientific experiment with the wind, see the 
third Essay below, II.] 

a A sizar at Cambridge was, in the original meaning of the word, 
a student whose poverty compels him to seek to maintain himself in 
whole or part by the performance of some duties which were originally 
of a menial character. By this institution a youth could live by the 
work of his hands while he pursued his studies. In our days there 
is but little distinction between the sizars and those above them ; except 
in college charges, none at all. Those who look upon universities as 
institutions for gentlemen only, that is, for persons who can pay their 
way according to a certain conventional standard, praise the liberality 
with which poorer gentlemen than others have been gradually emanci- 
pated from what seems to them a mere badge of poverty. But those 
who know the old constitution of the universities see nothing in it 
except the loss to the labouring man and the destitute man of his 
inheritance in those splendid foundations. If sizarships with personal 



NE WTON 9 

1664, Bachelor of Arts in 1665, Junior Fellow in 
1667, Master of Arts and Senior Fellow in 1668. In 
1669, Dr Barrow resigned the Lucasian Professor- 
ship of Mathematics, and Newton was appointed 
his successor. From this period, when all money 
cares were removed by the emoluments of his 
fellowship and professorship, we must date the 
beginning of Newton's public career. 

To go back a little ; it does not appear that 
Newton went to Cambridge with any remarkable 
amount of acquired knowledge, or any results of 
severe discipline of mind. He had read Euclid^ it 
is said, and considered the propositions as self- 
evident truths. 1 This is some absurd version of his 

services had not existed, Newton could not have gone to Cambridge ; 
and the Principia might never have been written. Let it be re- 
membered, then, that, so far as we owe this immortal work and its 
immortal work to the University of Cambridge, we owe it to the 
institution which no longer exists, by which education and advance- 
ment were as open to honest poverty seeking a maintenance by labour, 
as to wealth and rank. Let the juries who find on their oaths that 
scores of pounds' worth of cigars are reasonable necessaries for young 
college students, think of this, if they can think. [Cf. Edleston, 
op. cit., p. xli.] 

1 [Before Newton left Woolsthorpe, his uncle had given him a copy 
of Sanderson's Logic y which he seems to have studied so thoroughly 
that, when he afterwards attended lectures on that work, he found 
that he knew more of it than his tutor. Finding him so far advanced, 
his tutor told him that he was about to read Kepler's Optics to some 
Gentlemen Commoners, and that he might attend the reading if he 
pleased. Newton immediately studied the book at home, and when 
his tutor gave him notice that his lectures upon it were to begin, he 
was surprised to learn that it had been already mastered by his pupil. 
About the same time, probably, he bought a book on Judicial Astrology 
at Stourbridge fair a fair held yearly in Cambridge in September and, 
in the course of perusing it, he came to a figure of the heavens which 
he could not understand without a previous knowledge of trigonometry. 
He therefore bought an English uctid\vhh an index of all the problems 
at the end of it. Having turned to two or three which he thought 
likely to remove his difficulties, he found the truths which they 



io NEWTON 

early studies : many propositions, no doubt, are very 
evident ; but if Newton ever gave this account of 
himself, which we do not believe, it proves nothing 
but that the lad carried to the University as much 
of self-conceit as the man brought away of learning 
and judgment. That the young mechanician, 
desultory in the previous reading, deep beyond his 
years in construction, 1 and practical verification, 
found within himself at first some dislike to the 
beaten road of mathematics, and was willing to 
make it royal by admitting all he was asked to 
prove, is what we can easily believe : for such is the 
most frequent tendency of an unbalanced exercise of 
manual ingenuity. That he may have stated this 
when he expressed his regret that he had not paid 
greater attention to the geometry of the ancients, is 
not improbable. Were such his bent, the discipline 
of the University would soon show a mind like his 
the paramount necessity of a different mode of pro- 
enunciated so self-evident that he expressed his astonishment that any 
person should have taken the trouble of writing a demonstration of 
them. He therefore threw aside Euclid "as a trifling book," and 
set himself to the study of Descartes' Geometry, where problems not so 
simple seem to have baffled his ingenuity. Even after reading a few 
pages, he got beyond his depth and laid aside the work ; and he is said 
to have resumed it again and again, alternately retreating and advancing, 
till he was master of the whole, without having received any assistance. 
The neglect which he has shown of the elementary truths of geometry 
he afterwards regarded as a mistake in his mathematical studies, and 
expressed 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 " (Brewster, Memoirs, 1855, vol. i, pp. 21-22; cf. the third 
Essay below, II.).] 

1 Let it be remembered that we are not told that Newton, when very 
young, took greatly to anything except arts of construction. 



NE WTON 1 1 

ceeding. 1 Again, we are not told anything of 
Newton's pupillar career at Cambridge, except that 
he is known to have 2 bought a prism (an epoch in 
his life) in 1664 ; 3 and that, in the same or the next 
year, being competitor for a college law-fellowship 
with a Mr Robert Uvedale, the two candidates were 
of perfectly equal merit, and Dr Barrow accordingly 
elected Mr Uvedale as the senior in standing. We 
have no account of any great sensation produced by 
the talents of Newton during his college career. 



1 [See II. of the third Essay below for De Morgan's opinion on the 
story of Barrow forming, after an examination of Newton in Euclid in 
1664, an indifferent opinion of Newton's knowledge (Brewster, Memoirs, 
vol. i, p. 24).] 

2 The status pupillaris lasts about seven years, that is, until the 
degree of Master of Arts is taken. 

3 [The study of Descartes' Geometry seems to have inspired Newton 
with a love of the subject, and to have introduced him to higher mathe- 
matics the study of the works of Vieta, Schooten, and Wallis. In a 
note-book partly written in 1663-1664, in which mathematical notes on 
these writers were made, he also wrote down some observations on 
refraction, on the grinding of spherical lenses, and on the errors of 
lenses and the method of rectifying them. An entry in this same book 
made by Newton in 1699 is the statement that the annotations out of 
Schooten and Wallis were made in the winter between 1664 and 1665. 
At this time he found the Method of Infinite Series ; and, in the 
summer of 1665, being forced from Cambridge by the plague, he com- 
puted the area of the hyperbola at Boothby in Lincolnshire to fifty-two 
figures by the same method (Brewster, Memoirs, 1855, vol. i, pp. 23-24; 
vol. ii, pp. 10-15). In 1665 Newton committed to writing his first dis- 
covery of the method of fluxions. This paper was written by his own 
hand, and dated May the 2Oth, 1665, and the notation of dotted letters was 
here used. On another leaf of the same note-book, the method was de- 
scribed under the date of May the i6th, 1666. In the same book again, 
with a date of November the I3th, 1665, there was written another paper 
on fluxions with their application to the drawing of tangents and " the 
finding of the radius of curvity of any curve." In October 1666, 
Newton drew up another small tract, in which the method of fluxions 
was again put down without the notation of dotted letters and applied 
to equations involving fractions and surds and such quantities as were 
afterwards called transcendent (ibid. See also the Appendix to the 
second Essay below). ] 



12 NEWTON 

Even Barrow, the best judge in Cambridge, and, 
after Walk's, in England, writing to Collins in 1669 
(when he was on the point of resigning the mathe- 
matical chair to Newton), mentions him as an un- 
known man l of great promise, in terms of high, but 
not unusual commendation. 



ill 

The first period of Newton's life is twenty-seven 
years, ending with his appointment to the Lucasian 
professorship. The second, of twenty-six years, 
ending with his appointment to his first office in 
the Mint in i695, 2 was the period of the announce- 
ment of all his discoveries. The third and longest, 
of thirty-two years, containing his official residence 
in London, saw him in the uninterrupted possession 
of as much fame as man can have, and power never 
equalled over those of the same pursuits as himself. 
The merely biographical history of his second period 
is not long. On Dec. the 2ist, 1671, and Jan. the 
nth, 1672, the Royal Society entered on their 

1 "A friend of mine here, that hath an excellent genius to these 
things, brought me . . . papers . . . which I suppose will please 
you." And again, some days after, " I am glad my friend's paper 
gives you so much satisfaction ; his name is Mr Newton, a Fellow of 
our College, and very young (being but the second year Master of 
Arts), but of an extraordinary genius and proficiency in these things." 
[Barrow sent Newton's tract De Analysis Collins on July the 3ist, 1669 
(Brewster, Memoirs, 1855, vol. i, pp. 27, 36; vol. ii, pp. 14-15).] 

2 [Newton was appointed Warden of the Mint in 1696, and Master of 
the Mint in 1699. Cf. Edleston, op. >., pp. xxxv, Ixviii ; Brewster, 
Memoirs, 1855, vol. ii, pp. 191-193-] 



NEWTON 13 

minutes, in such terms as people use who have not 
the gift of prophecy, two of the most important 
announcements they ever had to make. f< Mr Isaac 
Newton, Professor of Mathematics in the University 
of Cambridge, was proposed candidate by the Lord 
Bishop of Salisbury (Dr Seth Ward)," and "Mr 
Isaac Newton was elected." During the whole of 
this second period, he was seldom out of Cambridge 
more than three or four weeks in one year. Having 
missed the Law Fellowship (which was a lay fellow- 
ship), he would have been required, in 1675, either 
to take orders or to vacate the fellowship which he 
did hold. But in that year he obtained a dispensa- 
tion from Charles II., no doubt granted at the appli- 
cation of the College. He lectured on optics in the 
year following his appointment to the professorship ; 
and it would appear that he lectured on elementary 
mathematics. ^\\Q Arithmetica Universalis (published 
by Whiston, it was said, against Newton's consent, 
which Whiston denies) was taken from the lectures 
delivered on algebra and its application to geometry, 
which were preserved in the depositories of the Uni- 
versity. 1 When, in 1687, James II., among his 
other attempts of the same kind, ordered the Uni- 
versity of Cambridge to admit a Benedictine as 
Master of Arts without taking the oaths, and upon 

1 [Newton's lectures on optics, arithmetic, and algebra, on the motion 
of bodies, and on the system of the world, are preserved in the University 
Library at Cambridge, and are described in Edleston ; op. cit., pp. 
xci-xcviii. Cf. also W. W. Rouse Ball, op. cit., pp. 27-28.] 



14 NEWTON 

the resistance of the University, Newton was appointed 
one of the delegates to the High Court for the purpose 
of stating the case. The king withdrew his order, 
and in the next year Newton was proposed as 
Member of Parliament for the University, and gained 
his election by a small majority. He sat accordingly 
in the Convention Parliament, which declared the 
throne vacant, though it appears by the records of 
the College that, except in 1688 and 1689, he was 
not absent from the University often enough or 
long enough to have taken much share in public 
business. 

IV 

In 1692 occurred the curious episode of his history 
which produced abroad, as has recently appeared, a 
report that he had become insane. Most readers 
know the tradition of his dog Diamond having up- 
set a light among the papers which contained his 
researches, and of the calmness with which he is 
said to have borne the loss. The truth, as appears 
by a private diary of his acquaintance Mr de la 
Pryme, recently discovered is, that in February 1692, 
he left a light burning when he went to chapel, which, 
by unknown means, destroyed his papers, and among 
them a large work on optics, containing the experi- 
ments and researches of twenty years. " When Mr 
Newton came from chapel, and had seen what was 
done, everybody thought that he would have run 



NEWTON 15 

mad ; he was so troubled thereat that he was not 
himself for a month after." Such phrases, reported, 
gave rise to a memorandum in the diary of the 
celebrated Huygens (the first foreigner who under- 
stood and accepted the theory of gravitation), 1 
stating that he had been told that Newton had 
become insane, either from study, or from the loss 
of his laboratory and manuscripts by fire that 
remedies had been applied by means of which he 
had so far recovered as to be then beginning again 
to understand his own Principia. That Newton 
was in ill-health in 1692 and 1693 is known, but his 
letters to Dr Bentley on the Deity, written during 
that period, are proof that he had not lost his 
mind. 2 

We now give a slight enumeration of the matters 
on which Newton's attention was fixed during the 
second period, which we have just quitted. 3 

1 [This is hardly correct; cf. Rosenberger, op. cit. t p. 234, and the 
whole of that chapter.] 

2 [See Brewster, Memoirs, vol. ii, pp. 123-124, 131-156; on the 
letters to Bentley, cf. Rosenberger, op. ctt., pp. 263-270.] 

3 [The only complete edition of Newton's works was edited by Bishop 
S. Horsley in five volumes from 1779-1785 under the title Isaaci 
Newtoni Opera qua existant omnia. Conimentariis illustrabat Samuel 
Horsley. Contents: Vol. i, (i) Arithmetica Universalis. (2) Tractatus 
de Raiionibus Primis Ultimisque. (3) Analysis per yEquationes numero 
terminorum Infinitas. (4) Excerpta quaedam ex Epistolis ad Series 
Fluxionesque pertinentia. (5) Tractatus de Quadratura Curvarum. 
(6) Geometria Analytica sive specimina Artis Analyticae. (7) Methodus 
Differentialis. (8) Enumeratio Linearum tertii Ordinis. Vol. ii, 
Principiorum Libri Priores duo, De Motu Corporum. Vol. iii, (i) 
Principiorum Liber Tertius, de Systemate Mundi. (2) De Mundi 
Systemate. (3) Theoria Lunse. 1(4) Lectiones Opticae. Vol. iv, 
(i) Opticks. (2) Letters on various Subjects in Natural Philosophy, 
published from the Originals in the Archives of the Royal Society. 
(3) Letters to Mr Boyle on the Cause of Gravitation. (4) Tabulae Duae, 



1 6 NEWTON 

V 

OPTICS 

The great discovery of the unequal refrangibility 
of the rays of light was made in 1666, the year in 
which he was driven from Cambridge by the plague. 
In 1668 he resumed his inquiries, and, judging that 
the decomposition of light which he had discovered 
would render it impossible to construct refracting 
telescopes free from colour, or achromatic, he applied 
himself to the improvement of the reflecting tele- 
scope. The telescope which he made with his own 
hands, now in possession of the Royal Society, was 
made in 1671. It was submitted to the Society 

Color um altera, altera Refractionum. (5) De Problematibus Bernoul- 
lianis. (6) Propositions for determining the Motion of a Body urged 
by two Central Forces. (7) Four Letters to Dr Bentley. (8) Com- 
mercium Epistolicum, etc., cum recensione prsemissa. (9) Additamenta 
Commercii Epistolici ex Historia Fluxionum Raphsoni. Vol. v, (i) 
Chronology of Antient Kingdoms amended. (2) Short Chronicle from 
a MS. the property of the Rev. Dr Ekins. (3) Observations upon the 
Prophecies of Holy Writ, particularly the prophecies of Daniel and the 
Apocalypse of St John. (4) An Historical Account of two Notable 
Corruptions of Scripture, in a Letter to a Friend. Horsley added the 
following papers : (i) Logistica Infinitorum, (2)'Geometria Fluxionum 
sive Additamentum tractatus Newtoniani de Rationibus Primis Ultimis- 
que, in vol. i ; (3) De viribus centralibus quae rationem triplicate dis- 
tantiarum a centro contrariam inter se constanter servant, in vol. iii. 
A Latin edition of Newton's works was published at Lausanne and 
Geneva in 1744, and is described in G. J. Gray, op. cit. t pp. 2-4. The 
various editions, from 1687 on, of the Prindpia, and its translations 
and commentaries were described by Gray (ibid., pp. 5-35). Here we 
will only mention that the only complete English translation of it was 
by Andrew Motte, and was first published at London in 1729 (American 
editions, New York, 1848 and 1850), and that the selection of works 
mentioned in Gray's ' ' Illustrations " is often ludicrous. Gray dealt 
with books on optics, fluxions, universal arithmetic, and minor works 
by Newton and others on pp. 35-46, 46-55, 56-59, and 59-61 
respectively.] 



NEWTON 17 

immediately after his election as a Fellow, and was 
followed by the account of his discovery of the 
decomposition of light. This explanation of the 
known phenomenon of the colours of the prismatic 
spectrum was fully appreciated by the Society ; but 
Newton had to reply to various objections from 
foreign philosophers, and to those of Hooke at home. 
At this time first appeared (indeed there had been 
nothing before to draw it out) that remarkable trait 
in his character of which we shall afterwards speak : 
extreme aversion to all kinds of opposition. ' 1 1 
intend," he says, "to be no further solicitous about 
matters of philosophy." And again, "I was so 
persecuted with discussions arising from the publi- 
cation 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." 

The researches on the colours of thin plates, and 
the explanation known by the name of the theory 
of " Fits of Reflexion and Transmission," was com- 
municated to the Royal Society in 1765-66. Those 
on the ''inflexion" of light, though probably made 
long before 1704, first appeared in that year, in his 
treatise on Opticks. He never would publish this 
work as long as Hooke lived, from that fear of 
opposition above noted. 1 

1 [On Newton's optical researches, see Brewster, Memoirs , 1855, 
vol. i, pp. 37-249 ; Rosenberger, op. '/., pp. 51-117, 289-341.] 



1 8 NEWTON 

VI 

PRINCIPIA : THEORY OF UNIVERSAL GRAVITATION 

The discoveries of Kepler 1 had laid down the 
actual laws of the planetary motions : and the idea 
of universal gravitation began to occupy the minds 
of those who thought on these subjects. " Gravita- 
tion " was a term of some antiquity, used to denote 
the effort of bodies on the earth to descend : weight L , 
in fact. The notion of matter acting upon matter 
as an agent of attracting force, and the possibility 
of such force extending through the heavens, and 
being the proximate cause of the motions of the 
planets, was floating through men's minds when 
Newton first turned his attention to the subject. 
There has hardly ever been a great discovery in 
science, without its having happened that the germs 
of it have been found in the writings of several 
contemporaries or predecessors of the man who 
actually made it. In the case before us it had even 
been asserted as matter of necessity, that supposing 
attraction to exist, it must be according to the law 
of the inverse squares of the distances : 2 and Huygens 

1 [Kepler (1571-1630) discovered in 1609, from the observations of 
Tycho Brahe and himself, that the planets move round the sun in 
ellipses in one of whose foci the sun is placed, and that the line join- 
ing sun and planet describes equal areas in equal times. In 1619 
he published his further discovery that the periodic times of any two 
planets are to one another as the cubes of their distances from the sun.] 

2 [On the precursors of Newton, and especially Kepler, Galileo, 
Descartes, Bouillaud, Borelli, and Hooke, see Brewster, Memoirs, 
1855, vol. i, pp. 250-288: Rosenberger, op. cit.> pp. 135-157.] 



NEWTON 19 

announced, in 1673, before Newton had completed 
any part of his system, the relations which exist 
between attractive force and velocity in circular 
motion. 1 Newton first turned his attention to the 
subject in 1666, at Woolsthorpe ; sitting alone in a 
garden, his thoughts turned towards that power of 
gravity which extends to the tops of the highest 
mountains, and the question whether the power 
which retains the moon in her orbit might not be 
the same force as that which gives its curvature to 
the flight of a stone on the earth. To deduce from 
what Kepler had exhibited of the laws of the 
planetary motions, that the force must vary in- 
versely as the square of the distance, came within 
his power : but on trying the value of that force, as 
deduced from the moon's actual motion, with what 
it should be as deduced from the force of gravitation 
on the earth, so great a difference was found as to 
make him throw the subject aside. The reason of 
his failure was the inaccurate measure which he used 
of the size of the earth. 2 The subject was not 

1 [This was in his Horologium Osdllatorium of 1673 (see Mach, 
op. ctt., pp. 155-187). At the end of the book were given some rules 
for the calculation of centrifugal forces in circular motions ; but no 
demonstrations were there given, and these demonstrations were only 
supplied by him in a tract published posthumously, in 1703, and trans- 
lated into German in No. 138 of OstwalcTs Klassiker. It must be 
remembered that Newton had used the chief result of Huygens in this 
direction in his earliest and unpublished investigation on gravity and 
the moon's orbit, in 1666.] 

2 [It is now usually maintained, on certain grounds that are dis- 
cussed in W. W. Rouse Ball, op. cit., pp. 7, II, 16-17, 61, 157, that 
Newton was fairly well satisfied with the result of his approximate 
calculation of 1666, and had a strong suspicion of the law of universal 



20 NE WTON 

resumed till 1679; not, as commonly stated, be- 
cause he then first became acquainted with Picard's 
measure of the earth (we think Professor Rigaud 
had shown this), but because leisure then served, 
and some discussions on a kindred subject at the 
Royal Society had awakened his attention to the 
question. 1 In 1679 he repeated the trial with 
Picard's measure of the earth : and it is said that 
when he saw that the desired agreement was likely 
to appear, he became so nervous that he could not 
continue the calculation, but was obliged to intrust 
to a friend. 2 From that moment the great dis- 
covery must be dated : the connexion of his specu- 
lations on motion with the actual phenomena of the 
universe was established. At the time when we 
write this, a distant result of that calculation has 
been announced, which Newton himself would hardly 

at any period of his life have imagined to have been 

/ 

gravitation, but he was stopped by the difficulty of calculating the 
attractions of a number of particles massed together. This he dis- 
covered at least in the most important case in 1685, and thus the 
propositions which he had previously (1679 an{ ^ 1680) found about the 
orbits of attracting particles could be applied at once to spherical bodies. 
Newton, in fact, discovered in 1685 by calculation that such bodies 
attract as if they were particles situated at the contents of the masses. 
Thus he must have only then realised that those propositions, which he 
had believed to be only approximately true when applied to the solar 
system, were almost completely exact.] 

1 [The subject was certainly resumed in 1679, but it was apparently 
in consequence of a problem proposed by Robert Hooke in a letter to 
Newton of N ovember of that year. In the correspondence that followed, 
Hcoke drew attention to Picard's measurements, and stimulated 
Newton's interest and curiosity by his happy insight into celestial 
problems and correction of a careless remark of Newton's. For this 
correspondence, see W. W. Rouse Ball, op. cit., pp. 18-24, 139-153.] 

2 [This story is probably apocryphal ; cf. W. W. Rouse Ball, op. 
cit., p. 23.] 



NEWTON 21 

possible. A planetary body, unknown and unseen 
till after the prediction, has made itself felt by 
its attraction on another. Unexplained (and very 
trivial) irregularities in the motion of Uranus sug- 
gested the idea of there being yet another planet 
by the attraction of which they were produced. 
From those irregularities the place and distance of 
that planet have been inferred, and, on looking into 
the part of the heavens at which its silent action 
proved it to be, if indeed it existed there it was 
found. A heavenly body has thus been calculated 
into existence, as far as man is concerned. 1 

How much Newton might have got ready it is 
not easy to say : all that is known is that he kept 
it to himself. At the end of 1683 Halley 2 had 
been considering the question, and was stopped by 
its difficulties ; but, being in August 1684 on a 
visit to Newton, the latter informed him of what 
he had done, but was not able to find his papers. 
After Halley's departure, he wrote them again, and 
sent them : upon which Halley paid another visit 
to Cambridge, to urge upon Newton the continuance 

1 [The almost simultaneous discovery in 1846 of Uranus by Adams 
and Le Verrier, by calculation, created a most powerful impression on 
nearly everybody, including De Morgan (cf. Mrs De Morgan's Memoir, 
pp. 126-138).] 

2 [The biographical sketch of Halley (1656-1742) in the Cabinet 
Portrait Gallery of British Worthies, vol. xii, London, 1847, pp. 5-15, 
is, judging from the style, by De Morgan. From Mrs De Morgan's 
Memoir, p. 108 (see the first note to the first Appendix to the third 
Essay below), we learn that De Morgan wrote the article "Halley" 
on pp. 161-168 of the first volume of The Gallery of Portraits : with 
Memoirs (London, 1833). The biography of Newton on pp. 79-88 
of this volume does not seem to be by De Morgan.] 



22 NE WTON 

of his researches ; and (December, 1684) informed 
the Royal Society of them, and of Newton's promise 
to communicate them. The Society, who knew 
their man, and how little they should get without 
asking, appointed a Committee (Halley and Paget, 
the mathematical master in Christ's Hospital) to 
keep Newton in mind of his promise ; so that 
(February, 1685) a communication was sent up, 
amounting to those parts of the first book of the 
Principia which relate to central forces. Newton 
went on with the work, and (April the 2ist, 1686) 
Halley announced to the Society that " Mr Newton 
had an incomparable treatise on Motion, almost 
ready for the press." On the 28th, Dr Vincent 
(the husband, it is supposed, of Miss Storey) pre- 
sented the manuscript of the first book to the 
Society, who ordered it to be printed, and Halley 
undertook to pay the expenses. But it was not 
yet in harbour : Hooke, who used to claim every- 
thing, asserted that he had been in possession of 
the whole theory before Newton ; with which the 
latter was so disgusted, that he proposed to omit 
the third book (being in fact all the application to 
our system). Halley, the guardian angel of the 
work, wrote him a letter, in which he soothed him 
almost as if he had been a child, and prevailed upon 
him to complete it as first intended. It appeared 
under the title of Philosophic Naturalis Principia 
Matheniatica^ about midsummer, 1687, containing 



NEWTON 23 

the mathematical discussion of the laws of solid and 
fluid motion, with their application to the heavenly 
motions, the tides, the precession of the equinoxes, 
and so on. The reader who understands the terms 
may refer to the Penny Cyclopaedia (article * * Prin- 
cipia "), in which the heads of all the propositions 
are given. No work on any branch of human know- 
ledge was ever destined to effect so great a change, 
or to originate such important consequences. 1 



VII 



FLUXIONS, NOW CALLED THE DIFFERENTIAL 
CALCULUS 

A curved figure differs from one the boundaries of 
which are consecutive straight lines in that there is 
always a gradual change of direction going on at 
the boundaries of the former, while at those of the 
latter the changes are made only at certain places, 
and as it were in the lump. To apply the doctrines 
of mathematics to cases in which such perfectly 
gradual changes take place, had been always the 
greatest difficulty of the science. Archimedes had 
conquered it in a few cases : the predecessors of 
Newton had greatly extended what Archimedes 
had done, and had given what, to those who come 

1 [On Newton's investigations of 1684, on the preparation and publi- 
cation of the Principia (1685-1687), for Hal ley's correspondence with 
Newton (1686-1687) about the publication of the Principia and about 
Ilooke's claims, cf. W. W. Rouse Ball, op. cit., pp. 25-73, 153-174.] 



24 NE WTON 

after Newton and Leibniz, would appear strong 
hints of an organized method of treating all cases. 
But the method itself, and an appropriate language 
for expressing its forms of operation, were still 
wanting. About 1663, Newton turned his attention 
to the writings of Descartes and Wallis, and, in 
the path which the latter had gone over, found the 
celebrated Binomial Theorem : Wallis having in 
fact solved what would now be called a harder 
problem. This, far from lessening the merit of the 
discovery, increases it materially. In 1665 Newton 
arrived at his discoveries in series, and substantially 
at his method of fluxions. In 1669 Barrow com- 
municated to Collins (on the occasion before referred 
to) a paper by Newton on series, not containing 
anything on fluxions. Various letters of Newton, 
Collins, and others, state that such a method had 
been discovered, without giving it. But one letter 
from Newton to Collins on December the loth, 
1672, states a mode of using one case of this method, 
confined to equations of what are called rational 
terms (it being admitted on all sides that the great 
pinch of the question then lay in equations of 
irrational terms]. Leibniz, who had been in 
England in 1673, and had heard something indefinite 
of what Newton had done, desired to know more : 
and Newton, on June the I3th, 1676, wrote a letter 
to Oldenburg, of the Royal Society, which he 
desired might be communicated to Leibniz. This 



NEWTON 25 

letter dwells on the binomial theorem, and various 
consequences of it ; but has nothing upon fluxions. 
Leibniz still desiring further information, Newton 
again wrote to Oldenburg, on October the 24th, 
1676, explaining how he arrived at the binomial 
theorem, giving various other results, but nothing 
about fluxions except in what is called a cipher. A 
cipher it was not, for it merely consisted in giving 
all the letters of a certain sentence, to be put to- 
gether if Leibniz could do it. Thus, the informa- 
tion communicated was 

aaaaaa cc d ae eeeeeeeeeeeee ff iiiiiii 111 nnnnnnnnn 
oooo qqqq rr ssss ttttttttt vvvvvvvvvvvv x. 

These are merely the letters of a Latin sentence 
which, translated word by word in the order of the 
words, is " given equation any whatsoever, flowing 
quantities involving, fluxions to find, and vice versa. " 1 
Even this letter had not been sent to Leibniz on 
March the 5th, 1677 ; it was sent soon after this date. 
But in the mean time, Leibniz, by himself, or as 
was afterwards said, having taken a hint from other 
letters of Newton, had invented his differential 
calculus. And, as open as Newton was secret, 
shortly after receipt of the above, he wrote to 
Oldenburg, on June the 2ist, 1677, a letter giving a 

1 [The Latin sentence is : " Data sequatione quotcunque fluentes 
quantitates involvente, fluxiones invenire ; et vice versa." The anagram 
may be more shortly written : 

6a 2c d ae 136 2f J\ 3! <)r\ 40 4q 2r 45 Qt I2v x.] 



26 NE WTON 

full and clear statement of everything he had arrived 
at : making an epoch as important in the pure mathe- 
matics, as was the discovery of the moon's gravita- 
tion in the physical sciences. In the Principia, 
Newton acknowledges this in the following 
"Scholium": "In letters which went between 
me and that most excellent geometer G. G. Leibniz, 1 
ten years ago, when I signified that I was in the 
knowledge of a method of determining maxima and 
minima, of drawing tangents and the like, and when 
I concealed it in transferred letters involving this 
sentence (' Data aequatione,' and so on, as above), 
that most distinguished man wrote back that he had 
also fallen upon a method of the same kind, and 
communicated his method, which hardly differed 
from mine except in the forms of words and symbols. 
The foundation of both is contained in this Lemma." 
In 1684 Leibniz published his method : while in the 
Principia y Newton still gave nothing more than the 
most general description of it, and avoided its direct 
use entirely. By 1695 it had grown into a power- 
ful system, in the hands of Leibniz and the Ber- 
noullis : while in England it was very little noticed. 
About 1695 an alarm began to be taken in England 
at its progress : and the friends of Newton began to 
claim what they conceived to be his rights. Wallis 
excused himself from mentioning the differential 

1 [Leibniz's names were Gottfried Wilhelm ; the initials " G. G." 
(Gothofredus Gulielmus) stand for the Latin version of these names.] 



NEWTON 27 

calculus in his works, on the ground that it was 
Newton's method of fluxions. In 1699, Fatio de 
Duillier, a Genevese residing in England, published 
an implied charge of plagiarism on Leibniz : the 
latter denied the imputation and appealed to Newton's 
own testimony. The Leipsic Acts * made something 
very like the same charge against Newton : and in 
the course of the dispute, Keill, an Englishman, 
asserted 2 that Leibniz had taken Newton's method, 
changing its name and symbols. This accusation 
roused Leibniz, who complained to the Society : and 
after some correspondence, in which allusion was 
made to the Oldenburg letters as being sources 
from which he might have drawn knowledge of 
Newton's method, the Royal Society appointed a 
Committee, consisting of eleven members, to examine 
the archives, and to defend Newton. This latter 
purpose, though not stated in words, was fully 
understood : and since the usual impression is that 
it was intended for a judicial committee, meaning 
of course an impartial one, we give in a note 3 some 

1 [The remark referred to was in an anonymous review by Leibniz, 
but was by no means a charge of plagiarism. (Cf. Rosenberger, op. 
cit., pp. 473-475)-] 

2 Phil. Trans., 1708. 

3 First, the Committee consisted of Halley, Jones, De Moivre, and 
Machin, Newton's friends, and mathematicians ; Brook Taylor, a 
mathematician, but not then otherwise known except as a friend of 
Keill, the accused party ; Robarts, Hill, Burnet, Aston, and Arbuthnot, 
not known as mathematicians, but the two latter intimate personal 
friends of Newton ; and Bonet, the Prussian minister. To call this 
a judicial committee would be to throw a great slur on the Society. 
Secondly, the names of the Committee were never published with their 
report, which would have been anything but creditable, if that report 



28 NE WTON 

heads of the proof of our assertion. The Committee, 
appointed at different times in March 1712, reported 
in April that they had examined, and so on, and 
that they were of opinion that Leibniz had no 
method till after the letter to Collins of December the 
loth, 1672, had been sent to Paris to be communi- 
cated to him, and that Keill, in asserting the priority 
of Newton, had done Leibniz no injustice. This 
is, to us, the main part of the report. It was 
published, with abundance of extracts from letters, 
and letters at length, most of which had been found 
among Collins's papers, under the name of Com- 
mercium Epistolicum, and so on, in 1712 and in 
1725. The conclusion was not to the point : 
Leibniz asked reparation for a charge of theft, and 
the answer is that there was no injustice to him in 
saying that the other party had the goods before 
the time when he was alleged to have stolen them. 

had been a judgment : but if the Committee were only counsel for 
Newton's case it mattered not who they were. Thirdly, the Society 
had committed .itself to Newton's side, by hearing his statement, and 
thereupon directing Keill to write the second letter in the controversy, 
and to "set the matter in a just light " : the only light they had sought 
being that which Newton himself could give. Fourthly, Burnet wrote 
to John Bernoulli while the matter was pending, stating in express terms 
not that the Royal Society was inquiring but that it was busy proving 
that Leibniz might have seen Newton's letters. Fifthly, De Moivre, as 
appears by the statement of an intimate friend, considered himself, by 
merely joining that Committee, as drawn out of the neutrality which he 
had till then observed : which shows that he did not consider himself a 
juryman. Sixthly, no notice was given to Leibniz of the proceeding, 
still less an invitation to produce documents on his own side. All these 
things put together show that the Committee was not judicial, nor meant 
to be so, nor asserted to be so on the part of the Society. If any one 
will have it that it was so, he must needs, we think, hold that it was 
one of the most unfair transactions which ever took place. 



NE WTON 29 

With regard to Collins's letter, besides its contain- 
ing no more than any good mathematician could 
have drawn from Barrow and Fermat together, no 
proof 1 was given to the world of Leibniz ever having 
seen it, which any man who valued his character 
would have ventured to produce in any kind of court 
with rules of evidence. In truth, though the Com- 
mittee were not unfair judges (simply because they 
were not judges at all), we cannot but pronounce 
them unscrupulous partisans, for the reasons given 



1 A parcel (collectio) of extracts from Gregory's letters are found in 
the handwriting of Collins, with a memorandum by Collins that they 
were to be sent to Leibniz and returned by him : with a letter to 
Oldenburg, desiring him to send them : no mention of any one but 
Gregory in either memorandum or letter. With the parcel is this letter 
to Collins : what reason the Committee have for supposing this letter 
belonged to the parcel they do not say : they do not even say whether 
it was a separate paper or not. The papers of dead mathematicians, 
after going through the hands of executors, are, we suspect, not always 
tied up exactly in the order they were untied. Whether the parcel is 
otherwise known to have found its way to Oldenburg than from the in- 
tention expressed in the memorandum, we are not told nor whether 
Oldenburg sent it to Paris nor whether, having arrived at Paris, it was 
sent on to Hanover ; and finally they state, without adding how they 
came to know it, that it was sent to Leibniz on June the 26th, 1676. If 
the letter belonged to the parcel, and if the parcel were sent to Olden- 
burg, and if Oldenburg sent it to Paris, and if his Paris correspondent 
sent it to Hanover, and if it arrived safe, and if Leibniz, meaning to 
make an unfair use of it, was unwise enough to return this evidence 
against himself the case of the Committee is good, with only one more 
if; that is, if the letter contained anything new to the purpose, which 
we think it palpably does not. That is to say, the letter itself is only 
what any strong mathematician might have drawn from Barrow and 
Fermat, who are almost the joint inventors of Fluxions, if that letter 
contained them. It is worth the remembering that Collins was not 
likely to tie up letters miscellaneously : he was a regular accountant, 
a methodical writer on and practiser of book-keeping, and a man of 
business. For aught we know, he may lie unquiet in his grave to this 
day, under the imputation of having sent a parcel which contained a 
paper neither mentioned in the docket nor in the letter of advice. 
Perhaps he never sent it at all : would not this methodical man have 
written on the parcel the date of its return ? 



30 NE WTON 

and others. Leibniz never made any formal answer, 
but his friends retorted the charge of plagiarism 
upon Newton, and John Bernoulli made a short 
anonymous reply. The Committee, content perhaps 
with the number of those who were ready to swear 
that black was both black and white, and neither, 
and to believe it too, rather than yield anything 
to a foreigner (and it is to be remembered that 
Leibniz, the servant of the Elector, was particularly 
obnoxious to all the Jacobites), published nothing 
further : the Society (May the 2Oth, 1714), in refer- 
ence to the complaint of Leibniz that he had been 
condemned unheard, resolved that it was never 
intended that the Report of the Committee should 
pass for a decision of the Society : but others 
persisted in calling it so. A mutual friend, the 
Abb6 Conti, being in England in 1715, Leibniz at 
the latter end of that year wrote him a letter, in 
the postscript of which he adverted to the usage 
he had received. This letter excited curiosity in 
London : and Newton, whose power in matters of 
science was then kingly, requested and obtained the 
presence of all the foreign ambassadors at the Royal 
Society to collate and examine the papers. After 
this had been done, Baron Kirmansegger, one of the 
ambassadors, stated his opinion that the dispute 
could not be terminated in that manner ; that 
Newton ought to write to Leibniz, state his own 
case, and demand an answer. All present agreed, 



NEWTON 31 

and the king (George I.), to whom the matter was 
mentioned that same evening, was of the same 
opinion. Newton accordingly wrote a letter to 
Conti, in which he relies mostly upon what Leibniz 
had either expressly or tacitly admitted. Nine 
times, on different points, he calls upon Leibniz 
to acknowledge something because he had once 
acknowledged it. Leibniz replied at great length. 
Newton did not rejoin, except in notes on the corre- 
spondence which he circulated privately among his 
friends. Leibniz died in November 1716, and 
Newton forthwith handed the whole correspondence, 
with his final notes, to Raphson, whose History of 
Fluxions was then in process of printing. The book 
appeared with this correspondence as an appendix : 
it is dated 1715, but the publication was retarded. 
And in the third edition of the Principia, published 
in 1726, Newton omitted the scholium we have 
quoted above, in spite of his doctrine that what was 
once acknowledged should be always acknowledged. 
In its place he put another scholium, with a similar 
beginning and ending, but referring not to Leibniz 
but to his own letter to Collins of December 1672. 
In the Conti correspondence that is, in the notes 
which he would not print while Leibniz was alive 
he had evaded the plain meaning of this scholium, 
asserting that it was not an admission, but a 
challenge to Leibniz to make it appear that the 
latter had the priority ; and further, that by refer- 



32 NEWTON 

ring to the letters, he left the reader to consult them 
and interpret the paragraph thereby. This was the 
climax of blind unfairness : for Newton does not 
specify the dates of the letters, and gives their 
description wrongly (for they were written to 
Oldenburg, not to him). And further, the reader 
could not use them, for they were not published, 
nor at that time intended for publication. 

We shall presently make some remarks on the 
conduct of Newton in this transaction ; but we now 
proceed to the merits of the question. That Leibniz 
derived nothing from Newton except the knowledge 
that Newton could draw tangents, find maxima and 
minima, etc., by some organised method, we have 
no doubt whatever, nor has any one else, at this 
time, so far as we know. But, though we may be 
singular in the opinion, we agree with Bernoulli that 
Newton did derive from Leibniz (without being 
aware of the extent of his obligation, we think) the 
idea of the permanent use of an organized mode of 
mathematical expression. On a simple question of 
fact, opinion and construction apart, we take the 
words of both as indisputable ; neither would have 
descended to bare falsehood. Now, in the first place, 
it is essential to observe that the genius of Newton 
did not shine in the invention of mathematical 
language : and, the disputed fluxions apart, he 
added nothing to it. The notation of the Principia 
is anything but a model. We know by the letter in 



NEWTON 33 

which Leibniz communicated his system to Newton, 
in 1677, that, at that period, Newton received 
communication of the idea of an organised and 
permanent language : and the question is whether 
he had it already. From his own Conti correspond- 
ence, written after it was within his knowledge 
that Bernoulli had asserted him to have taken his 
idea of notation from Leibniz, and when he makes 
the fullest and most definite assertions as to the 
extent to which he has carried the use'of his method, 
he does not assert that before receipt of Leibniz's 
letter he did more than " sometimes" use one dot 
for a first fluxion, two for a second, and so on. 1 
Neither of the parties knew of the importance which 
posterity would attach to this simple point : and it 
is our full conviction that Newton, who had only 
got the length of finding it occasionally convenient 
to use a specific language, would never have 
organised that language for permanent use had he 
not seen the letter of Leibniz. Even as late as the 
publication of the Principia he has no better con- 
trivance than using small letters to represent the 
fluxions of great ones. We are avowedly express- 
ing, in one point, our low estimate of Newton's 
power : and we believe the reason to have been, that 
he did not cultivate a crop for which he had no use. 
He who can make existing language serve his 

1 [We know from Newton's manuscripts that he used dots as early 
as 1665. Cf. the Appendix to the second Essay, below.] 

3 



34 NE WTON 

purpose never invents more : and Newton was able to 
think clearly and powerfully without much addition 
to the language he found in use. The Principia^ 
obscure as it is, was all light in Newton's mind ; and 
he did not attempt to conquer difficulties which he 
never knew. 1 

VIII 

We now pass on to the third period of Newton's 
life. In 1694, his old friend Charles Montague 2 
(afterwards Lord Halifax) became Chancellor of the 

1 [On the genesis and development of the ideas of Newton and 
Leibniz on the infinitesimal calculus, and the great controversy, see 
De Morgan's second Essay, below.] 

2 Montague was deeply attached, says Sir David Brewster, to 
Newton's half-niece, Catherine Barton, to whom he left a large part of 
his fortune. Mrs Barton, to use Sir D. Brewster's words, " though she 
did not escape the censures of her contemporaries, was regarded by 
those who knew her as a woman of strict honour and virtue." Sir 
D. Brewster, who copies the words from the Biographia Britannica t 
declines, in his reverence for all that belonged to Newton (a feeling with 
which we have more sympathy than our readers will give us credit for), 
to state the whole case. After the death of Montague's wife, he was 
disappointed in a second marriage which he projected, "which was 
the less to be regretted as he had some time before cast his eye upon a 
niece of his friend Sir Isaac Newton, to be the superintendent of his 
domestic affairs. This gentlewoman . . . was then a celebrated toast, 
being young, beautiful, and gay, so that she did not escape censure, 
which was however passed upon her very undeservedly, since we are 
well assured she was a woman of strict honour and virtue. 'Tis 
certain she was very agreeable to his Lordship in every particular." 
. . . No wonder she did not escape censure, especially when the legacy 
left by Lord Halifax is left, to use his own words, " as a token of the 
sincere love, affection, and esteem I have long had for her person, and 
as a small recompence for the pleasure and happiness I have had in her 
conversation." And all this from an apologist: what, then, was the 
truth? On reviewing this note, we think it right to add that the 
statement that there were feelings of love between the parties (which, 
if true, puts their relation to one another beyond any reasonable doubt) 
is not from the author here cited, but from Sir D. Brewster, who does 
not give his authority. [On De Morgan's later investigations on the 
relations between Catherine Barton and Lord Halifax, see the third 
Essay, below, VII., and the notes added to it] 



NEWTON 35 

Exchequer, and it was one of his plans to restore 
the adulterated coinage. He served both his friend 
and his plan by making Newton Warden of the Mint, 
a place of five or six hundred a year (March the iQth, 
1695 *) In I ^99> Newton was made Master of the 
Mint, on which occasion he resigned to Whiston, 
as his deputy, the duties and emoluments of the 
Lucasian professorship, and resigned to him the 
professorship itself of 1703. In 1701, he was again 
elected member for the University ; but he was 
turned out by two sons of Lords in 1705. In 1703, 
he was chosen President of the Royal Society, and 
was annually re-elected during the rest of his life, 
In 1705, he was knighted at Cambridge by Queen 
Anne. In 1709, he entrusted to Roger Cotes the 
preparation of the second edition of the Principia^ 
which appeared in 1713. All the correspondence 
relating to the alterations made in this edition is in 
the Library of Trinity College. 2 In 1714, at the 
accession of George I., he became an intimate 
acquaintance of the Princess of Wales (wife of 
George II.), who was also a correspondent of 
Leibniz. Some observations made by the latter on 
the philosophy of Locke and of Newton brought on 
the celebrated correspondence between Leibniz and 
Clarke. And at the same time, an abstract of 
Newton's ideas on chronology, drawn up for the 



1 [This ought to be 1696. See note on p. 4.] 

2 [This correspondence was published by Edleston in 1850 (pp. V.).] 



36 NE WTON 

Princess, and at her request communicated to Conti, 
got abroad and was printed at Paris : on which, in 
his own defence, he prepared his large work on the 
subject. On this it is not necessary to speak : his 
ideas on chronology, founded on the assumption of 
an accuracy in the older Greek astronomers which 
nobody now allows them, are rejected and obsolete. 
But the work does honour to his ingenuity and his 
scholarship, showing him to be not meanly versed 
in ancient learning. In 1726, Dr Pemberton com- 
pleted, at his request, the third edition of the 
Principia. With this he seems to have had little to 
do, for his health had been declining since 1722. 
He was relieved by gout in 1725. February the 
28th, 1727, he presided for the last time at the 
Royal Society. He died of the stone (so far as so 
old a man can be said to die of one complaint) on 
the 20th of March. All the tributes of respect to 
his memory belong rather to the biographies of those 
who had the honour to pay them than to his : the 
gradual reception of his philosophy throughout 
Europe belongs to the history of science. We 
shall now offer some remarks on his character as a 
philosopher and as a man. 

IX 

We have already adverted to the manner in which 
his biographers have represented him to be as 



NEWTON 37 

much above ordinary humanity in goodness as 
in intellectual power. That his dispositions were 
generally good and his usual conduct in the relations 
of life admirable to an extent which should make 
his worst enemy, if he had any regard to truth, hand 
him down as a man of high principle, no one who 
knows his history can deny. But when injustice 
is not merely concealed but openly defended ; when 
meanness is represented as the right of a great 
philosopher ; when oppression is tolerated, and its 
victims are made subjects of obloquy because they 
did not submit to whatever Newton chose to inflict ; 
it becomes the duty of a biographer to bear more 
hardly upon instances of those feelings, than, had 
they been properly represented, would have been 
absolutely necessary. Nor does it matter anything 
in such a case that the instances alluded to are the 
exception in the character and not the rule ; for- 
bearance and palliation are so much of injustice 
towards the injured parties. 

The great fault, or rather misfortune, of Newton's 
character was one of temperament : 1 a morbid fear 
of opposition from others ruled his whole life. 
When, as a young man, proposing new views in 
opposition to the justly honoured authority of 
Descartes and lesser names, he had reason to look 

1 [On this word, Mrs De Morgan (Memoir, p 257) remarked : " My 
husband always used this word for what I should call original character 
or inborn disposition." Cf. XII. of this Essay and VI. and XI. 
of the third Essay. ] 



38 NEWTON 

for opposition, we find him disgusted by the want 
of an immediate and universal assent, and represent- 
ing, as he afterwards said, that ' * philosophy was 
so litigious a lady, that ' a man might as well be 
engaged in lawsuits as have to do with her.'' How 
could it be otherwise ? What is scientific investiga- 
tion except filing a bill of discovery against nature, 
with liberty to any one to move to be made a party 
in the suit ? Newton did not feel this ; and, not 
content with the ready acceptance of his views by the 
Royal Society, a little opposition made him declare 
his intention of retiring from the field. He had the 
choice of leaving his opponents unanswered, and 
pursuing his researches ; committing it to time to 
show the soundness of his views. That this plan 
did not suit his temper shows that it was not the 
necessity of answering, but the fact of being 
opposed, which destroyed his peace. And he 
steadily adhered, after his first attempt, to his 
resolution of never willingly appearing before the 
world. His several works were extorted from him ; 
and, as far as we can judge, his great views on 
universal gravitation would have remained his own 
secret if Halley and the Royal Society had not used 
the utmost force they could command. A discovery 
of Newton was of a two-fold character he made it, 
and then others had to find out that he had made it. 
To say that he had a right to do this is allowable ; 
that is, in the same sense in which we and our 



NE WTON 39 

readers have a right to refuse him any portion of 
that praise which his biographers claim for him. 
In the higher and better sense of the word, he had 
no right to claim the option of keeping from the 
world what it was essential to its progress that the 
world should know, any more than we should have 
a right to declare ourselves under no obligation to 
his memory for the services which he rendered. To 
excuse him, and at the same time to blame those 
who will not excuse him, is to try the first 
question in one court and the second in another. 
A man who could write the Principia, and who 
owed his bread to a foundation instituted for the 
promotion of knowledge, was as much bound to 
write it as we are to thank him for it when written. 
When he was young and comparatively unknown, 
this morbid temperament showed itself in fear of 
opposition ; when he became king of the world of 
science it made him desire to be an absolute 
monarch ; and never did monarch find more ob- 
sequious subjects. His treatment of Leibniz, of 
Flamsteed, and (we believe) of Whiston is, in each 
case, a stain upon his memory. As to Leibniz, it 
must of course be a matter of opinion how far 
Newton was behind the scenes during the concoction 
of the Commercium Epistolicum : but from the 
moment of his appearance in propria persona, his 
conduct is unjust. Leibniz, whose noble candour 
in unfolding his own discovery, in answer to 



40 NE WTON 

Newton's a b c, and so on, must have been felt at 
the time as a stinging reproof, is answered with 
arrogance (dignified severity is the other name) 
and treated with unfairness. Nothing can excuse 
Newton's circulating his reply among his friends in 
writing, and printing it when he heard of the death 
of Leibniz : this conduct tells its own story in 
unanswerable terms. And, if it were Newton's own 
act and deed, nothing can excuse in him the 
omission of the Scholium from the third edition, 
or rather the alteration of it in such manner as to 
resemble the former one in its general tenor, But, 
as Newton was then very old, and as he had allowed 
it to stand in the second edition, published when the 
dispute was at its height, it is possible that he left 
the matter to Dr Pemberton, the editor, or some 
other person. 

The story of the treatment of Flamsteed has 
only recently become known, by the late Mr Baily's 
discovery of the correspondence. Flamsteed was 
Astronomer Royal, and his observations were to be 
printed at the expense of the Prince Consort. A 
Committee, with Newton at its head, was to super- 
intend the printing. If we took Flamsteed's word 
for the succession of petty annoyances to which 
he was subject, we might perhaps be wrong ; for 
Flamsteed was somewhat irritable, and no doubt the 
more difficult to manage because he was the first 
observer in the world, and not one of the Committee 



NEWTON 41 

was an observer at all But there are two specific 
facts which speak for themselves. The catalogue of 
stars (Flamsteed's own property) had been delivered 
sealed up, on the understanding that the seal was 
not to be broken unless Flamsteed refused to comply 
with certain conditions. After the Prince was dead, 
and the trust had been surrendered (it seems to have 
been transferred to the Royal Society), and without 
any notice to Flamsteed, the seal was broken, with 
Newton's consent, and the catalogue was printed. 
Halley was exhibiting the sheets in a coffee-house, 
and boasting of his correction of their errors. A 
violent quarrel was the consequence, and a scene 
took place on one occasion at the Royal Society 
which we cannot discredit (for Flamsteed's character 
for mere truth of narration has never been success- 
fully impugned, any more than Newton's), but which 
most painfully bears out our notion of the weak 
point of Newton's character. As to the breaking of 
the seal Newton pleaded the Queen's command an 
unmanly evasion, for what did the Queen do except 
by advice ? who was her adviser except the President 
of the Royal Society? Shortly afterwards the 
second edition of the Principia appeared. Flam- 
steed, whose observations had been of more service 
to Newton than those of any other individual, and 
to whom proper acknowledgment had been made 
in the first edition, and who had increased the 
obligation in the interval, had his name erased in all 



42 NEWTON 

the passages in which it appeared (we have verified, 
for this occasion, eight or nine places ourselves). 1 
To such a pitch is this petty resentment carried, 
that whereas in one place of the first edition (prop. 
1 8, book III.) there is, in a parenthesis, "by the 
observations of Cassini and Flamsteed " ; the corre- 
sponding place of the second is, " by the consent of 
the observations of astronomers." 

There is a letter of Newton to Flamsteed (January 
the 6th, 1699), written before they were in open 
rupture, containing an expression which has excited 
much surprise and some disapprobation. Flamsteed 
having caused a published reference to be made to 
Newton's continuation of his lunar researches, the 
latter says, ' ' I do not love to be printed on every 
occasion, much less to be dunned and teased by 
foreigners about mathematical things, or to be 
thought by your own people to be trifling away my 
time when I should be about the King's business." 
This letter was not intended for publication, still less 
for posterity : the phrase was pettish, unworthy even 
of Newton in a huff. But the feeling was the right 
one. If there were any thing unworthy of the 
dignity of Newton, it was in taking a place which 
required him to give up the glorious race in which 

1 [This is not quite correct. Edleston (pp. cit., p. Ixxv) also questions 
very much whether the suppression of Flamsteed's name in several 
places where it had appeared in the final edition was not such as was 
necessary in the process of improving the work. Newton's own experi- 
ments on the old echo in Trinity College cloister gave way, in the 
second edition, to more accurate researches.] 



NEWTON 43 

he had outstripped all men, and the researches which 
were for him alone, while the regulation of the Mint 
was not above the talents of thousands of his country- 
men. But, having taken it, it was his duty to attend 
to it in the most regular and conscientious manner, 
as in fact he did to the end of his days. His con- 
temporary Swift had the sense to refuse the troop 
of dragoons which King William offered him before 
he took orders : it would have been better for 
Newton's fame if he had left all the coinage, clipped 
and undipped, to those who were as well qualified 
as himself. His own share might not have been so 
large, 1 but money was not one of his pursuits. He 
was nobly liberal with what he got, 2 particularly to 
his own family : and it may be added that the 
position of his family, which was far from well off 
in the world, is the only circumstance which can 
palliate his giving up the intellectual advancement 

1 Sir D. Brewster represents Newton as having a very scanty income 
before he gained his office in the Mint. But in fact he had from his 
College board and lodging (both of the best) and the stipend of his 
fellowship : from the University the salary of his professorship : and 
from his patrimony about ;ioo a year. He could not have had 
less than ^"250 a year over and above board and lodging : which, in 
those days, was a very good provision for an unmarried man, and 
would not be a bad one now. 

2 [Here we may mention that Pemberton is said to have received 
two hundred guineas for his service in editing the third edition of the 
Principia (Brewster, Memoirs, 1855, vol. i, p. 318). For making a 
Latin translation of the Optics, Samuel Clarke and his children received 
five hundred pounds (ibid. , p. 248). Cf. ibid., vol. ii, pp. 411-413, 
for other instances of Newton's sometimes rather careless generosity. 
Further, on July the I3th, 1719, Newton gave to Pound, the astronomer, 
probably in acknowledgment of astronomical observations supplied by 
him for the Principia, a "free gift" of fifty guineas. On April the 
28th, 1720, Pound recorded another gift from Newton of fifty guineas. 
This generosity does not appear in his treatment of rivals.] 



44 NEWTON 

of all men, ages, and countries, to trifle away his 
time about the King's business. 1 

His treatment of Whiston, as published in the 
autobiography of the latter, 2 was always disregarded, 
as the evidence of a very singular person. Standing 
alone for his conduct to Leibniz was defended by 
national feeling, and his treatment of Flamsteed 
was unknown it never carried much weight. 
Whiston had excessive vanity and a peculiar fana- 
ticism of his own invention, which were sure to be 
made the most of ; for a man who loses his pre- 
ferment for his conscience had need be perfect, if 
he would escape those who think him a fool, and 
those who feel him a rebuke. And in Whiston's 
day the number was not small of the clergy who 
disavowed the articles to which they had sworn, 
without even having the decency to provide a non- 
natural sense. Newton refused him admission into 
the Royal Society, declaring that he would not 
remain president if Whiston were elected a fellow, 
A reason is asserted for this which we shall presently 
notice ; but Whiston's account is as follows. After 
alluding to Newton having made him his deputy, 
and then his successor, he adds : ' * So did I enjoy 
a large portion of his favour for twenty years to- 
gether. But he then perceiving that I could not 

1 [-For Brewster's version of the Flamsteed episode, see Memoir -s, 
1855, vol. ii, pp. 157-242.] 

2 [Memoirs of the Life of Mr William Whiston by himself, London, 

I749-] 



NEWTON 45 

do as his other darling friends did that is, learn 
of him without contradicting him when I differed 
in opinion from him, he could not in his old age 
bear such contradiction ; and so he was afraid of me 
the last thirteen years of his life. He was of the 
most fearful, cautious, and suspicious temper that 
I ever knew." 

It would have been more pleasant merely to 
mention these things as what unfortunately cannot 
be denied, than to bring them forward as if it were 
our business to insist upon them. But the manner 
in which the biography of Newton is usually written 
leaves us no alternative. We are required to worship 
the whole character, and we find ourselves unable 
to do it. We see conduct defended as strictly 
right, and therefore, of course, proposed for imita- 
tion, which appears to us to be mean, unjust, and 
oppressive. As long as Newton is held up to be 
the perfection of a moral character, so long must 
we insist upon the exceptional cases which prove 
him to have been liable to some of the failings of 
humanity. But to those who can fairly admit that 
his conduct is proof of an unhappy temper which 
sometimes overcame his moral feeling, and who 
therefore look for the collateral circumstances which 
are to excuse or aggravate, there are various con- 
siderations which must not be left out of sight. 

In the first place, this temperament of which we 
have given instances, is of all others the one which 



46 NE WTON 

occasionally lessens the control of the individual 
over his own actions. Every one knows how apt 
we are, from experience, to think of insanity as the 
possible termination of the morbidly suspicious 
habit. That the report which arose about Newton's 
mind was much assisted by a knowledge of this 
habit existing in him, we have little doubt : for 
we see, in our own day, how corroborative such a 
temper is held to be of any such rumour. In one 
instance, and in illness of a serious character, it did 
take a form which we can hardly hold consistent 
with sanity at the time. He spoke severely of 
Locke, his old and tried friend (in 1693), being under 
the apprehension that Locke had endeavoured to 
' ' embroil him with women and by other means " ; 
he thought there was a design to ' ' sell him an 
office and to embroil him." For these suspicions he 
wrote a letter, worthy of himself, asking pardon, 
and saying also that he had been under the im- 
pression that there was an evil intention, or ten- 
dency at least, in some of Locke's writings. The 
latter, in an affectionate answer, desired to know 
what passages he alluded to ; and the rejoinder was 
that the letter was written after many sleepless 
nights, and that he had forgotten what he said. As 
we have only the letters and no further information, 
we must decide as we can whether Newton did 
really express himself to others as he said he had 
done, or whether he only fancied it. In either case 



NE WTON 47 

there is, under illness, that morbid imagination of 
injury done or meditated, which seems to have been 
but the exaggeration of an ordinary habit. If we 
thought, from the evidence, that Newton had ever 
been insane, we should see no reason whatever for 
concealing our opinion : we do not think so ; but 
we think it likely that if his years from 1660 to 
1680 had been passed in the excesses of the 
licentious court of his day, instead of the quiet 
retirement of his college, there might have been 
another story to tell. 

Next, it is not fair to look upon the character 
of any man, without reference to the notions and 
morals of his time. Take Newton from his pinnacle 
of perfection, from the background of the picture, 
from the incidents of the era of political and social 
profligacy in which he lived, and his relative char- 
acter then seems to be almost of the moral magni- 
ficence which is made its attribute. Let the sum 
total of his public career be compared with that of 
others who were "about the King's business," and 
we cannot help looking upon the honest and able 
public servant, who passed a life in the existing 
corruption of public affairs without the shadow of a 
taint upon his official morals, with an admiration 
which must tend to neutralise the condemnation we 
may not spare upon some incidents of his scientific 
life. Further, the idolatrous respect in which he 
was held at the Royal Society, and the other haunts 



48 NE WTON 

of learning the worship his talents received at 
home and abroad, from Halley's 1 "nee fas est 
propius mortali attingere divos," to de PHopital's 
almost serious question whether Newton ate, drank, 
and slept the investment of his living presence 
with all the honours once paid to the memory of 
Aristotle make it wonderful, not that he should 
sometimes have indulged an unhappy disposition, 
but that he should have left so few decided instances 
of it on record. That both his person and his 
memory were held dear by his friends there is no 
doubt : this could not have been unless the cases 
we have cited had been exceptions to the tenor of 
his conduct ; and, knowing the disposition of which 
we have spoken to be one against which none but 
a high power can prevail, we are to infer that it was, 
in general, heartily striven against and successfully 
opposed. 2 

X 

The mind of Newton, as a philosopher, is to this 
day, and to the most dispassionate readers of his 
works, the object of the same sort of wonder with 
which it was regarded by his contemporaries. We 
can compare it with nothing which the popular 
reader can understand, except the idea of a person 

1 " Nor is it possible for man to be nearer to God " : the last line of 
Halley's verses on the Principia. 

2 [For De Morgan's view of Newton's character, see also end of II 
and VI. of the third Essay, below.] 



NE WTON 49 

who is superior to others in every kind of athletic 
exercise ; who can outrun his competitors with a 
greater weight than any one of them can lift standing. 
There is a union, in excessive quantity, of different 
kinds of force : a combination of the greatest 
mathematician with the greatest thinker upon ex- 
perimental truths ; of the most sagacious observer 
with the deepest reflecter. Not infallible, but com- 
mitting, after the greatest deliberation, a mistake 
in a simple point of mathematics, such as might 
have happened to any one : yet so happy in his 
conjectures, as to seem to know more than he 
could possibly have had any means of proving. 
Carrying his methods to such a point that his im- 
mediate successors could not clear one step in ad- 
vance of him until they had given the weapons with 
which himself and Leibniz had furnished them a 
completely new edge, yet apparently solicitous to 
hide his use of the most efficient of these weapons, 
and to give his researches the' appearance of having 
been produced by something as much as possible 
resembling older methods. With few advantages 
as a writer or a teacher, he wraps himself in an 
almost impenetrable veil of obscurity, so as to 
require a comment many times the length of the 
text before he is easily accessible to a moderately 
well-informed mathematician. He seems to think 
he has done enough when he has secured a possibil- 
ity of rinding one reader who can understand him 

4 



50 NE WTON 

with any amount of pains : as if, seeing Halley to 
be of all men he knew next to himself in force, he 
had determined that none but Halley at his utmost 
stretch of thought should follow him. Accordingly 
one, to whom in his later years he used to send 
inquirers, saying, "Go to Mr De Moivre, he knows 
these things better than I do," avowed that when 
he saw the Principia first, it was as much as he 
could do to follow the reasoning. It would be 
difficult to name a dozen men in Europe of 
whom, at the appearance of the Principia, it can 
be proved that they both read and understood the 
work. 

Newton himself attributed all his success to 
patience and perseverance more than to any peculiar 
sagacity : but on this point his judgment is worth 
nothing. Unquestionably, he had the two first in 
an enormous degree, as well as the third ; nor is it 
too much to say that there is no one thing in his 
writings which the sagacity of some of his contem- 
poraries might not have arrived at as well as his own. 
But to make an extensive system many things are 
necessary : and one point of failure is fatal to the 
whole. Again, it is difficult to put before the 
ordinary reader, even if he be a mathematician, a 
distinct view of the merit of any step in the forma- 
tion of a system. Unless he be acquainted with 
the history of preceding efforts, he comes to the 
consideration of that merit from the wrong direction ; 



NE WTON 5 1 

for he reads the history from the end. He goes to 
the mail-coach, back from the railroad instead of 
forward from the old strings of pack-horses : from 
a macadamised road lighted with gas to the rough 
stones and the oil-lamps, instead of beginning with 
the mud and the link-boys. Perhaps the same sort 
of wrong judgment may accompany the retrospect of 
its own labours in a mind like Newton's ; causing it 
to undervalue the intellectual part of which, in any 
case, it is least capable of judging. 

The world at large expects, in the account of such 
things, to hear of some marvellous riddles solved, 
and some visibly extraordinary feats of mind. The 
contents of some well-locked chest are to be guessed 
at by pure strength of imagination : and they are 
disappointed when they find that the wards of the 
lock -were patiently tried, and a key fitted to them 
by (it may be newly imagined) processes of art. 
Thus the great experiment, the trial of the moon's 
gravitation, seems wonderfully simple to those who 
have to describe it ; precisely what anybody could 
do. If the moon were not retained by some force, 
she would proceed in a straight line MB : l some- 
thing causes her to describe MA instead, which is 
equivalent to giving a fall of BA towards the earth. 
Now since EM, the distance of the moon from the 
earth's centre, is about 60 times EC, the earth's 

1 [This refers to a simple figure which it is not necessary to reproduce 
here, as anybody can reproduce it for himself from what is said in the 
text.] 



52 NEWTON 

radius, it follows that if there be gravitation at the 
moon, and if it diminish as the square of the distance 
increases, it ought to be 60 times 60, or 3600 times 
as great at the surface of the earth as at M ; or a 
body at the earth's surface ought to fall in one 
minute 3600 times as much as BA (supposing MA 
to be the arc moved over in one minute). A 
surveyor's apprentice, even in Newton's day, could 
with great ease have ascertained that such is the 
fact, if the data had been given to him. Now why 
was Newton the first to make this simple trial ? 
The notion of gravitation was, as we have said, 
afloat : and Bouillaud had declared his conviction 
that attractive forces, if they exist, must be inversely 
as the squares of the distances. Did he try this 
simple test ? Perhaps he did, and threw away his 
result as useless, not being able to make the next 
step. Or was it that neither he nor any one except 
Newton had any distinct idea of measuring from the 
centre of the earth ? If so, then Newton was in 
possession of what he afterwards proved, namely, 
that a spherical body, the particles of which attract 
inversely as the squares of the distances, attracts as 
if all its particles were collected in its centre. 1 In 
either case, this may serve to illustrate what a 
popular reader would hardly suppose, namely, that 
the wonder of great discoveries consists in there 

1 [Newton explicitly stated that he only discovered this theorem in 
1685; cf. above, note 30.] 



NEWTON 53 

being found one who can accumulate and put 
together many different things, no one of which 
is, by itself, stupendous after the fact, nor calculated 
to produce that sort of admiration with which the 
whole is regarded. 

XI 

We have not yet mentioned the theological writings 
of Newton, as his discussion of the prophecies of 
Daniel, and so on. About his opinions on this sub- 
ject there is a little controversy : and the various 
sects of opinion are in the habit of opposing to each 
other the great names which are on their several 
sides of the question. That Newton was a firm 
believer in Christianity as a revelation from God, is 
very certain : but whether he held the opinions of 
the majority of Christians on the points which 
distinguish Trinitarians from Arians, 1 Socinians, and 
Humanitarians, is the question of controversy. It 
is to be remembered that during the whole of 
Newton's life the denial of the doctrine of the 
Trinity was illegal, the statute of King William 
(which relaxed the existing law, for a man was 

1 These names are bandied about in vituperative discussions, until 
they are so misused that the chances are many readers will need explana- 
tion of them. An Arian believes in the finite pre-existence of Jesus 
Christ, before his appearance on earth : a Socinian believes him to be a 
man who did not exist before his appearance on earth, but who is still 
a proper object of prayer : a Humanitarian, with all others who come 
under the general name of Unitarian (the personal unity of the Deity 
being a common tenet of all), believes him to be a man, and not an 
object of prayer. 



54 NE WTON 

hanged in 1696 for denying the Trinity) making 
it incapability of holding any place of trust for the 
first offence, and three years' imprisonment with 
other penalties for the second. Few therefore wrote 
against the Trinity, except either as, in the Unitarian 
Tracts, without even a printer's name, or evasively, 
by arguing against the Trinity being an article of 
faith, that is, a necessary part of a Christian's hope 
of salvation. Premising this, we take the evidence, 
as it stands, for and against the heretical character 
of Newton's opinions. 

There is a widespread tradition that Horsley 
objected to publish a part of the " Portsmouth 
Papers " on account of the heresy of the opinions 
contained in them ; which statement used to be 
even in children's books, and was made by Dr 
Thomson in his History of the Royal Society. These 
papers have never been published, nor has any one 
of those who have had access to them denied the 
rumour on his own knowledge. The refusal of 
Horsley is not conclusive in itself; because, to 
use the words of one of the children's books we 
remember (called a ''British Plutarch," or some 
such name), he was a " rigid high priest," and 
heterodoxy short even of Arianism would probably 
have led him to such a determination. But the 
suppression still continues, long after the above 
rumour has been very effective in aiding the prob- 
abilities drawn from other sources, that Newton's 



NEWTON 55 

opinions were even more heterodox than Arianism ; 
and there is some force in this. 

Two witnesses from among Newton's personal 
friends, Whiston, an Arian (calling himself a 
Eusebian), and Hopton Haynes, who was employed 
under him in the Mint, and who was a Humanitarian, 
severally bear testimony to his having held their 
several opinions. Whiston, whose intimate acquaint- 
ance with him terminated some time before 1720, 
states in two places that Newton was a Eusebian 
(Arian) and a Baptist, and that he was " inclined to 
suppose " these two sects to be the two witnesses 1 
mentioned in the book of Revelations. Haynes 2 
declares him to have been a Humanitarian, and 
stated that he much lamented that his friend Dr 
Clarke had stopped at Arianism. On the other 
hand, the writer in the Biographia Britannica y who 

1 This is strange ; and if such had been Whiston's own opinion, we 
should not have hesitated to conclude that he had misinterpreted some 
civil decliner of controversy. But Whiston expressly states himself to 
have no such opinion. That he would intentionally utter a falsehood we 
believe to be out of the question. 

2 The testimony of Whiston is in his Memoirs : that of Haynes is less 
direct. The Unitarian minister, Richard Baron, who was a friend of 
Haynes, states the preceding as having passed in conversation between 
him and Haynes. The statement is made in the preface of the first 
volume of his collection of tracts, called A Cordial for Low Spirits 
(three volumes, London, 1763, third edition, I2mo), published under 
the name of Thomas Gordon. This is not primary evidence like that 
of Whiston ; and it loses force by the circumstance that in the pos- 
thumous work which Mr Haynes left on the disputed points (and which 
was twice printed) there is no allusion to it. But those who weigh 
testimony will of course take into continued consideration its amount of 
corroborative force. And a great many writers on the Antitrinitarian 
side deserve blame for not stating distinctly that it is only a testimony 
to a testimony : Baron was a man against whose character for truth we 
never heard anything, but the chances of misapprehension increase very 
rapidly with the number of steps, in the communication of oral tradition. 



56 NEWTON 

cites the last edition 1 (1753) of Whiston's Memoirs, 
says that Whiston states that Newton was so much 
offended with him for having represented him as an 
Arian, that this was the reason why he would never 
consent to his admission into the Royal Society. 
The edition of 1749, thirteen years after Newton's 

1 Though aware that we should have many results of bias to encounter, 
we had hoped that we should have got through our task without having 
to expose absolute and fraudulent falsification. Since writing what is in 
the text, we have obtained the loan of the edition of 1753, which is 
scarce compared with that of 1749. The Biogr. Brit, informs us 
(p. 3241) that in pages 178, 249, 250 of Whiston's Memoirs, edition 
of 1753, 8vo, we shall find the justification of these words: "Mr 
Whiston, who represented Sir Isaac as an Arian, which he so much 
resented that he would not suffer him to be a member of the Royal 
Society while he was President." We look, and in p. 178 we find that 
Whiston states Newton to be an Arian, and in pp. 249 and 250 we find 
that Newton excluded Whiston from the Royal Society, for which the 
reason Whiston gives is that Newton could not bear contradiction, in 
the words we have quoted in another part of this article. The biographer 
distinctly implies that he is giving, not his own reason, but Whiston's 
reason. And, having diligently compared the editions of 1749 and 
1753 ( tne latter of which had some additions, by which the false biographer 
hoped to gain credit from those who looked at the former), we find that 
the paragraphs cited only differ as follows: In the first, 1749 has 
Revelation, 1753 has Revelation. The former has "and friendly 
address to the Baptists" (pp. 14, 15), which the latter has not. In 
the second, 1749 has "desire " and 1753 has ' ' desires " (a little instance, 
by the way, of the disappearance of the old English subjunctive), and 
the former has "through confutation," when the latter has "thorough 
confutation." Sir D. Brewster (p. 284) has copied the false biographer 
without verifying the reference a common, but a dangerous practice. 
It was a mere accident that we went to the Biogr. Brit., for we 
distrust it from old acquaintance on all matters connected with Newton. 
We do not know at this moment that the false biographer, as we call 
him, is the original falsifier : but he must bear the blame for the present. 
We might have had to leave the explanation to Sir D. Brewster : for he 
who copies a reference without verification, and without stating that he 
copies, must take the responsibility of that reference. But as it stands, 
we need not say that Sir D. Brewster is as clear in this instance from 
the imputation of intentionally misleading his reader, as those could 
wish who respect his character and admire his labours : among the 
number of whom we desire to place ourselves. And his candour wiil 
lead him to acknowledge that he has had a happy escape from an 
imminent danger of misconstruction, with no blame to those who 
made it. 



NEWTON 57 

death, shows that Whiston had then no such know- 
ledge of the cause. But, if it were so, and Haynes's 
testimony be true, he might have had Priestley's 
objection to Arianism rather than Horsley's : and in 
either case, we know enough of Newton to be sure 
that he would be likely to take offence at any talk 
about opinions he did not choose to avow, particu- 
larly such as were illegal ; and above all, he would 
fear the tongue of a man like Whiston, all honesty 
and no discretion, who told the world long before 
his death all that he knew about himself and every- 
body else, without the least reserve. 

Newton wrote (about 1690), under the title of 
" Historical Account of two Notable Corruptions of 
Scripture," against the genuineness of two passages 
on which Trinitarian l writers then placed much 
reliance : that is, against the genuineness of i John 
v. 7, and that of the word 0eo? (God), I Timothy 
iii. 1 6. Now, though Trinitarians have often aban- 
doned the first passage, and given up the Protestant 
reading of the second, it has rarely happened, 
if ever, that they have written expressly against 
them : the world at large sees no difference between 
opposing an argument, and opposing the conclusion ; 
and parties in religion and politics require 2 assent, 

1 Protestant writers, we mean ; the reading contended for by 
Newton in the second instance has been that of Catholics from the 
time of Jerome. 

2 Dr Chalmers, for example, states Newton to have "abetted" the 
leading doctrine of the Unitarians : whether upon the evidence of this 
writing only, or the general evidence, does not precisely appear : 



58 NEWTON 

not merely to their tenets, but to each and every 
mode of maintaining them. And writers who go 
so far as to say anything against one mode of 
supporting their own side of a question, generally 
make a decided profession of adherence to the con- 
clusion while they reason against one mode of 
maintaining it. Newton does no such thing : his 
expressions are vague, or, if not vague, they are the 
formular x words under which the opponents of the 

probably upon the former alone. The author of the Life in the 
Biographia Britannica does not mention these letters. But it appears 
by the testimony of Le Clerc and Wetstein, that Locke sent them to 
Le Clerc, who did not know their author. The possessors of Newton's 
papers never published them until an incomplete edition had appeared 
abroad. 

1 Sir D. Brewster, to whom the admirers of Newton have much 
obligation, and from whom they expect more, in the larger Life on 
which he is known to be engaged, argues from these words, which he 
quotes formally, that Newton received the Trinity. But, having the work 
before him, he should also have destroyed the effect of the following words 
of Newton: " He (Cyprian) does not say the Father, the Word, and 
the Holy Ghost, as it is now in the 7th verse, but the Father, the Son, 
and the Holy Ghost, as it is in Baptism, the place from ^vh^ch they tried 
at first to derive the Trinity." We never were quite satisfied till we 
saw this passage. We found the Trinitarian writers evidently shy of 
the question : and the Antitrinitarians as evidently laying such an 
undue stress on Mr Haynes's testimony, or rather Mr Baron's testimony 
to Mr Haynes's testimony, as made us suspect that our authorities on 
both sides were not fully satisfied in their own minds. But we hold it 
to be out of the question that a Trinitarian could have written the 
words in our italics. That many would riot admit the baptismal form 
in itself to be a proof of the doctrine, is known ; but what Trinitarian 
ever talked of a " they" who tried a text to prove the doctrine, "at 
first," implying that they failed, and then went to others? the clear 
implication being that he thought they had the doctrine before they 
tried any texts. Again, there is the following. Speaking of the 
manuscript on which Erasmus at last introduced I John v. 7 into his 
text, he says that the English, " when they had got the Trinity into his 
edition, threw by their manuscript (if they had one) as an almanac out 
of date." Now most of our readers are Trinitarians, and know whether 
this is the way in which those who hold that doctrine speak of it. The 
citations above are from Horsley's Newton. 

When M. Biot said that there was absolutely nothing in Newton's 
writings which was other than orthodox, he must have meant in the 



NE WTON 59 

received doctrine avoided imprisonment. The truth 
is to be purged of things spurious : the faith sub- 
sisted before these texts were introduced or changed ; 
it is not an article of faith or a point of discipline, 
but a criticism, and so on. There is an expression 
towards the end which admits of a double interpre- 
tation : ' ' if the ancient churches, in debating and 
deciding the greatest mysteries of religion, knew 
nothing of these two texts ; 1 understand not, why 
we should be so fond of them now the debates are 
over." The first clause, by itself, might rather 
have been written by a Trinitarian : though a 
Unitarian might write it, more especially if he 
wanted a formular phrase. But the second clause 
looks very like a formula : for there was no time at 
which the debate raged so fiercely as in the day of 
Newton, which was that of Wallis, South, Sherlock, 
and so on, and hosts of anonymous writers. We 
find it difficult to suppose that Newton, whose 
friendship with Locke, Clarke, and Whiston at 
that time was notorious, would do that which none 
but Antitrinitarians, or very few, ever did, in a 
communication to an Antitrinitarian intended at 
that time for publication abroad, without making a 
definite avowal of the orthodoxy of his belief, if he 
had it to make. It is right to state, on the other 

writings which he had seen. This of course may have been the case. 
Moreover, what is more absurd than to argue from his silence that a 
man does not hold an opinion for which he might be ruined and 
imprisoned, or, up to 1699, even hanged? [See the first note to this 
Essay.] 



60 NEWTON 

side, Bishop Burgess's argument : that this was a 
writing which Newton suppressed from publication. 
Printing should have been the word : Newton 
published it when he caused it to be sent to 
Le Clerc. There is to us something corroborative, 
or at least significative of much difference from the 
most common opinion, in the Scholium which he 
added at the end of the second edition of the 
Principia. With Jewish and Christian writers, 
Deity is necessarily from eternity and without 
superior : the word God implies both necessary 
existence and omnipotence. With the Greeks, 
divine power might be communicated in such a 
manner that a hero, for instance, after death, might 
become as truly the object of worship as Jupiter 
himself. Newton adopts the Greek definition, or 
one very like it. The rule of a spiritual being 
makes him God. "Dominatio entis spiritualis 
Deum constituit." And as if this were not precise 
enough, he adds, in the third edition, a note stating 
that thus the souls of dead princes were called gods 
by the Gentiles, but falsely ', from want of dominion. 
He then proceeds to his well-known reflections on 
the Supreme Deity. 

We have entered into this question, not from any 
particular interest in it for there are too many 
great minds on both sides of the controversy to make 
one more or less a matter of any consequence to 
either, but because we have a curious matter of 



NEWTON 6 1 

evidence, and an instructive view of party methods 
of discussion. Whatever Newton's opinions were, 
they were in the highest degree the result of a love 
of truth, and of a cautious and deliberate search 
after it. His very infirmity is a guarantee for the 
existence of this feeling in no usual measure. With 
a competent livelihood, and the dread of discussion 
so strong that he would gladly have hidden his 
results from the world rather than encounter even 
respectful opposition, he could not have worked either 
for the hope of wealth or office, or even for the love 
of fame, except in a very secondary degree. The 
enthusiasm which supported him through the years 
of patient thought out of which the Principia arose, 
must have been strong indeed when he had no 
ultimate worldly end to propose to himself. Who 
can say how much of the truth of his system we may 
owe to this very position ? Had he been desirous 
of pleasing, he must have had strong temptation 
to build upon some of the prevailing notions ; to 
have a little mercy upon the physics of Descartes. 
Or even without going so far, a small portion of the 
vanity which loves to present complete systems and 
to confess no ignorance, might have biased him to 
adopt such an addition to his law of attractive force 
(such a one as Clairaut for a little while thought 
necessary) as, without interfering with the main 
phenomena, would have served to bring out some 
more explanations. But he had no such bias : and 



62 NE WTON 

speaking of his philosophic character, it may be said 
that never was there more of the disinterested spirit 
of inquiry, unspurred by love of system, unchecked 
by dread of labour or of opinion. For, however 
much he might dislike or fear opposition, there was 
one tribute to it which his philosophy never paid ; 
the pages which he would gladly have burned rather 
than encounter discussion, contain no concession 
whatever. l 

XII 

In concluding this brief outline of a truly great 
man, one of the first minds of any age or country, 
of whose labours the world will reap the fruits in 
every year of its existence, we cannot help express- 
ing our hope that future biographers will fairly 
refute, or fairly admit, the existence of those blots 
of temper to which the undiscriminating admiration 
of preceding ones has obliged us to devote so much 
of the present article. Of the facts, where we have 
stated them as facts, we are well assured ; and there 
can be no reason why the warnings which the best 
and greatest of the species must sometimes hold out 
to the rest, should be softened, or, what is worse, 
converted into examples of imitation, by fear of 
opposing an established prejudice, or by the curious 
tendency of biographers to exalt those of whom 

1 [On Newton's religious opinions, see also VIII. of the third 
Essay, below.] 



NE WTON 63 

they write into monsters of perfection. Surely it is 
enough that Newton is the greatest of philosophers, 
and one of the best of men that all his errors are 
to be traced to a disposition which seems to have 
been born l with him that, admitting them in their 
fullest extent, he remains an object of unqualified 
wonder, and all but unqualified respect. 

For reasons which will be easily understood, the 
author of this article subscribes his name. 

A. DE MORGAN. 

1 We cannot trace, in Newton's character, an acquired failing', 
nothing but the manifestations of the original disposition due to 
different circumstances. 






II 

A SHORT ACCOUNT OF SOME 

RECENT DISCOVERIES RELATIVE 

TO THE CONTROVERSY ON THE 

INVENTION OF FLUXIONS 



A SHORT ACCOUNT OF SOME 

RECENT DISCOVERIES IN ENGLAND 

AND GERMANY RELATIVE TO THE 

CONTROVERSY ON THE INVENTION 

OF FLUXIONS 1 

THE celebrated controversy on the invention of 
fluxions has, any one would suppose, been so fully 
argued that it would be difficult to make out a 
reasonable case for introducing the subject again. 
It is nevertheless true that several disclosures of 
great importance in the way of evidence have never 
been made at all until very lately. 

This controversy resembles one of those well-worn 
law cases which must be cited and discussed when- 
ever a certain question arises. Every dispute about 

1 [This Essay was printed in The Companion to the Almanac: or, 
Year-Book of General Information for 1852, pp. 5-20, which was 
published at London by Charles Knight as a supplement to The British 
Almanac of the Society for the Diffusion of Useful Knowledge, for the 
year of our Lord 1852, and of which the first part, in which the present 
Essay was included, contained "general information on subjects of 
mathematics, natural philosophy and history, chronology, geography, 
statistics, etc." It seems to have been the first English consideration 
of the fluxional controversy in the light of the discoveries of Gerhardt 
among Leibniz's manuscripts in the Royal Library of Hanover. Notes 
on the literature relating to the controversy, and on the early fluxional 
manuscripts of Newton and Leibniz, are given below in the Appendix to 
this Essay.] 

67 



68 FLU XI ON AL 

priority of mathematical invention l revives it. At 
the same time, the main and turning points of it 
can be presented without any such amount of 
mathematical language as would render an article 
upon the subject unfit for the majority of readers. 
We therefore propose to present some of these 
points, with an account of the recently published 
materials, and of their bearing on the result. 

When, after some petty and indecisive controversy, 
Leibniz appealed (1711) to the Royal Society for 
protection against imputations of plagiarism which 
had at last assumed a distinct form, the Society, in 
1712, appointed the celebrated partisan 2 Committee 
to maintain the side of Newton. The report of this 
Committee, published with epistolary evidence in 
1712, under the name of Commercium Epistolicum* 
contains the following sentence, which is the whole 

1 One most fortunate circumstance about it, as a precedent, is that 
it fixed the meaning of the word "publication" to the genuine and 
legal sense. It is the sufficient answer to any one who would restrict 
this word to its colloquial sense of circulation by means of type. 

2 We have shown the Committee to have had this character in Phil. 
Trans. , part ii. for 1 846, and in the life of Newton in Knighfs British 
Worthies ; and nobody has contested the point. It was, however, 
universally believed that the intended function of the Committee was 
judicial, and both Newton and Leibniz speak of it as if it had been so. 
But though the Committee itself overstepped its own proper function in 
the form of its decision, and thereby gave rise to the misconception, we 
hold the intention of its proposers to have been stated with perfect 
clearness. [On De Morgan's paper in the Philosophical Transactions 
for 1846, and on the subsequent occurrences, see the above Preface to 
these Essays and Appendix ii. to the third Essay below. ] 

3 We cannot here detail all the circumstances. The reader may 
consult the articles " Commercium Epistolicum" and "Fluxions" in 
the Penny Cyclopaedia^ the life of Newton already cited, Brewster's 
Life of Newton, that in the Library of Useful Knowledge, or Weld's 
History of the Royal Society. 



CALCULUS 69 

of that report, so far as it insinuates that Leibniz 
did take, or might have taken, his method from' 
that of Newton : " And we find no mention of his 
(i. e. Leibniz's) having any other Differential Method 
than Moutoris before his Letter of 2ist of June 
1677, which was a Year after a Copy of Mr Newton's 
Letter, of loth of December 1672, had been sent to 
Paris to be communicated to him ; and about four 
Years after Mr Collins began to communicate that 
Letter to his Correspondents ; in which Letter the 
Method of Fluxions was sufficiently describ'd to any 
intelligent Person." 

The Committee in their English have "any in- 
telligent person " ; in their Latin, subjoined for 
foreigners, they have ' ? idoneo harum rerum cog- 
nitori." Raphson, no stickler for accurate de- 
scription, as we shall see, could not second this ; 
so he converts the Latin into the original, and gives 
his own English translation, * ' to any proper judge 
of these matters." But even this was too much; 
so some one else (copied by Hutton in his Dictionary ; 
we do not think Hutton did it himself) has invented 
a new report, in which we find (< a man of his 
sagacity." 

How far this celebrated letter deserves the char- 
acter here given of it, is one question ; whether 
Leibniz actually received it, is another. Compara- 
tively little notice was taken of either ; so that in 
many subsequent writings it reminds us of the tree 



70 FLUXIONAL 

which was cut down that the action for trespass 
might try the ownership of the estate. It gives, 
nevertheless, the only possibility, such as it is, 
which the evidence offers of Leibniz having seen 
anything to the point from the pen of Newton. 

In order to prove the passage quoted above, it 
is stated that there existed, among the papers of 
Collins in the possession of the Royal Society, in 
the handwriting of Collins, a parcel (collectid) of 
papers containing extracts from Gregory's letters, 
together with the letter of Newton above-mentioned 
(but which was not alluded to in the title or docket 
which Collins placed on the parcel), and that the 
parcel was marked as to be communicated to 
Leibniz, and was accompanied by a copy of a letter 
to Oldenburg, the party who was to make the 
communication. Not a word is said on the date 
at which the parcel was transmitted : so that the 
Committee, in their report, actually added a state- 
ment for which there was no pretext of evidence, 
namely, that Newton's letter was transmitted about 
a year before the 2ist of June, 1677. Further, the 
evidence does not mention the date at which Collins 
died (1682), nor how his papers came into the 
possession of the Society, nor whether there was 
any guarantee that papers found tied together in 
1712 had been so tied up by Collins before 1682, 
nor whether there was any evidence that Collins 
had fulfilled his intention of sending the parcel on 



CALCULUS 71 

to Oldenburg, and so on. When Leibniz, who did 
not remember receiving any such letter, declared 
that he did not think it necessary to answer any- 
thing so weak, his contempt for this unattested 
statement was of course construed by the other 
side as being of that kind which parties who cannot 
answer find it convenient to assume. 

The editors, whoever they were, of the reprint l 
of the Commercium Epistolicum, made under the 
sanction of the Royal Society in 1722, took the 
liberty of secretly making a few additions 2 and 
alterations. Among these, they add the date at 
which Collins died, and the date of transmission of 
the parcel : they say it was sent on June the 26th, 
1676. How they got this date is not said ; but as 
the next parcel sent by Oldenburg to Leibniz was 
stated to have been sent on June the 26th, it may 
have happened that the revisers of the second edition 
borrowed this date for their purpose. 

So the matter rested until recently, when the 
publication of a portion 3 of Leibniz's papers took 

1 We say "reprint," and not "second edition," because even the 
old title-pages and the old date (1712) were reprinted. Everything 
was done which could lead the reader to suppose that he had in every 
respect a repetition of the original work, preceded by a preface of the 
new editors. 

2 This fact was discovered by us in 1848 ; and the additions are 
exposed in the Philosophical Magazine for June 1848. The first 
edition is now scarce. [See the above Preface and Appendix ii. to 
the third Essay.] 

3 Leibnizens mathematische Schriften, herausgegeben von C, J. Ger- 
hardt, Berlin, 8vo. Erste Abtheilung, Band I, 1849, Band II, 1850. 
We have not seen any more, if indeed any more has yet appeared. 
[Leibnizens mathematische Schriften were edited by C. I. Gerhardt as 



72 FLUXION AL 

place. And it now appears that if the manuscripts 
which Leibniz left behind him, and which found 
their way into the Royal Library at Hanover, had 
been examined, it could have been ascertained what 
Leibniz really did receive from Oldenburg. It 
appears that the latter wrote to the former from 
London, with the date of July the 26th, 1676, not 
forwarding Collins's parcel, but describing its 
contents 1 himself. He gives various matters con- 
nected with Gregory's researches, and then proceeds 
to allude to a method in a letter from Newton of 
December the loth, 1672. But though he gives, 
almost verbatim, what we may call the descriptive 

the third series (Dritte Folge: MathemaliK) of G. H. Pertz's edition 
of Leibnizens gesammelte Werke aus den Handschriflen der Kbniglichen 
Bibliothek zu Hannover, and were published in seven volumes. In the 
first division (Abtheilung}, vol. i (Berlin, 1849) contained the corre- 
spondence with Oldenburg, Collins, Newton, Galloys, and Vitale 
Giordano ; vol. ii (Berlin, 1850) contained the correspondence with 
Huygens and de 1'Hopital ; vol. iii (Halle, 1855) contained that 
with Jacob, Johann, and Nicolaus Bernoulli; and vol. iv (Halle, 
1859) that with Wallis, Varignon, Guido Grandi, Zendrini, and 
Tschirnhaus. The second division consists of three volumes of 
Leibniz's mathematical writings, published and unpublished. How- 
ever, none of the important papers written by Leibniz when discovering 
the calculus, which were published by Gerhardt in 1848 and 1855 (see 
the Appendix to this Essay), were included in these volumes. Vol. v 
(numbering consecutively to the others) was published at Halle in 1858, 
and contained those mathematical writings which were either published 
(1666-1713) or intended for publication ; vol. vi (Halle, 1860) con- 
tained writings on dynamics from 1671 to 1706; and vol. vii (Halle, 
1863) was on " Initia mathematica ; Mathesis universalis ; Arithmetica ; 
Algebraica;" and "Geometrica." Gerhardt also published at Berlin 
in 1899 the Briefwechsel mentioned in the Appendix to this Essay.] 

1 Collins had desired, in the title of the parcel, that the contents 
after being read by Leibniz, should be returned to himself. Olden- 
burg appears to have thought it more prudent to write his own 
account than to trust the papers to accident by land and sea, (At 
least, this was our impression before we came to the discovery presently 
mentioned. ) 



CALCULUS 73 

paragraph'*- of this letter, he does not even allude 
to the example of the method, in which, according 
to the report of the Committee, the method of 
fluxions is sufficiently described to any intelligent 
person. So that, with reference to this asserted 
description of the method of fluxions, there is now 
clear and positive evidence that Leibniz did not 
receive it as stated, but received only an account 
of the rest of the letter, which describes the sort of 
results attainable. 

Towards the end of 1850 the Master and Fellows 
of Trinity College, Cambridge, published (from 
among their manuscripts) 2 the* correspondence of 

1 " Defuncto Gregorio," says Oldenburg, " congressit Collinius 
amplum illud commercium litterarium, quod ipsi inter se coluerant, in 
quo habetur argumenti hujus de seriebus historia : cui Dn. Newtonus 
pollicitus est se adjecturum suam methodum inventionis illius, prima 
quaque occasione commoda edendam ; de qua interea temporis hoc 
scire prseter rem non fuerit, quod scilicet Dn. Newtonus cum in literis 
suis Dcbr. 10. 1672 communicaret nobis methodum ducendi tangentes 
ad curvas geometricas ex gequatione experimente relationem ordinatarum 
ad Basin, subjicit hoc esse unum particulare, vel corollarium potius, 
methodi generalis, quse extendit se absque molesto calculo, non modo 
ad ducendas tangentes accomodatas omnibus curvis, sive Geometricas 
sive Mechanicas, vel quomodocunque spectantes lineas rectas, aliisve 
lineis curvis ; sic etiam ad resolvenda alia abstrusiora problematum 
genera de curvarum flexu, areis, longitudinibus, centris gravitatis etc. 
Neque (sic pergit) ut Huddenii methodus de maximis et minimis, 
proinde que Slusii nova methodus de tangentibus (ut arbitror) restricta 
est ad aequationes, surdarum quantitatum immunes. Hanc methodum 
se intertextuisse, ait Nowtonus (sic), alteri illi, quse sequationes expedit 
reducendo eas ad infinitas series ; adjicit que, se recordari, aliquando 
data occasione, se significasse Doctori Barrovio lectiones suas jam 
edituro, instructum se esse tali methodo ducendi tangentes, sed avoca- 
mentis quibusdam se prsepeditum, quominus earn ipsi describeret." 

The word nobis , put by us in italics, should be ei ; Oldenburg forgot 
that he was describing, not copying, the account Collins had given him. 

2 Correspondence of Sir Isaac Newton and Professor Cotes . . . now 
first published from the originals in the Library of Trinity College, 

Cambridge, together with an appendix . . . by J. Edleston, M.A., 
Fellow of Trinity College, Cambridge, London, 1850, 8vo. 



7 A FLUXIONAL 

Newton and Cotes, with what is called a synoptical 
view of Newton's life. This is far below sufficient 
description ; for the synopsis is followed by a body 
of notes of such research and digestion as make it 
difficult to give adequate praise to the whole without 
appearance of exaggeration. We differ much from 
the editor as to many matters of opinion and state- 
ments the character of which is determined by 
opinion ; and we take particular exception to the 
following account 1 of the point before us : 

' ' Doubts have been expressed whether these 
papers 2 were actually sent to Leibniz. We have, 
however, Collins's own testimony that they were 
sent as had been desired, 3 besides Leibniz's and 
Tschirnhaus's acknowledgments of the receipt of 
them. 4 It may also be observed that the papers 
actually sent (in a letter dated July the 26th, 1676) 
to Leibniz by Oldenburg have been recently printed 
from the originals in the Royal Library at Hanover, 5 
and that in them, as in Collins's draught, which is 
preserved at the Royal Society ('To Leibnitz, the 
1 4th of June, 1676 About Mr. Gregories remains,' 
MSS. Ixxxi.), we find the contents of Newton's 
letter of December the loth, 1672, except that 
instead of the example of drawing a tangent to a 
curve, there is merely allusion made to the method. 

1 Op. ''/., p. xlvii. 2 Comm. Epist., p. 47 ; 2nd ed., p. 128. 

3 Ibid., pp. 48 or 129 respectively. 

4 Ibid., pp. 58, 66 or 129, 142 respectively. 

5 Leibn. Math. Schrift., Berlin, 1849. 



CALCULUS 75 

Collins's larger paper (called ' Collectio ' and ' Hist- 
oriola ' in the Commercium Epistolicum), of which 
the paper just quoted ' About Mr. Gregories remains ' 
is an abridgment, and which contains Newton's 
letter of December the loth without curtailment, 
is stated in the second edition of the Commercium 
to have been sent to Leibniz, but whether that was 
the case may be fairly questioned." 

There are two things in which we have never 
failed. We have never examined a point of mathe- 
matical history without finding either error or 
difficulty arising from bad bibliography : and we 
have never come fresh to this controversy of 
Newton and Leibniz without finding new evidence 
of the atrocious unfairness of the contemporary 
partisans of Newton. Nor had we a perception, 
until we wrote out the preceding paragraph, of the 
full extent of what it proves. It proves that at the 
time when the Committee of the Royal Society 
mentioned the ' ' collectio " which contained Newton's 
letter uncurt ailed of any part relating to fluxions, 
and asserted in their final report (without venturing 
to mention it in its place) that this letter had been 
forwarded to Leibniz they had, and must have 
seen, among the papers they were appointed 1 to 
examine, Collins's own abridgment of this "collectio," 
headed "To Leibnitz," and containing Newton's 

1 There is not the least reason to suppose that any papers of Collins's 
ever came into the possession of the Royal Society after the Comm. 
Epist. was published. 



76 FLUXION AL 

letter curtailed of the very part of which they asserted 
that it described the method of fluxions sufficiently 
for any intelligent person. Of this abridgment they 
make no mention. We now see why the statement 
that the ' ' collectio " was sent to Leibniz was not 
allowed to appear in its place ; that is, when the 
"collectio" was mentioned in the body of the work. 
Had the blot been hit, they would have pleaded 
some mistake or forgetfulness, would have produced 
the abridgment, and would have taken their stand 
on the fragment of the letter descriptive of results. 
We neither believe, nor would have others believe, 
that in the proceeding just described we are 
necessarily to impute guilty unfairness to the Com- 
mittee of 1712, or to some of them : though all the 
circumstances make it impossible to avoid including 
this hypothesis among the probable ones. Inde- 
pendently of our knowledge of what hero-worship 
can lead to, even in our own day, we are bound to 
remember that all the notions as to what is fair and 
what is unfair in controversy, have undergone much 
change since the commencement of the last century. 
And above all, the idea that a party in literary 
controversy resembles one in a court of law, who 
may, with certainty of allowance, choose his own 
evidence, suppress what does not suit, and mystify 
what does, is now much less in force. In the 
particular case before us, perhaps something is to 
be allowed for hurry. The Committee was appointed 



CALCULUS 77 

in parcels on March the 6th, 2Oth, 27th, and April 
the 1 7th; and their report was read on April the 
24th. But the hurry, if any, was their own fault. 
This striking fact, that the very papers which were 
examined in 1712 prove that the celebrated letter 
was not 1 sent to Leibniz, but only a description 
(amounting to extract) of a part of it, and that part 
not the one which most appears to sustain the 
report of the Committee, throws into the background 
the remarks which we intended to make on part of 
the paragraph above extracted from the synoptical 
life of Newton. These must now be mixed up with 
remarks on the whole. 

The editor begins by stating that doubts have 
been thrown on the question whether " these papers 
were actually sent to Leibniz." By these papers, 
the reference tells us we are to understand the 
' ' collectio " which has been spoken of. To remove 
the doubts and prove that * * these papers " were 
actually sent, we are first referred to Collins's own 
testimony. The reference given would exclude 

1 It is now clear that the Royal Society owes the world more publica- 
tion from its archives than has yet taken place : unfortunately, it is not 
yet alive to the feeling that such disclosures as those of the surreptitious 
additions to the reprint of the Cotnm. Episl., and of the suppres- 
sion now noted, would come most gracefully from itself. It is on 
record that in 1716, the Abbe Conti, a friend of both parties, spent 
some hours in looking over the letter books of the Royal Society to see 
if he could find anything omitted in the Conitn. Epist. which made 
either for Leibniz, or against Newton ; and that he found nothing. 
But it now appears either that he did not know what to look for, or 
that there were papers which did not come in his way. Be it one or 
the other, the credit of his search is now upset ; and Mr Edleston's 
discovery proves that another is wanted. 



78 FLUXIONAL 

Newton's letter, since nothing is there mentioned 
as sent to Paris except either Gregory's writings, 
or what had been done on the method of series : 
the drawing of tangents to curves was a perfectly 
distinct thing in the language of the day. But this 
reference leads us to a proof (though one is not 
needed) that the Committee actually saw the 
abridgment which was sent, and contrived to intro- 
duce reference to it in an unintelligible way ; so 
that no one who was ignorant of the existence of 
the abridgment could infer that anything was sent 
except the complete * ' collectio. " The reference is 
to the Commercium Epistolicum^- where we find a 
letter from Collins to David Gregory (the brother of 
James, whose papers were in question) of August the 
nth, 1676, in which Collins says that he had put 
together an " historiola " of the writings of his 
brother and others, in about twelve 2 sheets, for 
preservation in the archives of the Society ; and 
that he would find from what followed the letter 
(ex sequentibus comperies) that care had been taken 
to satisfy the wishes of the French mathematicians. 
Annexed to the letter is a memorandum to the 
effect that the ' ' sequentia " had been sent both to 
the members of the French Academy, 3 and to 

1 Pp. 47, 48 ; 2nd ed., p. 129. 

2 It is now, Mr Edleston informs us, extant in thirteen sheets ; from 
which it is clear that this "historiola," as Collins calls it, is what the 
Committee called the ' ' collectio " ; as the editor notes. 

3 Among these was Leibniz, who, as we learn from the letter of 
Collins to Oldenburg, attached to the "collectio," was one of the 



CALCULUS 79 

David Gregory. Here, then, are two things ; the 
" historiola " mentioned in the letter, and the 
"sequentia" of the letter: the latter was sent to 
Paris, and therefore by the " sequentia " we are to 
understand Collins's abridgment. That is to say, 
the Committee, which extracted as much from Collins 
as would prove that something was sent, did not 
give a word to explain what was sent : and inserted 
in their report a deliberate statement that the whole 
of what they chose to call the fluxional part of 
Newton's letter had been sent. 

We are next told that Leibniz 1 acknowledged the 
receipt of ' ' these papers " : we look at the reference 
indicated, and we find that Leibniz does (August the 
2/th, 1676) acknowledge letters of July the 26th, 



French Academy who had desired to have an account of Gregory's 
writings. In fact, Leibniz was at Paris when he received Oldenburg's 
account of Collins's abridgment. The Committee, who say that 
Newton's letter was sent to Paris to be communicated to him, may 
seem by this phrase to have supposed him to have been at Hanover. 

1 Our extract says, Leibniz and Tschirnhaus. Now though the 
latter did write from Paris, in September, acknowledging something, 
yet he does not sufficiently say what, and even the Committee have put 
a note to his letter, doubting, from its internal evidence, whether he 
could have seen those extracts from Gregory which were sent to Leibniz. 
So that the Committee knew nothing positive as to what was trans- 
mitted to Tschirnhaus. Moreover, Tschirnhaus was not Leibniz. The 
whole of the passage on which this note is written struck us as so 
singular, so contrary, in the antagonism of its two portions, to the 
usual clearness of the whole of which it forms a part, that we could 
not help suspecting that the editor had been misled by some pre- 
decessor. And at last we found out by whom. Keill, in the account 
of the ' ' Commercium Epistolicum " published in English in the Phil. 
Trans, for 1715, and in Latin as a preface to the reprint, has the whole 
argument with the affirmation of Collins and the replies of Leibniz and 
Tschirnhaus. Keill was more noted, while alive, for getting his friends 
into embarrassments than for his discoveries : will he never leave off his 
old tricks ? 



8o FLU XI ON AL 

which the editor himself immediately proceeds to 
inform us, both from the Hanoverian publication 
and from Collins's draught, did not contain " these 
papers," but only an abridgment. Finally, the 
editor concludes that it may be " fairly questioned" 
whether the transmission ever took place. How 
can this be ? The doubts as to the transmission, he 
has just told us, are removed by the testimony of 
Collins the transmitter and Leibniz the receiver. 
The answer is, that the editor himself immediately 
proceeds to prove, both from the transmitter and 
the receiver, that what was transmitted was not the 
"collectio" of the Commercium Epistolicuin, but 
an abridgment. We cannot but suppose that the 
editor imagined the existence of the abridgment to 
be known, and having no idea that he himself was 
the first to draw it from its retirement, considered 
the "collectio" and its abridgment as convertible 
documents, and the information they conveyed as 
substantially the same. We, however, had never 
found a trace, in any writing upon the subject, of 
any mention of the smaller document ; and it is 
clear that the omission of the example of Newton's 
method, poor as the pretext against Leibniz would 
have been even if it had been there, destroys the 
pretext 1 altogether. 

1 If the editor meant that Newton's letter is substantially the same 
as to the real information it could give, whether with or without the 
example of the method of tangents, we not only agree with him as to 
the fact, but should have agreed, if he had asserted that a sheet of 



CALCULUS 8 1 

We shall join the complete elucidation of the last 
assertion with the establishment of another state- 
ment of Leibniz, namely, that the Committee of the 
Royal Society had been guilty of gross suppression 
of facts unfavourable to themselves, and within 
their own knowledge. We, who have not right of 
access to the archives of the Society, can of course 
only further show this (beyond what is shown by 
the suppression of the abridgment) by proving 
suppression of documents which had been already 
printed ; that is, by showing that the Committee 
either entirely suppressed what they ought to have 
brought forward, or contented themselves with 
reference where they ought to have produced 
extracts. We shall confine ourselves to what is 
immediately connected with the unlucky fragment of 
Newton's letter, which was never sent. 

First, the Committee refer to the method which 
Sluse had given for drawing tangents, 1 and which 
was printed in the Phil. Trans, as early as 1673. 
They give Oldenburg's communication to Sluse of 
Newton's letter, in which Sluse learns that what he 
had communicated was already known to Newton. 2 
They also give Newton's admission 3 that Sluse not 



blank paper (after what Sluse had already published) would have done 
just as well. But our reader must remember that it is not the rational 
interpretation of the letter which is the matter in discussion, but the 
interpretation of the Royal Society's Committee. 

1 Comm. Epist., p. 106 ; we quote the second edition as more 
accessible than the first. 

2 Ibid., p. 1 06. 3 Ibid., p. 107. 

6 



82 FLU XI ON AL 

only had probably an actual priority of discovery, 
but that, whether or no, he was the first promulgator. 
All this, so far as it goes, is fair, though it militates 
strongly against the conclusion of their report with 
respect to Leibniz. But it was not fair to suppress 
all account of the manner in which this celebrated 
letter of Newton was drawn out. When they state 
that Collins had been for four years circulating the 
letter in which the method of fluxions was sufficiently 
described to any intelligent person, they suppress 
two facts : first, that the letter itself was in con- 
sequence of Newton's learning that Sluse had a 
method of tangents ; secondly, that it revealed no 
more than Sluse had done. In the third volume 
(1699) of Wallis's works 1 is a fragment of a letter 
from Collins to Newton, of June the i8th, 1673, m 
which he reminds Newton, for what purpose does 
not appear, of his having communicated the fact of 
Sluse's discovery, and having received an answer 
(which was no doubt the letter) for the purpose of 
transmission to Sluse. Again, this method of Sluse 
is never allowed to appear ; reference is made to 
the Philosophical Transactions, though many things 
which had been printed before appear in the Com- 
mercium Epistolicum when they serve the right 
purpose. 

To show what we assert we shall compare the 
two methods. 

1 In Latin p. 617, in English p. 636. 



CALCULUS 83 

The paragraph of Newton's letter, from the 
original in the Macclesfield collection, is as follows 
(December the loth, 1672): 

" I am heartily glad at the acceptance, which our 
rev. friend Dr. Barrow's Lectures find with foreign 
mathematicians, and it pleased me not a little to 
understand that they l are fallen into the same 
method of drawing tangents with me (eandem . . . 
ducendi tangentes methodum). What I guess their 
method to be you will apprehend by this example. 
Suppose CB, applied to AB in any given angle, be 
terminated at any curved line AC, and calling AB x 
and BC 'y, let the relation between x and y be ex- 
pressed by any equation as 

^3 _ 2x*y 4. bx* - b*x + by* y* = o, 

whereby this curve is determined. To draw the 
tangent CD, the rule is this. Multiply the terms of 
the equation by any arithmetical progression accord- 
ing to the dimensions of y t suppose thus 

x* - 2x*y + bx* - b*x+ by* -y* . 
01 0023* 

also according to the dimensions of x y suppose thus 

x* - 2x*y + bx* - b*x+ by* -y* . 
32 2 100 

1 There is no end of the curiosities of this Committee. After their 
Latin for the word "they," they inserted in brackets (Sluse and 
Gregory), the latter not being a foreigner. If they had given the 
letter of Collins, just referred to, of June the i8th, 1673, the reader 
would have known that Sluse and Ricci are the parties understood. 



84 FLU XI ON AL 

The first product shall be the numerator, and the 
last divided by x the denominator of a fraction, which 
expresseth the length of BD y to whose end D the 
tangent CD must be drawn. The length. of BD 
therefore is 

2x L y + 2by L 3?> 3 divided by 3*2 <\xy + 2bx - b\ " 

Not many days afterwards (January the I7th, 
X 673) Sluse wrote an account of the method which 
he had previously signified to Collins, for the Royal 
Society, by whom it was printed. 1 The rule is pre- 
cisely that of Newton, the exponents are multipliers, 
without any subsequent reduction of the exponents 
(which prevents both explanations 2 from describing 
the method of fluxions to any intelligent person), 
and instead of dividing by x, Sluse changes one x 
into BD y and then equates the two results. To 
have given this would have shown the world that 
the grand communication which was asserted to 
have been sent to Leibniz in June 1676 might have 
been seen in print, and learned from Sluse, at any 
time in several previous years : accordingly, it was 
buried under a reference. But, worse than this, the 
Committee had evidence before them that it had been 

1 Phil. Trans., No. 90 ; also Lowthorp, vol. i, pp. 18-20. [J. Low- 
thorp abridged the Philosophical Transactions to the end of 1706 into 
three volumes.] 

2 If Newton's example had been sent to Leibniz, and the latter had 
not known the method already from Sluse, the direction to multiply by 
the terms of any arithmetical progression (a mere slip of the pen on 
Newton's part, properly preserved by the Latin translator) might have 
puzzled any " idoneus harum rerum cognitor. '' 



CALCULUS 85 

so seen by Leibniz, and this evidence they deliberately 
mutilated. 

On March the 5th, 1677, Collins wrote to Newton, 
giving him certain extracts from a letter of Leibniz, 
dated November the i8th, 1676. This was printed 
(1699) in the third volume of Wallis. Leibniz had 
seen Hudde at Amsterdam, and had found that 
Hudde was in possession of even more than Sluse ; 
and this he states, referring to the published method 
of Sluse, as known to himself. He gives also an 
example, or rather its result, not as showing the 
method, which was known, but in order further to 
show how to eliminate one of the co-ordinates from 
the result. The Committee omit this example, with- 
out any notice of omission, though they give the 
passages between which it lies. 

We are obliged frequently to recur to the assertion 
of the Committee that Newton's example, which we 
have translated, was description enough of the method 
of fluxions for any intelligent person. That this, 
which we shall believe to be the most reckless 
assertion ever made on a mathematical subject, until 
some one produces its match, was solemnly put 
forward by the Committee, is not in our day excuse 
enough for dwelling upon it. But the sufficient 
excuse is that writers of note, upon the Newtonian 
side of the question, still quote the assertion with 
approbation. In Sir David Brewster's Life of Newton, 
for instance, the whole Report of the Committee is 



86 FLUXIONAL 

printed, and a virtual adhesion given to it. On the 
other hand, the defenders of Leibniz, most of whom 
are not English, prefer to establish his rights inde- 
pendently, and evade an encounter which is rendered 
repulsive by its dealing more with the comparison of 
old letters than with mathematical explanations. 

Some little question has arisen as to the position 
in which the Royal Society stands in this matter. 
According to Leibniz, Chamberlayne wrote to him 
to the effect that the Royal Society did not wish the 
report to pass for a decision of its own. Mr Weld l 
found the minute in question (passed May the 2oth, 
1714), in which it is stated that "if any person had 
any material objection against the Commercium^ or 
the Report of the Committee, it might be recon- 
sidered at any time." This Mr Weld considers as 
an adoption of the Report of the Committee : in 
which we cannot join, though we admit that it throws 
the question open, which as long as Chamberlayne's 
communication stood unanswered, was settled : and 
enables us to infer adoption from previous acts. In 
all probability he informed Leibniz that the Report 
of the Committee was not to pass for a decision, 
meaning the stress to lie there, and stating why : 
and this would be correct, for a question which may 
be reconsidered at any time is not decided, except 
in a technical sense. And very likely he added * c of 
the Society " : for it was the full impression of the 

1 Phil. Mag., 1847 5 Hist. Roy. Soc. t vol. i, p. 415, 



CALCULUS 87 

time that the Society was one with its Committee. 
There can be no doubt that the hearty adherence 
given by the Society to the conclusions, the circula- 
tion of the Commercium Epistolicum throughout 
Europe, the admission of Keill's " recensio " into the 
Transactions, the sanction of the reprint ten years 
after, and the obstinate determination, which lasts 
down to our own time, not to confess one atom of 
the error nor right one atom of the wrong, amount 
to an adoption which could not be more than ade- 
quately represented by any quantity of minutes. 

It seems the fate of this controversy that whatever 
the English partisans of the eighteenth century 
supposed to have happened between the two parties 
really happened the other way, the places of the 
parties being changed, and to no effect upon the 
question. Much stress was laid on Collins trans- 
mitting from Newton to Leibniz an example of the 
method of tangents : it appears that the example 
was not sent, that the abridgment sent did not con- 
tain it ; but it appears that Collins really forwarded 
a result from Leibniz to Newton, which was the only 
one that passed between them. Not that this gave 
Newton any information ; but neither would Newton's 
example, if sent, have given any to Leibniz, after 
Sluse's publication and Hudde's oral communication. 
Again, it was frequently stated that the differential 
calculus was only the method of fluxions with the 
notation changed. Now the fact is, that as to every- 



88 FLUXION AL 

thing elementary that was published with demonstra- 
tion under the name of fluxions , up to the year 1704 
(when Newton himself first published anything under 
that name) the method of fluxions was nothing but 
the differential calculus with the notation changed. 
We know that Newtek's letters did not treat of 
fluxions, nor contain anything from which the writer 
of a system could draw his materials. No one 
ventured to print an elementary treatise in England 
until the seed had grown into a strong plant under 
the care of Leibniz, the Bernoullis, and so on. When 
de 1'Hopital, in 1696, published at Paris a treatise so 
systematic, and so much resembling one of modern 
times, that it might be used even now, he could find 
nothing English to quote, except a slight treatise 
of Craig on quadratures, published in 1693. He 
mentions all that he could of Newton, and even says 
of the Principia that it was full of the calculus ', which 
is not true ; he should have said it was full x of the 
principles on which the calculus is founded, and of 
application of them in which the reader (whatever 
might have been the case with the author) is directed 
by thought without calculus. But the distinction is 
one which was not then appreciated : in fact it needed 
the calculus, such as it became, to show it. It must 
be remembered that, when de 1'Hopital wrote (for 

1 "C'est encore une justice due au scavant M. Newton, et que M. 
Leibnis luy a rendue luy-meme : Qu'il avoit aussi trouve quelque 
chose de semblable au calcul dififerentiel, comme il paroit par 1'excellent 
Livre intitule . . . Principia . . . lequel est presque tout de ce calcul." 
Preface. 



CALCULUS 89 

he could then have seen the first volume of Wallis), 
there neither was, nor had been, one word of accusa- 
tion or of national reflection, to create any bias for 
or against any one. The first thing of this kind took 
place in 1695, when Wallis, in the preface to the 
first volume of his collected works, not only claimed 
the differential calculus as derived from the method 
of fluxions, but (in ignorance, as he afterwards knew) 
grounded the claim upon the two celebrated letters 
of' Newton to Oldenburg, of which little notice is 
taken here, because not even the Committee of the 
Royal Society venture a mention of them in their 
report, as any ground of tonfirmation against Leibniz. 
The note of alarm thus sounded, our countrymen 
began to write upon fluxions. Some writings are 
so advanced that they do not define their terms : 
from these therefore we cannot tell whether x means 
the velocity with which x changes, or an infinitely 
small increment of x. Such (at least so we suppose 
from the enlarged second edition of 1718) was the 
little tract of Craig, to which de PHopital refers, as 
we have seen : and such were Dr Cheyne's tract on 
fluents (1703) and De Moivre's answer to it (1704). 
Newton himself, in the Principia, was not a fluxionist, 
but a differentialist. Though imagining quantity 
generated by motion or flux (in the celebrated Lemma 
in which he gives a brief description), he calculates, 
not by velocities but by moments, or " momentaneous 
increments and decrements," which are infinitely 



90 FLUX ION AL 

small quantities, for "moments, so soon as they 
become finite magnitudes, cease to be moments." 
Of Wallis we shall presently speak. De Moivre 1 
represents fluxions as momentaneous increments or 
decrements. And the only elementary writers, 
Harris 2 and Hayes, 3 are strictly writers on the 
differential calculus, as opposed to fluxions, in every 
thing but using x instead of dx. Harris says, " By 
the Doctrine of Fluxions we are to understand the 
Arithmetick of the Infinitely small Increments or 
Decrements ..." These, he says, Newton pro- 
perly calls fluxions ; and he proceeds to show 
that his own ideas are not very clear, by asserting 
that "'Tis much more natural to conceive the 
Infinitely small Increments or Decrements of the 
variable and Flowing Quantities, under the notion 
of Fluxions (that is, according to him, of infinitely 
small increments or decrements) than under that of 
Moments or Infinitely small Differences, as Leibnitz 
. . . chose rather to take them." And then he 

1 Phil. Trans., 1695, No. 216. 

2 The first elementary work on fluxions in England is a tract of 
twenty-two pages in A New short treatise of Algebra. . . . Together 
with a specimen of the Nature and Algorithm of Fluxions. By John 
Harris, M.A., London, 1702, octavo (small). 

3 A Treatise of fluxions ; or an Introduction to Mathematical 
Philosophy. Containing a full Explication of that Method by which 
the Most Celebrated Geometers of the present Age have made such vast 
Advances in Mechanical Philosophy. A Work very Useful for those 
that would know how to apply Mathematicks to Nature. By Charles 
Hayes, Gent., London, folio, 1704. This work, which has had very 
little notice (Hayes, born 1678, died 1760, wrote many works, but 
never set his name to any but this), is a very full treatise, nearly three 
times as large as that of de 1'Hopital, having 315 closely printed folio 
pages on fluxions, besides an introduction on conic sections. 



CALCULUS 91 

proceeds to speak of velocities : in fact he jumbles 
de PHopital, whom he did understand, with Wallis, 
whom he did not. Hayes, a much clearer writer, 
begins thus: "Magnitude is divisible in infinitum 
. . . the infinitely little Increment or Decrement 
is called the Fluxion of that Magnitude. . . . 
Now those infinitely little Parts being extended, are 
again infinitely Divisible ; and these infinitely little 
Parts of an Infinitely little Part of a given Quantity, 
are by Geometers called Infinitesimce Infinitesi- 
marum or Fluxions of Fluxions. " And again * 
". . . suppose half the infinitely little increment 
of X to be \ x, and half the Fluxion or infinitely 
little Increment of Z to be \ z." And thus it 
appears that all explanation that was tendered in 
print, up to the year 1704, whether by Newton him- 
self, or by any of his followers (except only Wallis, 
as presently mentioned), was Leibnitian in principle. 
But when Newton, in 1704, published the treatise 
on the Quadrature of Curves which he had written 
before Leibniz communicated the differential cal- 
culus to him, he starts with nothing but the notion 
of quantity increasing or diminishing with velocity, 
and this velocity or celerity is the fluxion. And in 
the Introduction, written at the time of publication, 
he says, " I do not consider mathematical quantities 
as consisting of the smallest possible parts (paries 
quam minima) but as described by continuous 
1 ibid,, p. 5. 



92 FLU XI ON AL 

motion." This is the first public declaration of the 
meaning of a " fluxion " that was made by the author 
of the word, in his own name. 

It may appear strange that we defer till now to 
mention a very fluxional view of fluxions which 
appeared as early as 1693. But we wish to give pro- 
minence to what is really Newton's first publication 
on the subject, though it has received but little notice 
until lately. The second volume of Wallis's works, 
containing the Algebra, in which the matter spoken 
of occurs, was published in 1693, the first in 1695, 
but false title-pages 1 make them appear as of 1699. 
Again, those who look at the preface to the first 
volume see that Wallis excuses himself from men- 
tioning the differential calculus, because it was 
nothing but the fluxions which Newton, he says, 
had communicated to Leibniz in the celebrated 
Oldenburg letters, and which he (Wallis) had de- 
scribed, from those letters, nearly word for word, in 
his Algebra. No one of later times would thereupon 
refer to this Algebra for information ; since they 
would know that nothing upon fluxions could be 
given word for word, but only letter for letter. For 
all that is said upon fluxions, in those celebrated 

1 The Comrn. Epist, says that two volumes appeared in 1695 5 prob- 
ably the second volume got a new title-page in that year. The third 
volume was published in 1699, and then the first volume certainly got 
a title-page of that date. This vile practice of altering title-pages will 
be put down by the scorn of all honest men, so soon as its tendencies 
are seen. A person who reads Wallis's collected works under the date 
of 1699 easily convicts the author, as honest a man as ever lived, of 
the grossest unfairness, upon his own testimony. 

. 



CALCULUS 93 

epistles, is, as is well known, in two anagrams, one 
of which is 

6a 2c d ae 136 2f f\ 3! gn 40 4q 2r 45 Qt I2v x, 

the information given being that whoever can form 
a certain sentence properly out of six a's, two c's, a 
</, and so on, will see as much as one sentence can 
show about Newton's mode of proceeding. No one 
but Raphson 1 imagined that any human being 
derived any information from this ; and probably 
therefore few would be induced by Wallis's preface 
to consult the work. They would not know (and 
we shall see that Wallis himself could hardly have 
anything to make him remember) that Wallis had 
been in communication with Newton, had obtained 
not only the key of the anagrams but their meaning, 
and had added a brief account of fluxions, with an 
extract from what Newton afterwards published in 
the treatise of 1704, besides other matter expressly 
obtained from Newton in explanation of the second 

1 The sentence was " Data yEquatione quotcunque, fluentes quanti- 
tates involvente, fluxiones invenire, et vice versa," given any equation 
involving fluent quantities, to find the fluxions, and vice versa. Many 
writers have called this a cipher , which it is not : a cipher gives, in some 
way, the order of the letters as well as substitutes for the letters them- 
selves. Raphson declared that Leibniz had first deciphered the anagram, 
and then detected the meaning of the word fluxion, after which he 
forged a resemblance. But Raphson was the unscrupulous man of the 
time, if any one could deserve that name. Newton stated distinctly 
that Leibniz sent him the details of a Method which was his own in all 
respects except language. Raphson says (Hist, of Fluxions, p. I ) that 
Leibniz " writ in answer that he had found out a Method not unlike it, 
as Sir Isaac himself had hinted, page 253, Princip. ..." The im- 
pudence of this paraphrase is one of the minor gems of the controversy : 
and we could rub it brighter if we had room. 



94 FLU XI ON AL 

anagram. The reader cannot detect the new infor- 
mation, except in that additional part which explains 
the second anagram : all that can be said of the rest 
is, that to a reader who compares chapters 91 and 

95 there are a couple of sentences which would 
perhaps puzzle a person who did not know that a 
new source of information was referred to in these 
sentences. The reviewer of Wallis in the Acta 
Eruditorum, in complaining of the suppression of 
the differential calculus, hit the real reason, namely, 
Wallis's ignorance of a good deal of what had been 
done abroad : and Wallis, who wrote to Leibniz the 
day after he saw this review, acknowledges that he 
knew nothing of what Leibniz had written, except 
two slight and old papers, and had never heard the 
name of the differential l , calculus until the preface 
was in the press, when a friend mentioned with 
indignation that Newton's fluxions were current in 
Belgium under that name. Then, and probably 
without consulting what he had written, Wallis 
added the sentence we have mentioned to his pre- 
face. In the third volume, Wallis printed all his 
correspondence with Leibniz, and all the correspond- 
ence with others on the subject which he could 

1 Nevertheless, Leibniz and the differential method are mentioned in 
the second volume, that is, in the account of fluxions on which we are 
writing ; but (as discovered by Professor Rigaud) Wallis's copy pre- 
served in the Savilian Library has manuscript additions which note 
and explain this forgetfulness. It appears that the whole communica- 
tion is Newton's, and is inserted in Newton's words : an author can 
hardly remember another person's writing, to which he gives admission, 
as if it were his own. 



CALCULUS 95 

collect, and mentions fluxions and the differential 
calculus as two distinct things in the preface. What 
we have here to do with, however, is the nature of 
the publication of fluxions which was made in 1693. 
We now come to the independent proofs of the 
separate invention of Leibniz, as contained in his 
recently published papers. Preliminary, however, 
to these, we may notice one which was published 
in 1671, and which shows the way in which the 
current of his ideas was setting. Dr Hales, in his 
Analysis Fluxionum^ says that Leibniz had given 
no obscure germs of his differential method in his 
Theoria Notionum Abstractarum^ dedicated to the 
French Academy in 1671 : and Dr Hutton 2 refers 
to this theory of abstract notions. Both are wrong 
in the name ; for the paper which Leibniz dedicated 
to the Academy in that year is Theoria Motus 
Abstradi^ This paper is certainly a witness to 
character ; throughout it there occurs a frequent ap- 
proximation to the idea of infinitely small quantities 
having ratio to each other, but not to finite quantities. 
One extract (translated) will serve as a specimen : 
"A point is not that which has no parts, nor of 
which part is not considered ; but which has no 
extension, or whose parts are indistant, whose 
magnitude is inconsiderable, inassignable, less than 
any which has ratio (except an infinitely small one) 

1 London, 1800, 4to. 2 Math. Diet., Art. "Fluxions." 

3 Op. Leibn., vol. ii, part ii, p. 35. 



96 FLUXIONAL 

to a sensible quantity, less than can be given ; and 
this is the foundation of Cavalieri's method, by 
which its truth is evidently demonstrated, namely, 
to suppose certain rudiments, so to speak, or 
beginnings of lines and figures, less than any 
assignable." So that, in 1671, it was working in 
Leibniz's mind that in the doctrine of infinitely 
small quantities lay the true foundation of that 
approach to the differential calculus which Cavalieri 
presented. 1 

Dr Gerhardt, the editor of the correspondence 
already referred to, found among the papers of 
Leibniz preserved in the Royal Library at Hanover 
various original draughts, containing problems in 
which both the differential and integral calculus are 
employed, and has published them in a separate 
tract. 2 The editor dwells so much on the matter 

1 [In his paper " On the Early History of Infinitesimals in England," 
published in the Philosophical Magazine for November, 1852, and 
mentioned in the above Preface, De Morgan developed his thesis that 
Fluxions at first (up to 1704) had an infinitesimal basis. This thesis 
is supported by Newton's own early papers published by Rigaud (see 
the Appendix to this Essay), by Newton's Method of Fluxions^ by the 
first edition of the Principia^ as compared with the second, by Newton's 
De Quadratura Curvarum, by works of John Craig, De Moivre, 
Halley, Cotes, Cheyne, and Fatio de Duillier, besides the books by 
Harris and Hayes mentioned in the text above.] 

2 Die Entdeckung der Differentialrechnung durch Leibniz. Von 
Dr C. J. Gerhardt. Quarto. No date nor place ; preface dated 
"Salzwedel, im Januar 1848:" [Accordingly we must conclude that 
Gerhardt's tract, in the form in which it often exists, under the title 
Die Entdeckung der Differentialrechnung durch Leibniz, mit Benutzung 
der Leibnizischen Manuscripte auf der Koniglichen Bibliothek zu 
Hannover, Halle, 1848, has a different title-page from the one seen by 
De Morgan, which was probably the extract it was from the Programm 
of the school at Salzwedel. Two years earlier, Gerhardt had published 
a very important manuscript of Leibniz's under the title Historia et 



CALCULUS 97 

and consequences of the manuscripts, that he forgets 
to satisfy curiosity as to their form, the circumstances 
of the discovery, and so on : they ought to be re- 
published with proper facsimiles of the handwriting. 
Not that we at all doubt them ; for, independently 
of the full credit due to Dr Gerhardt, we do not 
believe that human ingenuity could have forged so 
genuine a mess of spoiled exercises. We cannot 
attempt a full account of them ; but this is of little 
consequence, since they will of necessity be fully 
described in more appropriate quarters, so soon as 
they are better known to exist. 

These papers are seven in number, dated l Novem- 
ber the nth, 2 ist, 22nd, 1675, June the 26th, July, 
November, 1676, and one without a date. They 
are not descriptions of the principles, but study 
exercises 2 in the use, of both differential and 
integral calculus. Except out of the problems 
themselves, we learn nothing of the extent to which 

Origo Calculi Differentialis a G. G. Leibnitio conscripta. Zur zweiten 
Sacularfeier des Leibnizischen Geburtstages aus den Handschriften der 
Koniglichen Bibliothek zu Hannover, Hanover, 1846. Further infor- 
mation about Gerhardt's publications on Leibniz is given in the Appendix 
to this Essay.] 

1 The editor tells us that some one had been meddling with the date 
of the first paper, and had turned the 5 of 1675 into a 3. Leibniz, 
speaking from recollection in 1714, says that his discovery was made, 
as near as he could remember, in 1676. 

2 Professor Rigaud has published, from the Macclesfield collection, 
a manuscript draught of Newton, of November I3th, 1665. But this 
is formally written out, proposition, resolution, and demonstration. An 
earlier essay, of May 2Oth, is not given, which is to be regretted. But 
from the description we see that Newton used the peculiar notation of 
fluxions in May, and abandoned it in November. His formal pro- 
position uses distinct letters for fluxions of other letters. In Leibniz, 
everything in language is progression : no step gained is ever abandoned. 

7 



98 FLUXIONAL 

the structural operations were in the power of the 
writer. We find strange mistakes of operation, 
such as beginners now make : and it is clear that 
the writer is trying to push his calculus forward 
into discovery of new results in geometry before 
he has either sounded its extent or settled its 
language. In the first of the papers he enters 
(among other things) upon the examination whether 

dx.dy is the same with d(xy) and d(-) with : at 

\y' dy 

first he inclines to the affirmative, but in the next 
page decides in the negative. This will not surprise 
the mathematician of our day, who remembers that 
these are the private memoranda of a discoverer in 
the very process of investigation : but nevertheless 
he will look to find some particular cause of con- 
fusion of ideas at the outset. We suspect it to be 
as follows. Leibniz frequently supposes dx=i, or 
dy = i : that is, he establishes two kinds of units, 
without any symbolic distinction, the unit of finite, 
and the unit of infinitely small, quantity. In integra- 
tion, he halts between the use of I y and oilydx, 

as the expression of an integral. There are also 
obvious slips of the pen, and operations set down 
for thought, which lead to nothing. 

The first problems treated are in the direct and 
inverse method of tangents, in which the method of 
Sluse is referred to by name. The two following 



CALCULUS 99 

extracts, in which the Latin is literally translated, 
of the date of November the nth, 1675, will be as 
much as we can afford room for. They give two 
of the earliest problems solved, the first and third. 

The problem is to find a curve in which the 
subnormal (w) is reciprocally proportional to the 
ordinate. Putting z instead of dx, Leibniz proceeds 
thus : " It appears from what I have shown else- 



f '- V V 

where, that //=<-, or w % = -?-" The d in the 

denominator is the symbol of differentiation of the 
whole : it frequently happens in the first papers. 
1 ' But from the quadrature of the triangle this is 
y." We should write ydy, but Leibniz tacitly makes 
dy=i t and he afterwards says he has here thought 
of making an abscissa of the ordinate. " Now from 

the hypothesis w = - . . . whence =i/, and #=?-. 
y y b 

But [z=x. Therefore;^ $L But &m* by the 
} J b J b $da 

i/ 3 
quadrature of the parabola ; therefore x -^. " This 

a is not of easy explanation. It is afterwards given 
to make the subnormal reciprocally proportional to 

a 2 [ v 2 

the abscissa. ''Here ; = ; but \w = y whence 

X J 2 

y=/y/(2jWj or f j(2\ ( \ t Now \w cannot be found 

except by the help of the logarithmic curve. There- 
fore the figure required is that in which the ordinates 



ioo FLU XI ON AL 

are in the subduplicate ratio of the logarithms of 
the abscissae." 

If the Committee of the Royal Society had had 
these papers before them, they would have justly 
contended that the calculus of Leibniz, of which 
the principles and algorithm were settled, received 
a great accession of working power when Newton 
communicated the binomial theorem in the " epistola 
prior" to Oldenburg; which "epistola prior," by 
the rule of contraries already instanced, has been 
much less insisted on than the "epistola posterior" 
with its anagrams. 

On August the 27th, 1676, Leibniz acknowledged 
the receipt of this communication ; and his paper of 
November 1676 shows that Newton's algebra had 
borne its fruit. Previously to this date, we cannot 
find any fractional power differentiated except the 
square root. In pure algebraical discovery, Leibniz 
does not rank with Newton : and he always acknow- 
ledged that in the method of series (the phrase by 
which the algebraical improvements of the day 
were designated) Newton was before him and 
beyond him. We have every right to presume, 
from his conduct, and from the manner in which 
all subsequent disclosures establish his veracity, 
that had he lived to publish his own Commercium 
Epistolicum, he would have pointed out the difference 
between the invention of the differential calculus 
and the improvement of the algebra which gives it 



CALCULUS',: v\ vi' 10 1 



language and guides its nteehamsiJV afl,d 
illustrated from his own papers the power which 
Newton's improvements in algebra enabled him to 
add to his existing differential calculus. We believe 
(with John Bernoulli) that Newton might have made 
a similar acknowledgment to Leibniz as to the 
idea of a fixed and uniform method of denoting 
operations in the fluxions of which he had already 
possession. 

We have not alluded to the faults on the other 
side of the controversy, partly because they were 
much less gross in character, partly because they 
have been amply insisted on in this country. Nor 
have we, indeed, in this paper, given anything like 
a history of the unfair proceedings in this country, 
but have, for the most part, confined ourselves to 
points which are particularly effected by recent 
information. Whether there be anything still to 
be drawn out must be matter of conjecture, and will 
be matter of suspicion, until we can be well assured 
that all the private depositories of information have 

been exhausted. 

A. DE MORGAN. 

UNIVERSITY COLLEGE, LONDON, 
October 2, 1851. 



APPENDIX 1 ON THE MANUSCRIPTS AND 
PUBLICATIONS OF NEWTON AND 
LEIBNIZ 

IN this Appendix is given, in chronological order, a list of 
the manuscripts and other works of Newton and Leibniz 
relating to the discovery and communication of the in- 
finitesimal calculus and publications dealing with the con- 
troversy that subsequently took place between them and 
their respective supporters. References have been given on 
each point, and it is hoped that both the list and the refer- 
ences are complete in the sense that nothing important has 
been omitted. It is rather remarkable that nothing has 
hitherto been done in this direction, for it would seem to be 
very important that regard be paid to Newton's early manu- 
scripts. Many important manuscripts of Leibniz's which 
relate to his discovery have been published by Gerhardt, 
and commented on by Gerhardt and others ; but only a few 
of Newton's manuscripts have as yet been published, and 
these publications by Raphson in 1715 and Rigaud in 
1838 have apparently been completely ignored by all the 
modern historians of mathematics. After a list of works 
consulted, together with some brief comments on some of 
them and the abbreviations by which their titles are cited in 
this Appendix, are given : (i) References on the history of 
infinitesimal ideas before Newton and Leibniz ; (2) Refer- 
ences to Newton's fluxional manuscripts and publications ; 
(3) References to Leibniz's manuscripts and publications on 

1 The whole of this Appendix is by the Editor of the present collec- 
tion of Essays by De Morgan, and is supplementary to the second Essay. 

102 



NEWTON AND LEIBNIZ 103 

the infinitesimal calculus; and (4) Brief references to the 
literature of the controversy about the invention of the 
calculus. It is hoped that this Appendix will be gradually 
made complete, either in future editions of the present book 
or as a separate publication. 

WORKS CONSULTED, WITH ABBREVIATIONS 

MORITZ CANTOR : Vorlesungen iiber Geschichte der Mathe- 
matik; vol. i (to A.D. 1200), 3rd ed., Leipsic, 1907; 
vol. ii (1200-1668), 2nd ed., Leipsic, 1900; vol. iii 
(1668-1758), 2nd ed., Leipsic, 1901 (contains an 
account of Leibniz's, but not of Newton's, manuscripts). 
Abbreviation : Cantor. 

KARL FINK : Geschichte der Elementar-Mathematik : trans- 
lated by W. W. Beman and D. E. Smith under the 
title A Brief History of Mathematics (Chicago, 3rd 
ed., 1910; pp. 168-172 contain a brief summary of 
the origin and discovery of the infinitesimal calculus). 

W. W. ROUSE BALL : A Short Account of the History of 
Mathematics^ London, 4th ed., 1908. In this work, 
a whole chapter (pp. 319-352) is devoted to "The Life 
and Works of Newton," in which Newton's early manu- 
scripts are referred to, but without references, and in 
this chapter the communications with Leibniz are dis- 
cussed; but the controversy is dealt with when an 
account of Leibniz's work is given (pp. 353-365), where 
Leibniz's manuscripts are hardly referred to, and he 
himself is treated with suspicion. 

JOSEPH RAPHSON : The History of Fluxions, shewing in a 
compendious manner the first rise of and various improve- 
ments made in that incomparable Method, London, 1715. 
A Latin translation was published at London in the 
same year (see G. J. Gray's work mentioned below, 
p. 54). Abbreviation : Raphson. 

STEPHEN PETER RIGAUD : Historical Essay on the First 



104 DISCOVERIES OF 

Publication of Sir Isaac Newton's Principia, Oxford, 
1838. In this book, the pages of the text of the first 
part and those of the Appendix are numbered separately. 
In the Appendix are given some of Newton's early 
manuscripts on fluxions from the collection of Lord 
Macclesfield. Abbreviation : Rigaud. 

STEPHEN PETER RIGAUD : (though Rigaud's name does not 
appear on the title-page, it was he who made this 
collection) Correspondence of Scientific Men of the Seven- 
teenth Century ', including Letters of Barrow, Flamsteed, 
Wallis, and Newton, printed from the Originals in the 
Collection of the Right Honourable the Earl of Maccles- 
field. Two volumes (posthumous, edited by Rigaud's 
son, Stephen Jordan Rigaud), Oxford, 1841. Table 
of contents and index added by De Morgan (see Mrs 
De Morgan's Memoir, p. 414) in 1862. Fifty-nine 
letters from and to Newton, beginning in 1669, were 
published on pp. 281-437 of vol. ii. Abbreviation : 
Mace. Corr. 

J. EDLESTON : Correspondence of Sir Isaac Newton and 
Professor Cotes, including Letters of Other Eminent 
Men, now first published from the originals in the 
Library of Trinity College, Cambridge', together with 
an Appendix containing other unpublished Letters and 
Papers by Newton ; with Notes, Synoptical View of the 
Philosopher's Life, and a Variety of Details illustrative 
of his History, London and Cambridge, 1850. Ab- 
breviation : Edleston. 

Sir DAVID BREWSTER : Memoirs of the Life, Writings, and 
Discoveries of Sir Isaac Newton, 2 vols., Edinburgh, 
1855. A second edition apparently unaltered, even 
as to the mistakes was published at Edinburgh, 1860. 
Abbreviation (to the 1855 edition) : Brewster. 

A Catalogue of the Portsmouth Collection of Books and 
Papers, written by or belonging to Sir Isaac Newton, 
the Scientific Portion of which has been presented by the 



NEWTON AND LEIBNIZ 105 

Earl of Portsmouth to the University of Cambridge. 
This catalogue was drawn up by the Syndicate 
appointed the 6th of November, 1872, and the Preface 
is signed by H. R. Luard, G. G. Stokes, J. C. Adams, 
and G. D. Liveing, and published at Cambridge in 
1888. Abbreviation: Portsmouth Catalogue. 

G. J. GRAY : A Bibliography of the Works of Sir Isaac 
Newton together with a List of Books illustrating his 
Works. Second edition, Cambridge, 1907. The first 
(and less full) edition was privately printed in 1888. 
Abbreviation : Gray. 

FERDINAND ROSENBERGER : Isaac Newton und seine physika- 
lischen Principien. Ein Hauptstiick aus der Entwicke- 
lungsgeschichte der modernen Physik. Leipsic, 1895. 
Abbreviation : Rosenberger. 

C. I. GERHARDT (herausgegeben von) : Historia et Origo 
Calculi Differential a G. G. Leibnitio conscripta. Zur 
zweiten Sdcularfeier des Leibnizischen Geburtstages aus 
den Handschriften der Koniglichen Bibliothek zu Hann- 
over > Hanover, 1846. Abbreviation : G. 1846. 

C. J. GERHARDT : Die Entdeckung der Differentialrechnung 
durch Leibniz, mit Benutzung der Leibnizischen Manu- 
scripte auf der Koniglichen Bibliothek zu Hannover, 
Halle, 1848. Abbreviation: G. 1848. 

C. I. GERHARDT : Die Geschichte der hoheren Analysis. 
Erste Abtheilung [the only one which appeared] ; Die 
Entdeckung der hoheren Analysis, Halle, 1855. Ab- 
breviation : G. 1855. 

HERMANN WEISSENBORN : Die Principien der hoheren 
Analysis in ihrer Entwicklung von Leibniz bis auf 
Lagrange, als ein historisch-kritischer Beitrag zur Ge- 
schichte der Mathematik dargestellt, Halle, 1856. Ab- 
breviation : W. 1856. A further contribution of 
Weissenborn's is dealt with below. 

Die philosophischen Schriften von G. W. Leibniz, herausge- 
geben von C. J. Gerhardt, 7 vols., Berlin, 1875-90. 



106 DISCOVERIES OF 

Leibnizens mathematische Schriften, herausgegeben von C. J. 
Gerhardt, 7 vols., Berlin and Halle, 1849-1863. The 
contents of these volumes are described in note 3 on 
pp. 71-72. 

Der Brief wechsel von Gottfried Wilhelm Leibniz mit Mathe- 
matikern, Herausgegeben von C. I. Gerhardt, vol. i, 
Berlin, 1899. Leibniz's manuscripts of October, 1675, 
are dealt with on pp. xii-xiv, and those of November 
1675 an d July 1676 on pp. xiv-xv. Leibniz's relations 
with Tschirnhaus are dealt with on pp. xvii-xviii. Cf. 
note i on p. 79. The volume contains the correspond- 
ence between Leibniz and Oldenburg, Newton, Collins, 
and Conti, from 1670 to 1716, and also many supple- 
mentary documents. Among these are reproduced 
(pp. 147-167) some of Leibniz's manuscripts of 1675 
and (pp. 201-203) one of July 1676, which are referred 
to in the list given below. In the valuable introduction 
(pp. 3-38) to this correspondence, Leibniz's mathe- 
matical work from 1669 onwards is dealt with on pp. 5- 
38. Mention is made of Die philosophischen Schriften 
von G. W. Leibniz, but not of Leibnizens mathematische 
Schriften, nor of G. 1846, G. 1848, and G. 1855. 
Abbreviation : Bw. 1899. 

G. E. GUHRAUER : Gottfried Wilhelm Freiherr von Leibnitz : 
Eine Biographic, 2 volumes, Breslau, 1846. 

LON BRUNSCHVICG : Les Stapes de la Philosophic mathe- 
matique, Paris, 1912. The third book (pp. 153-249) 
contains: (i) A sketch of the growth of infinitesimal 
ideas from ancient times ; (2) Accounts of the dis- 
coveries of Leibniz and Newton in the domain of the 
infinitesimal analysis, in which, however, almost no 
account is taken of the manuscripts of Leibniz and 
none of those of Newton ; (3) An account of Leibniz's 
mathematical philosophy ; (4) A discussion of mathe- 
matical idealism and metaphysical realism. 



NEWTON AND LEIBNIZ 107 



I 

INFINITESIMAL IDEAS BEFORE THE TIME OF NEWTON 
AND LEIBNIZ 

Euclid, Archimedes, Pappus, Arabians, Middle Ages and 
Renascence, Valerius, Kepler, Cavalieri, Torricelli, Fermat, 
Roberval, Pascal, Wallis, Mercator, St Vincent, Descartes, 
Huygens, Sluse, Hudde, Barrow : Cantor^ vols. i to iii ; 
Brews ter, vol. ii, pp. 3-9 ; G. 1855, PP- 3~5 ; Rosenberger, 
pp. 424-430. Cf. also W. 1856, pp. 5-21 (Roberval and 
Barrow as precursors in the method of fluxions), and pp. 
70-84 (Gregorius a St. Vincent, Barrow, etc., as precursors 
of the differential calculus). 1 



II 

NEWTON'S MANUSCRIPTS AND PUBLICATIONS ON THE 
FLUXIONAL CALCULUS 

Newton's early study of mathematics at Cambridge in the 
years 1661-4 is dealt, with by Brewster (vol. i, pp. 21-23). 
Having read Descartes, Schooten, and Wallis, Newton (MS. 
note of 1699, given in ibid. t pp. 23-24) found the method 
of infinite series in 1664-5, and, in the summer of 1665, 
computed the area of the hyperbola at Boothby in Lincoln- 
shire to fifty-two places by this method. 2 Cf. Brewster, vol. 

1 The subsequent history of the principles of the calculuses with 
Maclaurin, the Bernoullis, Neuwentiit, Taylor, Euler, and Lagrange 
are also dealt with in the book mentioned. 

2 Among the "Portsmouth Papers " (Section I. " Early Papers by 
Newton") is this calculation of the area of the hyperbola {Portsmouth 
Catalogue, p. i). All the papers of Newton on fluxions in this collec- 
tion, many of which it would be important to publish, are catalogued 
on pp. 1-8 of this Catalogue. The " Early Papers" also include a little 
note on tangents, a tract written in 1666 on the solution of problems by 
motion, on the gravity of conies, and problems about curves. There 
are also manuscripts on " Elementary Mathematics," which include 
"Observations on the Algebra of Kinckhuysen" (ibid., p. 2); and 
several manuscripts on fluxions and their geometrical and mechanical 



1 08 DISCOVERIES OF 

ii, p. 10. See also G. 1855, pp. 90-92. In the following 
list of manuscripts use has been made of the "Synoptical 
Life " in JEdleston, pp. xxi-lviii. 

1665, May 2oth. Paper on fluxions in which the nota- 
tion of dots is used. It shows how to take the fluxion of 
an equation containing any number of variables. It is re- 
ferred to in a paper which seems to be part of a draft of 
Newton's observations on Leibniz's letter of April 9th, 1716. 
Rigaud, Appendix, p. 23; Raphson, p. 116; Brewster, 
vol. i, p. 25, vol. ii, p. 12. 

1665, Nov. 1 3th. Paper on fluxions and their applica- 
tions to tangents and curvature of curves. Rigaud, Ap- 
pendix, No. II, pp. 20-23 (printed at length); Raphson 
and Brewster, as before. Horsley, in vol. iv (p. 611) of 
his edition of Newton's collected works, gives this paper, 
from Raphson. It may be mentioned that, according to 
Lord Teignmouth's Life of Sir William Jones (p. 8), Newton 
saw the first sheets of Raphson's History and was much dis- 
satisfied with them. 

1666, May 1 6th. Another paper on fluxions (Rigaud) 
Appendix, p. 23; Brewster^ vol. i, p. 25, vol. ii, p. 12). 

1666, October. Small tract on fluxions and fluents, with 
their applications to a variety of problems on tangents, 
curvature, areas, lengths, and centres of gravity of curves. 
In this tract, Newton's previous method of taking fluxions 
is extended to surds. The area of a curve whose ordinate 
is y is denoted by a small square prefixed to the letter y. 
Cf. Rigaud^ Appendix, pp. 23-24; Brewster, vol. i, p. 25, 
vol. ii, pp. 12-14. These early papers are, as De Morgan 
remarked (see the second Essay), infinitesimal in character. 
They are all in the Macclesfield Collection (Brewster^ vol. i, 
p. 25, note 3). 

1666, November, Tract similar to the preceding, but 

applications, on the quadrature of curves, and on the fluxional contro- 
versy (ibid., pp. 2-8). One of the papers on fluxions was marked by 
Horsley as " very proper to be published " (ibid., p. 2). 



NEWTON AND LEIBNIZ 109 

apparently more comprehensive (Raphson, p. 116; Wilson's 
Appendix to Robins's Tracts, vol. ii, pp. 351-356). Nota- 
tion by dots for first and second fluxions. Basis of his 
larger tract of 1671. 

1669, July 3 1 st. De Analyst sent through Barrow to 
Collins. Cf. Brewster, vol. ii, pp. 14-15. 

This seems a good place to give references to places 
where Newton's tract, Analysis per aquationes numero 
terminorum infinitas, was published or discussed. It was 
first published at London in 1711, and reprinted in 1712 
(Gray, p. 59), in 1723 (ibid., p. 10), in 1744 (ibid., p. 2), 
and in vol. i (1779) of Horsley's edition of Newton's Opera. 
An English translation, with a commentary, was made by 
John Stewart in 1745 (ibid., p. 60). See also Cantor, 
vol. iii, pp. 67-75, 105-108, 156-160; Rosenberger, pp. 
431-434; R. Reiff, Gcschichte der unendlichen Reihen, 
Tubingen, 1889, pp. 20-38; and Brill in A. Brill and M. 
Noether's report : " Die Entwicklung der Theorie der 
algebraischen Functionen in alterer und neuerer Zeit," 
Jahresber. der Deutschen Mathcm.-Vereinigung, vol. iii, 1894, 
pp. 116-123. 

1669, December. Newton writes notes upon Kinckhuysen's 
Algebra sent by Collins through Barrow (Brewster, vol. i, 
pp. 68-69, vol. ii, pp. 15-16; G. 1855, P- 83). 

Newton's letters to Collins reporting progress on, and 
comments on, Kinckhuysen's Algebra are given in Mace. 
Corr., and are mentioned by Edleston under the dates of 
Jan. 1 9th, Feb. 6th, Feb. i8th, July nth, July i6th, and 
Sept. 27th, 1670. See also Brewster, vol. i, p. 69. A 
reference to his " discourse on infinite series " occurs in 
a letter to Collins, mentioned by Edleston, of July 2oth, 
1676. 

Towards the end of 1671, Newton was occupied in 
enlarging his method of infinite series and preparing twenty 
optical lectures for the press. The method was never 
finished. It was published by Horsley (vol. i, pp. 391-518) 



no DISCOVERIES OF 

under the title of " Geometria Analytica." It first appeared 
in 1736 in Colson's translation; see Pemberton's preface to 
his View of Newton's Philosophy, London, 1728. See also 
Cantor, vol. iii, pp. 168-179, 108-109; Brewster, vol. ii, 
pp. 15-16; Rosenberger, pp. 434-438; Gray, pp. 46-48, 

I, 2. 

Newton's Tractatusde Quadratura Curvarum(o,i. Brewster 
vol. ii, pp. 17-18) was printed at the end of the first edition 
of the Opticks (London, 1704, cf. Gray, pp. 35-36, 37-38). 
Extracts from the work had previously been printed in John 
Wallis's Opera Mathematica, of which four volumes were 
published at Oxford from 1693 to 1699. For other editions, 
see Gray, pp. 59, i, 2. An English translation of it was 
published by John Stewart in 1745 (ibid., p. 60), and a 
German annotated translation by G. Kowalewski is in No. 
164 of Ostwald's Klassiker. On Newton's fluxional works, 
see W. 1856, pp. 21-58. 

In a letter of May 25th, 1672, to Collins, Newton said 
that he did not intend to publish his lectures, but might 
possibly complete his method of infinite series, " The better 
half of which was written last Christmas" (Mace. Corr., 
vol. ii, p. 332). 

1672, Dec. loth. Letter to Collins'containing an account, 
requested by Collins in a letter received two days before, of 
his method of tangents (see Edleston, note 35 on p. xlvii). 

1673, June 23rd. Letter to Oldenburg on Slusius's method 
of tangents (see Edleston, p. 251). 

1675. In a letter of Collins to James Gregory, dated Oct. 
i9th, 1675. "Mr Newton ... I have not writ to or seen 
these eleven or twelve months, not troubling him as being 
intent upon chemical studies and practices, and both he and 
Dr Barrow beginning to think mathematical speculations to 
grow at least dry, if not somewhat barren" (Mace. Corr., 
vol. ii, p. 280). 

1675, J an - 22n d. Letter to Michael Dary on length of an 
elliptic arc. 



NEWTON AND LEIBNIZ in 

1676, June 1 3th. Letter to Oldenburg, containing a 
general answer to Lucas and "some communications of 
an algebraic nature for M. Leibnitz, who by an express 
letter to Mr Oldenburg had desired them." The part for 
Leibniz was sent to him at Paris, July 26th, and was after- 
wards printed in Wallis's Opera, vol. iii, pp. 622-629, and 
from that work in the Comm. Epist., where the typo- 
graphical error of " 26 Junii " for " Julii," which is corrected 
in Wallis's Errata, is also copied in the heading of the 
letter. Cf. second Essay, above. 

1672, Sept. 5th. Letter to Collins (infinite series of no 
great use in the numerical solution of equations. The 
University Press cannot print Kinckhuysen's Algebra ; the 
book is in the hands of a Cambridge bookseller with a view 
to its being printed : shall add nothing to it. Will alter 
an expression or two in his paper about infinite series, if 
Collins thinks it should be printed). 

1676, Oct. 24th. Latin letter to Oldenburg for Leibniz, 
who desired explanation with reference to some points in 
the letter of June i3th. See note 55 in Edleston, pp. li-lii. 

1676, Oct. 26th. Letter to Oldenburg with corrections 
for his letter of Oct. 24th. See note 56 in Edleston, p. Hi. 

1676, Nov. 8th. Letter to Collins thanking him for 
copies of the letters of Leibniz and Tschirnhaus, with 
remarks showing that Leibniz's method is not more general 
or easy than his own (Maa. Corr., vol. ii, p. 403). 

1676, Oct. i4th. Letter to Oldenburg (further alterations 
of his letter of Oct. 24th). Cf. note 58 of Edleston, p. Hi. 

1677, March 5th. Letter of Collins to Newton, printed in 
Wallis's Opera, vol. iii, p. 646 (extracts from it in the 
Comm. Epist.}. 

1687. Method for finding volume of a segment of a 
parabolic conoid (Edleston, end of note 90 on p. Iviii). 

1692, August 27th and Sept. i7th. Letters to Wallis, 
with illustrations of the calculus of fluxions and fluents 
t sent at Wallis's request (Wallis, Opera, vol. ii, p. 391). 



ii2 DISCOVERIES OF 

1693, March i/|.th. Letter to Fatio (proposing to make 
him such an allowance as might make his subsistence at 
Cambridge easy to him ; Edleston^ note 108 on p. Ix). 

1693, Oct. 1 6th. Letter to Leibniz (Edleston, pp. 276- 
279). 

1697, Jan. 3oth. Solution of John Bernoulli's two 
problems (Edleston, note 128 on p. Ixviii) : read to the 
Royal Society Feb. 24th, and printed without Newton's 
name in the Philosophical Transactions for January. 

1704. Equivocal expressions in the review of Newton's 
tract, De Quadratura Curvarum in the Leipsic Acts 
(Edleston, note 1 48 on pp. Ixxi-lxxiii). This was the origin 
of the dispute as to priority. 

Ill 

LEIBNIZ'S MANUSCRIPTS AND PUBLICATIONS ON 
THE INFINITESIMAL CALCULUS 

Development of Leibniz's mathematical education. 
G. 1848, pp. 7-20 (also on Descartes, Fermat, and others), 
29-32 ; G. 1855. 

Leibniz's first discoveries in mathematics (Pascal's 
influence, G. 1846, pp. 1-20 (Hist, et origo; see notes 
21-31) ; G. 1855, p. 33 ; Leibniz and St Vincent, G- 1855, 
pp. 37-38; Leibniz and Barrow, G. 1855, P- 4^ ; G. 1848^ 
p. 15). Cf. also Cantor, vol. iii, pp. 76-84, 161-164; 
Rosenberger, pp. 438-441. 

Leibniz's manuscripts. 1 

1673, August. Method of tangents (inverse problem also 
dealt with). G. 1855, pp. 55-57 ; G. 1848, pp. 20-22. 

1674, October. Inverse problem is that of quadratures. 
G. 1855, P- 57 ; G. 1848, p. 22. 

1674, October. Summation of series. G. 1855, pp. 57- 
58; G. 1848, pp. 22-23. 

1 If the manuscript is printed at length, it is stated so explicitly. 
On the genuineness of the dates, see G. 1848, p. 6. 



NEWTON AND LEIBNIZ 113 

1675, January. Descartes' method not sufficient for 
inverse problem. G. 1855, p. 58 ; G. 1848, pp. 23-24. 

1675, O ct - 2 5 tn - Method of quadrature. G. 1855, pp. 
58, 117-119 (printed in full); Bw. 1899, pp. 147-149 
(printed in full). 

1675, Oct. 26th. The same subject. G. 1855, pp. 58, 
119-121 (printed in full); Bw. 1899, pp. 149-151 (printed 
in full). 

1675, Oct. 29th. The same subject (uses J ). G. 1855, 

PP- 5 8 ~59> 121-127, 161-162; Bw. 1899, pp. 151-156. 

1675, Nov. ist. The same subject. G. 1833, pp. 60, 
127-131 ; Bw. 1899, pp. 157-160. 

I675, 1 Nov. nth. Example of the inverse method (d 
used). G. 1855, pp. 160-161, 132-139; G* 1848, pp. 
23-24, 32-40; Bw. 1899, pp. 161-167. 

1675, Nov. 2 1 st. On d (xy). G. 1853, pp. 62-63; 
G. 1848, pp. 4i-45> 24-25. 

1675, Nov. 22nd. Problem of tangents. G. 1848, pp. 25, 
46-48. 

1676, June 1 6th. Direct problem of tangents can also 
be treated. G. 1855, pp. 63-64; G. 1848, pp. 49- 
5> 25. 

1676, July. G. 1848, pp. 25-26, 51-54; Bw. 1899, pp. 
201-203. 

1676. Leibniz in England, Holland; and Germany. G. 
1848, pp. 54-56 (Bw. 1899, pp. 228-230), 26-27. 

1676, Nov. Differential calculus of tangents. G. 1855, 
pp. 65, 140-142; G. 1848, pp. 27, 56-59; Bw. 1899, pp. 
229-231. 

1677. Correspondence with Newton. 

1677, July n. Tangents (for publication). G. 1835^ 
pp. 66, 143-148; G. 1848, pp. 27-28, 59-65. 

1684. Leibniz's publication; his relations with Tschirn- 
haus. G. 1855, pp. 66-72 ; G. 1848, p. 28. 

1 Here somebody has tried to turn the 5 into a 3. 

8 



ii4 DISCOVERIES OF 

MS. "Elementa calculi novi . . . ," G. 1855 ', pp. 72, 
i49- J 55; G. 1846, pp. 32-38. 

Another MS., G. 1846, pp. 39-50. 

On Leibniz's manuscripts, see also Cantor, vol. iii, pp. 
164-168; Rosenberger, p. 447, note; and W. 1856, pp. 
84-115, 

Gerhardt 1 published a note on the history of the con- 
troversy about the first discovery of the differential calculus, 
together with some critical remarks on Weissenborn's book. 

In Weissenborn's book reference was often made to an 
essay of his in explanation of some points in Leibniz's 
manuscripts in Vol. XXV of Grunerts Archiv. As this 
essay did not appear, Weissenborn published the most 
important part of it under the title " Bemerkungen zu 
einigen in Dr C. J. Gerhardt's ' Entdeckung der hoheren 
Analysis ' verorfentlichten Manuscripten Leibnizens " in 
SchlomilcKs Zeitschrift for 1 856.2 This should be read in 
connection with Gerhardt's publications. 

On the letters and publications of Newton and Leibniz, 
see Cantor, vol. iii, pp. 179-215, and Rosenberger, pp. 441- 
455. Leibniz's publications are reprinted in Vol. V of his 
Mathematische Schriften edited by Gerhardt (see note 3 on 
pp. 71-72); and annotated German translations, by G. 
Kowalewski, of papers in the Ada Eruditorum of 1684, 
1691, 1693, 1694, 1702 and 1703; and the Miscellanea 
Berolinensia, in No. 162 of Ostw aid's Klassiker. 

IV 

THE CONTROVERSY 

See, in the first place, Cantor, vol. iii, pp. 285-328; 
Rosenberger, pp. 423, 460-506. Various letters, from 
1714-1719, on the controversy are mentioned in Edleston, 
pp. xxxviii-xxxix (see also the notes referred to). An 

1 Archiv der Mathematik und Physik, vol. xxvii, 1856, pp. 125-132. 

2 Zeitschrift fur Mathematik und Physik, vol. i, 1856, pp. 240-244. 






NEWTON AND LEIBNIZ 115 

account of the controversy, from the point of view of a 
partisan of Newton, is given in Brewster, vol. ii, pp. 23- 
83 ; and, from this point of view, reference may be made 
to H. Sloman's book, The Claims of Leibniz to the 
Invention of the Differential Calculus, translated from the 
German, with considerable additions and new addenda by 
the author, Cambridge, 1860 (cf. also Gray, p. 55). J On 
the editions of the Commercium Epistolicum, and so on, 
see Gray, pp. 49~5 2 > r > 2 ~3- 

1 With reference to this book, it must be remarked that Gerhardt 
(cf. Biv. 1899, p. 25) found that Leibniz first saw, and made extracts 
from, Newton's Analysis in 1676. 



Ill 

REVIEW (1855) OF BREWSTER'S 
"MEMOIRS OF NEWTON" 



REVIEW (1855) OF BREWSTER'S 
"MEMOIRS OF NEWTON" 

Memoirs of the Life, Writings, and Discoveries of 
Sir Isaac Newton. By Sir David Brewster, 
K. H. , etc. , etc. Two volumes, 8vo. Constable 
& Co., Edinburgh, 



I 

NOTHING is more difficult than to settle who is the 
most illustrious, the most to be admired, in any 
walk of human greatness. Those who would brain 
us if they could but imagine us to have any brains 
for hinting that it may be a question whether 
Shakspere be the first of poets, would perhaps 
have been Homerites a century ago. In these 
disputes there is more than matter of opinion, or of 
taste, or of period : there is also matter of quantity, 
question of how much, without any possibility of 
bringing the thing to trial by scale. This element 
of difficulty is well illustrated by an exception. 
Among inquirers into what our ignorance calls the 

1 [On this book, see note I on p. 3 ; and, on the subject of this 
review, see the Preface.] 

119 



120 REVIEW OF BREWSTER y S 

"laws of nature," an undisputed pre-eminence is 
given to Isaac Newton, as well by the popular voice, 
as by the deliberate suffrage of his peers. The 
right to this supremacy is almost demonstrable. It 
would be difficult to award the palm to the swiftest, 
except by set trial, with one starting-place and one 
goal : nor could we easily determine the strongest 
among the strong, if the weights they lifted were of 
miscellaneous material and bulk. But if we saw 
one of the swiftest among the runners keep ahead 
of nearly all his comrades, with one of the heaviest of 
the weights upon his shoulders, we should certainly 
place him above all his rivals, whether in activity 
alone, or in strength alone. Though Achilles were 
the swifter, and Hercules the stronger, a good 
second to both would be placed above either. This 
is a statement of Newton's case. We cannot say 
whether or no he be the first of mathematicians, 
though we should listen with a feeling of possibility 
of conviction to those who maintain the affirmative. 
We cannot pronounce him superior to all men in the 
sagacity which guides the observer of we mean 
rather deducer from natural phenomena, though 
we should be curious to see what name any six 
competent jurors would unanimously return before 
his. But we know that, in the union of the two 
powers, the world has never seen a man comparable 
to him, unless it be one in whose case remoteness of 
circumstances creates great difficulty of comparison. 



" MEMOIRS OF NEWTON" 121 

Far be it from us to say that if Newton had been 
Caenopolis, a Sicilian Greek, he would have sur- 
passed Archimedes ; or that if Archimedes had been 
Professor Firstrede, of Trinity College, Cambridge, he 
would have been below Newton, The Syracusan is, 
among the ancients, the counterpart of the English- 
man among the moderns. Archimedes is perhaps 
the first among the geometers : and he stands alone 
in ancient physics. He gave a new geometry the 
name was afterwards applied to the infinitesimal 
calculus out of which he or a successor would soon 
have evolved an infinitesimal calculus, if algebra 
had been known in the West. He founded the 
sciences of statics and hydrostatics, and we cannot 
learn that any hint of application of geometry to 
physics had previously been given. No Cavalieri, 
no Fermat, no Wallis, went before him in geometry : 
there was not even a chance of a contemporary 
Leibniz. We cannot decide between Archimedes 
and Newton : the two form a class by themselves 
into which no third name can be admitted ; and the 
characteristic of that class is the union, in most 
unusual quantity, of two kinds of power not only 
distinct, but so distinct that either has often been 
supposed to be injurious to the favourable develop- 
ment of the other. 

The scientific fame of Newton, the power which 
he established over his contemporaries, and his own 
general high character, gave birth to the desirable 



122 ' REVIEW OF BREWS TER'S 

myth that his goodness was paralleled only by his 
intellect. That unvarying dignity of mind is the 
necessary concomitant of great power of thought, 
is a pleasant creed, but hardly attainable except by 
those whose love for their faith is insured by their 
capacity for believing what they like. The hero is 
all hero, even to those who would be loath to pay 
the compliment of perfect imitation. Pericles, no 
doubt, thought very little of Hector dragged in the 
dust behind the chariot : and Atticus we can easily 
suppose to have found some three-quarter excuse for 
Romulus when he buried his sword in his brother's 
body by way of enforcing a retort. The dubious 
actions of Newton, certainly less striking than those 
of the heroes of antiquity, have found the various 
gradations of suppressors, extenuators, defenders, and 
admirers. But we live, not merely in sceptical days, 
which doubt of Troy and will none of Romulus, but 
in discriminating days, which insist on the distinc- 
tion between intellect and morals. Our generation, 
with no lack of idols of its own, has rudely invaded 
the temples in which science worships its founders : 
and we have before us a biographer who feels that 
he must abandon the demigod, and admit the im- 
pugners of the man to argument without one cry of 
blasphemy. To do him justice, he is more under the 
influence of his time, than under its fear : but very 
great is the difference between the writer of the 
present volumes and that of the shorter Life in the 



"MEMOIRS OF NEWTON" 123 

" Family Library" in 1831 ; though, if there be any 
truth in metaphysics, they are the same person. 

The two deans of optical science, in Britain and 
in France, Sir David Brewster and M. Biot, are 
both biographers of Newton, and take rather different 
sides on disputed points. Sir D. Brewster was the 
first writer on optics in whose works we took an 
interest ; but we do not mean printed works. We, 
plural as we are, remember well the afternoon, we 
should say the half-holiday, when the kaleidoscope 
which our ludi-magister most aptly named for that 
term had just received from London was confided 
to our care. We remember the committee of con- 
servation, and the regulation that each boy should, 
at the first round, have the uninterrupted enjoyment 
of the treasure for three minutes ; and we remember, 
further, that we never could have believed it took so 
very short a time to boil an egg. A fig for Jupiter 
and his satellites, and their inhabitants too, if any ! 
What should we have thought of Galileo, when 
placed by the side of the inventor of this wonder of 
wonders, who had not only made his own telescope, 
but his own starry firmament ? The inventor of the 
kaleidoscope must have passed the term allotted to 
man, before he put his hand to the actual concoction 
of these long-meditated volumes, in which we find 
the only life of Newton written on a scale com- 
mensurate with Newton's fame. But though he has 
passed the term, he has not incurred the penalty ; 



124 REVIEW OF BREWS TER'S 

his strength is labour without sorrow. We trust 
therefore that the still later age, the full fourscore, 
will find him in the enjoyment of the additional fame 
which he has so well earned. And since his own 
scientific sensibilities are keen, as evidenced by 
many a protest against what he conceives to be 
general neglect on the part of ruling powers, we 
hope they will make him fully feel that he has linked 
his own name to that of his first object of human 
reverence for as long as our century shall retain a 
place in literary history. This will be conceded by 
all, how much soever they may differ from the 
author in opinions or conclusions ; and though we 
shall proceed to attack several of Sir D. Brewster's 
positions, and though we have no hesitation in 
affirming that he is still too much of a biographer, 
and too little of an historian, we admire his earnest 
enthusiasm, and feel as strongly as any one of his 
assentients the service he has rendered to our 
literature. When a century or two shall have 
passed, we predict it will be said of our day 
that the time was not come when both sides of the 
social character of Newton could be trusted to his 
follower in experimental science. Though biography 
be no longer an act of worship, it is not yet a 
solemn and impartial judgment : we are in the inter- 
mediate stage, in which advocacy is the aim, and in 
which the biographer, when a thought more candid 
than usual, avows that he is to do his best for his 



"MEMOIRS OF NEWTON" 125 

client. We accept the book as we find it ; we 
expect an ex parte statement, and we have it. 
The minor offence is sometimes admitted, with what 
we should call the art of an able counsel, if we did 
not know that the system of the advocate in court is 
but the imitation of all that is really telling in the 
natural practices of the partisan defender. But Sir 
D. Brewster stands clear of the imputation of art 
by the mixture of all which art would avoid. A 
judicious barrister, when he has to admit some 
human nature in his client, puts an additional trump 
upon the trick by making some allowance for the 
other side ; and nothing puts the other side in so 
perilous a predicament. It is not so with Sir D. 
Brewster. When sins against Newton are to be 
punished, we hear Juvenal ; when Newton is to be 
reprimanded, we hear a nice and delicate Horace, 
who can 

" In reverend bishops note some small defects ; 
And own the Spaniard did a waggish thing, 
Who cropt our ears, and sent them to the king." 

We have more reasons than one for desiring that it 
should have been so, and not otherwise. Sir D. 
Brewster is the first biographer who has had re- 
stricted access to the " Portsmouth Papers " ; he has 
been allowed to have this collection in his own 
possession. Had the first Life written upon know- 
ledge of these papers taken that view of Newton's 
social conduct which stern justice to others requires, 



126 REVIEW OF BREWSTERS 

a condonation of all the previous offences of 
biographers would have followed. There was not 
full information ; the fault lay with those who 
suppressed the truth ; and so forth. And every 
great man who has left no hoard of papers would 
have had a seal of approval placed upon all his 
biographies ; for, you see, Newton was exposed by 
the publication of the " Portsmouth Papers," that is 
easily understood ; but A B left no papers, there- 
fore no such exposure can take place, etc., etc. 
We, who hold that there is, and long has been, 
ample means of proving the injustice with which 
Newton and his contemporaries once and again 
treated all who did not bow to the idol, should have 
been loath to see the garrison which our opponents 
have placed in the contested forts march out with 
the honours of war, under a convention made on 
distant ground, and on a newly-discovered basis of 
treaty. Again, there is a convenient continuity in 
the first disclosure of these documents coming from 
an advocate ; the discussion which they excite will 
be better understood when the defender of Newton is 
the first to have recourse to Newton's own papers. 



II 

Of Newton's birth, of his father's death, and the 
subsequent marriage of his mother, we need say 
nothing. He was not born with a title, though 



"MEMOIRS OF NEWTON" 127 

he was the son of a lord of a very little manor, a 
yeoman's plot of land with a baronial name. But 
the knighthood clings strongly to his memory. Sir 
David (and on looking back, we see that the doctor 
did just the same) seldom neglects it. When the 
school-boy received a kick from a school-fellow, it 
was " Sir Isaac" who fought him in the churchyard, 
and it was <( Sir Isaac" who rubbed his antagonist's 
nose against the wall in sign of victory. 1 Should 
we survive Sir David, we shall Brewster him : we 
hold that those who are gone, when of a certain 
note, are entitled to the compliment of the simplest 
nomenclature. The childhood and boyhood of 
Newton were distinguished only by great skill in 
mechanical contrivance. No tradition, no remain- 
ing record, imputes any very early progress either 
in mathematics or general learning, beyond what 
is seen in thousands of clever boys in any one year 
of the world. That he was taken from farming 
occupations, and sent back to school, because he 
loved study, is told us in general terms ; but what 
study we are not told. We have always been of 
opinion that the diversion of Newton's flow of reason 
into its proper channel was the work of the University 
and its discipline. He was placed at Trinity College 
as a subsizar in his nineteenth year. We have no 
proof, but rather the contrary, that he had then 
opened Euclid. That he was caught solving a 

1 [C/. Brewster, Memoirs^ 1855, vol. i, pp. 7-8.] 



128 REVIEW OF BREWS TER'S 

problem under a hedge is recorded : perhaps a knotty 
question of wheelwork. He bought a Euclid at 
Cambridge, and threw it aside as a trifling book, 
because the conclusions were so evident : he betook 
himself to Descartes, and afterwards lamented that 
he had not given proper attention to Euclid. All 
this is written, and Sir David is bound to give it ; 
but what Newton has written belies it. We put 
faith in the Principia, which is the work of an in- 
ordinate Euclidian, constantly attempting to clothe 
in the forms of ancient geometry methods of pro- 
ceeding which would more easily have been pre- 
sented by help of algebra. Shall we ever be told 
that Bacon complained of the baldness of his own 
style, and wished he had obtained command over 
metaphor? Shall we learn that Cobbett lamented 
his constant flow of Gallicism and west-end slang, 
and regretted that his English had not been more 
Saxon ? If we do, we shall have three very good 
stories instead of one. We may presume as not 
unlikely, that Newton, untrained to any science, 
threw away his Euclid at first, as very evident : no 
one need be Newton to feel the obvious premise, or 
to draw the unwise conclusion. But it would belong 
to his tutor to make him know better : and Newton 
was made, as we shall see, to know better accord- 
ingly. Our reader must not imagine that deep 
philosophy and high discovery were discernible in 
the young subsizar. He was, as to what had come 



"MEMOIRS OF NEWTON" 129 

out, a clever and somewhat self-willed lad, rather 
late at school, with his heart in the keeping of a 
young lady who lived in the house where he had 
boarded, and vice versa, more than commonly in- 
genious in the construction of models, with a good 
notion of a comet as a thing which might be imitated, 
to the terror of a rustic neighbourhood, by a lantern 
in a kite's tail, and with a tidy and more than boyish 
notion of an experiment, as proved by his making 
an anemometer of himself by trial of jumping with 
and against the wind. In that tremendous storm 
in which many believed that Oliver Cromwell's 
reputed patron came to carry him away, and in 
which he certainly died, the immortal author of the 
theory of gravitation was measuring he little knew 
what, by jumping to and fro. We do not desire to 
see boys take investiture of greatness from their 
earliest playtime : we like to watch the veneration 
of a biographer growing with its cause, and the 
attraction varying with some inverse power of the 
distance. And further, we are rather pleased to 
find that Newton was what mammas call a great boy 
before he was a great man. 

Of all the books which Newton read before he 
went to Cambridge, only one is mentioned Sander- 
son's Logic : this he studied so thoroughly that when 
he came to college lectures he was found to know it 
better than his tutor. The work is, for its size, un- 
usually rich in the scholastic distinctions and the 

9 



130 REVIEW OF BREWSTERS 

parva logicalia ; very good food for thought to those 
who can sound the depths. Newton's Cambridge 
successors are apt to defend their neglect of logic 
by citing his supposed example, and that of other 
great men : but it now appears that Newton was not 
only conversant with Barbara, Celarent, etc., but 
even with Fecana, Cajeti, Dafenes, Hebare, Gadaco, 
etc. We have often remarked that Newton, as in 
the terminal scholium of the Principia, had more 
acquaintance with the- mode of thought of the 
schoolmen than any ordinary account of his early 
reading would suffice to explain. We strongly 
suspect that he made further incursions into the 
old philosophy, and brought away the idea of 
fluxions, which had been written on, though not 
in mathematical form, nor under that name. 
Suisset's tract on intension and remission is fluxional, 
though not mathematical : in the very first para- 
graph he says that the word "intension" is used 
"uno modo pro alteratione mediante qua qualitas 
acquiritur : et sic loquendo intensio est motus. " 
For "qualitas" read "quantitas," and we are as 
near to Newton's idea as we can well be. 

In less than four years from the time concerning 
which we have presumed to ridicule the joint 
attempt of Conduitt and the biographers to create 
a dawn for which there is no evidence, the sun rose 
indeed. Shortly after Newton took his B.A. 
degree, in 1665, he was engaged on his discovery 



" MEMOIRS OF NEWTON" 131 

of fluxions : but there is neither record nor tradition 
of his having taken his degree with any unusual 
distinction. Conduitt's information on this period 
must be absurdly wrong in its dates. We are to 
believe that the young investigator who conceived 
fluxions in May 1665, was, at some time in 1664, 
found wanting in geometry by Barrow, and thereby 
led not only to study Euclid more attentively, but 
to ' ' form a more favourable estimate of the ancient 
geometer when he came to the interesting proposi- 
tions on the equality of parallelograms. ..." And 
this when he was deep in Descartes's geometry of 
co-ordinates. We entertain no doubt that the un- 
wise contempt for demonstration of evident things, 
so often cited as a proof of great genius, and its 
correction by Barrow, all took place in the first few 
months of his residence at Cambridge. 1 His copy 
of Descartes, yet existing, is marked in various 
places, " Error, error, non est Geom." 2 No such 
phrase as "non est Geometria " would have been 
used, except by one who had not only read Euclid, 
but had contracted some of that bias in favour of 
Greek geometry which is afterwards so manifest in 
the Principia. Pemberton, who speaks from com- 
munication with Newton, and is a better authority 
than Conduitt, tells us that Newton regretted he 
had not paid more attention to Euclid. And Doctor 

1 \Cf. note I on pp. 9-10, and Brewster, Memoirs^ 1855, vol. i/ 
pp. 21-22, 24.] 

2 [Brewster, Memoirs, 1855, vol. i, p. 22, note.] 



132 REVIEW OF BREWSTERS 

Sangrado, when the patient died, regretted that he 
had not prescribed more bleeding and warm water. 
The Principia bears already abundant marks of 
inordinate attachment to the ancient geometry ; in 
one sense, it has died in consequence. If Newton 
had followed his own path of invention, and written 
it in fluxions, the young student of modern analysis 
could have read it to this day, and would have read 
it with interest : as s it is, he reads but a section or 
two, and this only in England. Before 1669, the 
year of his appointment to the Lucasian chair, all 
Newton's discoveries had germed in his mind. The 
details are notorious, and Sir D. Brewster is able 
to add a remarkable early paper on fluxions to those 
already before the world. 1 

We here come upon the well-known letter to Mr 
Aston, a young man about to travel, which, as Sir 
David says, " throws a strong light on the charac- 
ter and opinions of its author." It does indeed, 
and we greatly regret that the mode in which that 
character has been represented as the perfection of 
high-mindedness compels us to examine this early 
exhibition of it, in connexion with one of a later 
date. Newton is advising his young friend how to 
act if he should be insulted. Does he recommend 
him, as a Christian man, to entertain no thought of 
revenge, and to fear his own conscience more than 
the contempt of others ? Or, as a rational man, 

1 [See the Appendix to the second Essay, above. ] 



"MEMOIRS OF NEWTON" 133 

does he dissuade him from the folly of submitting 
the decision of his difference to the logic of sword or 
pistol ? Or, supposing him satisfied by well-known 
sophisms that the duel is noble and necessary, does 
he advise his friend to remember that dishonour is 
dishonour everywhere ? He writes as follows : 

"If you be 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 return 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. " 

This letter has often been printed, in proof of 
Newton's sagacity and wisdom. If Pepys or 
Boswell had written the preceding advice, they 
would not have been let off very easily. Again, 
when, many years after, Newton wrote, as member 
for the University in the Parliament which dethroned 
King James, to Dr Covel the Vice-Chancellor, he 
requests a reasonable decorum in proclaiming 
William and Mary, "because," says he, " I hold 
it to be their interest to set the best face upon 
things, after the example of the London divines." 
And again, "Those at Cambridge ought not to 
judge and censure their superiors, but to obey and 
honour them, according to the law and the' doctrine 
of passive obedience." What had Newton and 
passive obedience just been doing with King James ? 



134 REVIEW OF BREWS TER'S 

These instances, apart from science, show us the 
character of Newton out of science : he had not 
within himself the source from whence to inculcate 
high and true motives of action upon others ; the 
fear of man was before his eyes. 1 But his mind 
had been represented as little short of godlike : and 
we are forced upon proof of the contrary. Had it 
been otherwise, had his defects been duly admitted, 
it would have been pleasant to turn to his uncom- 
promising philosophic writings, and to the manner 
in which, when occupied with the distinction be- 
tween scientific truth and falsehood, no meaner 
distinction ever arose in his mind. This would 
have been, but for his worshippers, our chief con- 
cern with him. The time will come when his social 
weaknesses are only quoted in proof of the com- 
pleteness with which a high feeling may rule the 
principal occupation of life, which has a much slighter 
power over the subordinate ones. Strange as it 
may seem, there have been lawyers who have been 
honest in their practice, and otherwise out of it : 
there have been physicians who have shown human- 
ity and kindness, such as no fee could ever buy, at 
the bedside of the patient and nowhere else. 

Ill 

Sir David Brewster gives Newton's career in 
optics at great length ; it is his own subject, and 

1 [The letter to Aston is given, with comments, in Brewster's 
Memoirs, 1855, vol. i, pp. 34, 385-389.] 



"MEMOIRS OF NEWTON" 135 

he makes us feel how completely he is at home. 
He gives a cursory glance at the science even down 
to our own time ; and he does the same with 
astronomy. The writer would rather have had 
more of the time of Newton, and particularly, more 
extracts from the " Portsmouth Papers." But we 
must think of our neighbours as well as of our- 
selves ; and the general reader will be glad to know 
that so much of the work is especially intended for 
him. We have not space to write an abstract ; 
but the book is very readable. In the turmoil of 
discussion which arose out of his optical announce- 
ments, Newton made the resolution, which he 
never willingly broke, of continuing his researches 
only for his own private satisfaction. I see, said 
he, that a man must either resolve to put out 
nothing new, or to become a slave to defend it. It 
seems that he expected all his discoveries to be 
received without opposition. 

About 1670, or later, Newton drew up a scheme 
for management of the Royal Society, which Sir 
D. Brewster found among the papers. Certain 
members, some in each department, should be paid, 
and should have fixed duties in the examination 
of books, papers, experiments, etc. In this paper 
our writer, whose views on this subject are very 
large and of old standing, sees the recommendation 
of an Institute, which indeed, on a small scale, the 
plan seems to advocate. Sir David would have all 



136 REVIEW OF BREWSTERS 

the societies congregated at Kensington Gore, under 
liberal patronage, and images to himself that 
* * each member of the now insulated Societies would 
listen to the memoirs and discussions of the as- 
sembled Academy, 1 and science and literature would 
thus receive a new impulse from the number and 
. variety of their worshippers ! " If all Fellows were 
savants, and if all savants studied all sciences, this 
might be practicable. There is one body in London 
which cultivates a large range of subjects, the Royal 
Society itself: and all the world knows that the 
meetings of this Society, abounding in Fellows of 
such universality of knowledge as in our time is 
practicable, are less interesting and worse attended 
than those of any of the societies for special objects. 
And reason good : the astronomer or the geologist 
goes down to his own place for he knows what ; 
but the astronomer is shy of a society of which it 
is as likely that any one evening may give him a 
treat of physiology as of astronomy, and the 
geologist, who wants a stone when he asks for 
bread, turns very sleepy under a dose of hyper- 
determinants or definite integrals. 

Newton's reputation rests on a tripod, the feet 

1 The members of the French Institute receive a part of their 
emoluments at the Board, and the quotum of each day on which any 
one is absent is forfeited. This insures good attendance, and we have, 
on pay-day, seen men of profound science, during the memoirs and 
discussions of the assembled Academy, practising the first rule of 
arithmetic, called numeration, upon rouleaux of five-franc pieces. To 
this it must be added that the Institute has much patronage, and 
constant attendance is necessary to keep up influence and connexion. 



"MEMOIRS OF NEWTON" 137 

of which are fluxions, optics, gravitation. Each 
one of these words must be used in a very large 
sense : thus by fluxions we mean all mathematics 
as bearing upon a system of which the fluxional 
calculus is at the completion. Of the three supports 
of this tripod one only has received any damage, 
though left quite strong enough, in conjunction with 
the rest, to support the fabric through all time. In 
optics only, the subject on which Newton showed 
his first impatience of opposition, his opinion, even 
his system, has been set aside in our own day. The 
hypothesis of an undulating ether, as the immediate 
agent in the production of light, has superseded 
that of particles emanating from the luminous body : 
and though the undulationists, now a large majority, 
have long maintained their theory with a higher 
order of certainty than they were entitled to, yet 
it seems that time is drifting their conclusions to a 
stable anchorage. There is something like coinci- 
dence in the almost simultaneous appearance of the 
first elaborate biography of Newton, who well-nigh 
strangled the undulatory theory in its cradle, and 
of that of Young, who first played a part of power 
in its resuscitation. As yet, Young is fully known 
but to a few : his early education was not, like that 
of Newton, conducted under a system which corrects 
the false impressions of green age. Had he been 
trained in a University, he would have been, as 
they say of the globe, rectified for the latitude of 



138 REVIEW OF BREWSTERS 

the place : but speculation on what he might have 
become may be deferred until what he did become 
is of more popular notoriety. Dean Peacock's Life 
is one of the best of scientific biographies, and the 
three volumes of Young's collected writings are 
treasures to all who know what intellectual wealth is. 



IV 

We come to the Principia^ and we confess that we 
heartily wish it were but just and right to persuade 
ourselves that the author of this work could do no 
wrong. One of the greatest wonders about it is the 
manner in which it was thrown off in eighteen 
months. Certainly the matter had fermented in 
Newton's mind many years before : but it was not 
the irresistible call of his own genius which drew 
him to the work in December 1684 ; it was Halley, 
and the influence of the Royal Society brought to 
bear by Halley. Sir D. Brewster very properly 
contends that to Halley, not to the Society, the 
Principia is due. Who found out, casually, that 
Newton had had some great success in the question 
which had occupied many of the first minds, the 
connexion of the planetary motions with mechanical 
second causes ? Who went to Cambridge .to learn 
the truth of the report, obtained specimens from 
Newton with a promise to go on, got himself ap- 
pointed by the Royal Society to c ' keep Mr Newton 



"MEMOIRS OF NEWTON" 139 

in mind of his promise," did keep Mr Newton in 
mind, and doubtless let him have no peace unless he 
continually reported progress? Who, when Newton, 
disgusted with the unfair claim of Hooke, proposed 
to leave out the third book (that is, all the applica- 
tion of the previous books to the actual solar system)^ 
soothed him with skilful kindness, and made what 
Sir D. Brewster calls his "excellent temper" re- 
cover its serenity ? Who paid the expense of print- 
ing, when the Royal Society found it could not afford 
to fulfil its engagement ? To all those questions the 
answer is Halley, who shines round the work, as 
Newton shines in it. When Newton proposed to 
leave out the third book, he felt that Philosophies 
Naturalis Principia Mathematica was no longer the 
true title, but rather De Motu Corporum Libri Duo ; 
but, feeling this, he intended to preserve the wrong 
title, because, as he says to Halley, "'Twill help 
the sale of the book, which I ought not to diminish 
now 'tis yours." The greatest of all works of dis- 
covery, with a catch-penny title ! We can hardly 
excuse this, even though the penny were angled for 
by a feeling of gratitude. We never liked the 
"Erne, lege, fruere," which figures in the title-page 
of Copernicus : this was the work of an injudicious 
friend ; but Newton was only saved from worse by 
his incomparable adviser. 

We are come to the time when the morbid dislike 
of opposition which would, but for Halley, first have 



140 REVIEW OF BREWS TERS 

prevented the Principia from being written, and next 
have deprived it of its essential conclusions, is no 
longer regarded as the modesty of true greatness, 
and served up for us to admire, as we shall answer 
the contrary at our peril. It is passed without com- 
ment ; we are now in slack water, and the turn of 
tide will be here in due season. The sooner the 
better ; for the indulgence due to the mother failings 
of a great public benefactor cannot be cheerfully 
and cordially given so long as our gratitude is re- 
quired to show itself in misnomers and make-believes. 
Candid acknowledgment would convert censure into 
regret : sufficient acknowledgment would turn the 
reader into an extenuator : the Principia would 
neutralise greater faults than Newton's ; but it will 
not convert them into merits. The quarrel is not 
with Newton for his weaknesses, but with the 
biographer for his misconception of his own office. 
How indeed would it be possible to think for a 
moment with harshness of a great man of all time, 
and a good man of an evil time, on account of 
errors which we never could have known but for the 
benefits to ourselves in the achievement of which 
they were committed ? 

If faults had exhibited themselves in matters 
affecting society at large, by offences, as it were, 
against the Crown, the fountain of justice would 
also have been that of mercy, and the evidence to 
character and services would have secured a nominal 



"MEMOIRS OF NEWTON" 141 

sentence. But the suits we have to deal with are 
in civil process. The memory of more than one 
illustrious contemporary brings an action for damages, 
and palliation of the defendant is injustice to the 
plaintiff. 

Though not much relying on Conduitt's memo- 
randa of mathematical conversations, we trust that 
which follows, and it will much please young mathe- 
maticians to read of Newton in one of their own 
scrapes. When Halley visited him in 1684, 

. . . . * ' he at once indicated the object of his visit 
by asking Newton what would be the curve described 
by the planets on the supposition that gravity 
diminished as the square of the distance. Newton 
immediately answered, an Ellipse. Struck with joy 
and amazement, Halley asked him how he knew it ? 
Why, replied he, I have calculated it ; and being 
asked for the calculation, he could not find it, but 
promised to send it to him. After Halley left 
Cambridge, 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." 

This anecdote 1 carries truth on the face of it, for 
Conduitt was neither mathematician enough to have 
conceived it, nor to have misconceived it into any- 

1 [Brewster, Memoirs ^ 1855, vol. i, p. 297.] 



H2 REVIEW OF BREWS TERS 

thing so natural and probable as what he has given. 
Little things illustrate great ones. Newton, whose 
sagacity in pure mathematics has an air of divina- 
tion, who has left statements of results without 
demonstration, so far advanced that to this day we 
cannot imagine how they were obtained, except by 
attributing to him developments of the doctrine of 
fluxions far, far beyond what he published, or any 
one of his time this Newton was liable, both in 
his own closet and in his printed page, to those little 
incurite which the man of pen and ink must some- 
times commit, and which the man who can push 
through a mental process may indeed commit, but 
is almost sure to detect when he empties his head 
upon paper. Now join what precedes to Newton's 
own assertion that he had no peculiar sagacity, but 
that all he had done was due to patience and perse- 
verance ; an assertion at any common interpretation 
of which we may well smile, but which, all things 
put together, may justify us in such an irreverent 
simile as the supposition that he hunted rather by 
scent than by sight. 

V 

We now come to the second volume, and to those 
points on which we more especially differ from Sir 
D. Brewster. Our plan must be to take one or two 
prominent cases, and to discuss them with the 
biographer. We do not express disapprobation at 



" MEMOIRS OF NEWTON" 143 

the facility with which he credits the opponents of 
Newton with bad motives : we are glad of it, and 
thank him for it. There is a pledge of earnest 
sincerity in the wildness with which the barbed 
arrow is fired at Leibniz or at Flamsteed ; and if the 
partisan be too much led away by his feelings to be 
a judicious counsel, it is not we, to whom trouble is 
saved, who ought to blame him for it. We take the 
following as an instance, chiefly because we can be 
brief upon it. 

Newton and others, acting for Prince George, 
entered into an agreement with Flamsteed : articles 
of agreement were signed, out of the execution of 
which quarrels arose. We must know, as Sir David 
justly observes, what these articles were before we 
can judge. No signed copy appears : Mr Baily 
found none among Flamsteed's papers, Sir David 
found none among Newton's. But draught articles 
occur in both repositories : and, wonderful to relate, 
the unsigned draughts actually differ ; Flamsteed's 
draughts bind him less, Newton's draughts bind 
Flamsteed more. The case is a very common one ; 
the manner in which Sir David treats it is not quite 
so common. Speaking of Flamsteed, he informs us 
that ' ' of these he has left no copy, because he had 
wilfully violated them " : speaking of the draughts 
in Newton's possession, he says, * * I regret to say 
that they are essentially different from those 
published by Mr. Baily " ; by which he means that 



H4 REVIEW OF BREWSTERS 

Newton's unsigned papers are of course copies of 
the signed agreement, and Flamsteed's of course no 
such thing ; the false draughts being purposely 
retained by Flamsteed, in preference to the final 
articles purposely destroyed. We need not tell our 
readers that a man is not to be pronounced dis- 
honest because his draught proposals do not agree 
with his signed covenants, still less because they do 
not agree with the other parties' draught proposals. 
Newton and Flamsteed were both honest men, with 
very marked faults of different kinds : we may be 
sure neither of them privately destroyed a document 
for the suppression of evidence. When Sir D. 
Brewster not merely opines, but narrates, that 
Flamsteed left no copy because he had wilfully 
violated them, he is our very good friend, and 
lightens our task very much. 

When Newton allowed himself to perpetrate, not 
the suppression of a document, for a third edition 
does not suppress the first and second, but a revoca- 
tion so made as to do all that could be done towards 
suppression, Sir David Brewster is his defender, and 
in this instance, we really believe, one of the last of 
his defenders. He thinks the step was "perhaps 
unwise," but proceeds to say that Newton was " not 
only entitled but constrained " to cancel the passage. 

When Leibniz applied to Newton for information 
on the nature of the discoveries with rumours of 
which the English world was ringing, Newton com- 



"MEMOIRS OF NEWTON" 145 

municated some of his algebraic discoveries, but 
studiously concealed a descriptive mention of 
fluxions under the celebrated anagrams, or sentences 
with their letters transposed into alphabetical order. 
Leibniz (1677) replied, almost immediately, with a 
full and fair disclosure of his own differential calculus, 
and in so doing became the first publisher of that 
method, and under the symbols which are now in 
universal use. He adds that he thinks Newton's 
concealed method must resemble his own ; thus 
holding out an invitation to Newton to say yes 
or no. Not one word of answer from Newton. 
Accordingly, when Leibniz printed his discovery 
in the Leipsic Acts for 1684, he did not affirm that 
Newton was in possession of a method similar to his 
own. What ought he to have done, we ask of our 
readers, under these circumstances ? Ought he to 
have given Newton's assertions about his method, 
as assertions, leaving it to a suspicious temper to 
surmise that the reader was desired not to believe 
without proof? Ought he, as a matter of compli- 
ment, to have promulgated what Newton was doing 
everything in the power to conceal? Seven years 
had passed, and Newton had made no sign : was 
Leibniz bound, either in fairness or in courtesy, to 
take on himself to affirm that he had a method 
similar to his own ? Not in fairness ; for if a man 
studiously conceal and continue to conceal his dis- 
covery, those to whom he may have stated that he 

10 



146 REVIEW OF BREWSTERS 

had a discovery are not bound to be his trumpeters 
until such time as he shall please to reveal himself. 
Not in courtesy ; a man who sends only anagrams, 
and when he receives from his correspondent a full 
and open account of that correspondent's discoveries, 
and an invitation to state whether his own resemble 
them, returns no answer, cannot complain of want 
of courtesy if his correspondent keep silence about 
him thenceforward. What Leibniz did was merely 
to state that no one would successfully treat such 
problems as he had treated, except by his own 
calculus, or one similar to it. Sir D. Brewster calls 
his silence with respect to Newton the first fault in 
the controversy : we see no fault at all ; and if we 
did, we should call it the second. The paper had 
no historical allusions ; Cavalieri, Fermat, and 
Hudde, each of whom had shown the world some- 
thing approaching to calculus, are not named in it : 
and either of these had more claim to mention than 
Newton at that time. But, two years afterwards, 
in 1686, Leibniz published a paper in the same 
Leipsic Acts, a paper which Newton did not cite 
when, long after, he was writing against Leibniz, 
a paper which the Newtonians are very shy of 
citing, and of which, apparently, Sir David knows 
nothing. In this paper he explains the foundation 
of the integral calculus, the matter of which was 
much more likely to recall Newton to mind than 
his former paper on the differential calculus : for 



"MEMOIRS OF NEWTON" 147 

his application to Newton, in the first instance, 
was to know what he had done on series, and 
especially with reference to their use in quadratures > 
which we now call integration. Here he gives an 
historical summary ; and speaking of those who had 
performed quadratures by series, he proceeds thus ; 
" A geometer of the most profound genius, Isaac 
Newton, has not only arrived at this point inde- 
pendently of others, but has solved the question by 
a certain universal method : and if he would publish, 
which I understand he is now preparing to do, 
beyond doubt he would open new paths, to the 
great increase, as well as condensation, of science. " 
A passing word on Leibniz. We shall not stop to 
investigate the various new forms in which Sir D. 
Brewster tries to make him out tricking and paltry. 
We have gone through all the stages which a reader 
of English works can go through. We were taught, 
even in boyhood, that the Royal Society had made 
it clear that Leibniz stole his method from Newton. 
By our own unassisted research into original docu- 
ments we have arrived at the conclusion that he was 
honest, candid, unsuspecting, and benevolent. His 
life was passed in law, diplomacy, and public business ; * 
his leisure was occupied mostly by psychology, and 
in a less degree by mathematics. Into this last 
science he made some incursions, produced one of 
the greatest of its inventions, almost simultaneously 
with one of its greatest names, and made himself 



148 REVIEW OF BREWSTERS 

what Sir D. Brewster calls the " great rival" of 
Newton, in Newton's most remarkable mathematical 
achievement. 1 

Newton, in the first edition of the Principia^ 
gave a fair and candid account of the matter. But, 
many years after, when this important passage 
was quoted against those (and we now know that 
Newton was always one of them) who endeavoured 
to prove Leibniz a plagiarist, he tried to explain 
away the force of his own admission. This he 
did twice ; once in a private paper which Sir D. 
Brewster has published and, strange to say, in 
vindication of the suppression of the passage which 
took place in the third edition and once in those 
observations on Leibniz's last letter which he cir- 
culated among friends until Leibniz died and then 
sent at once to press. We give the Scholium from 
the Principia, and the two explanations. 

Scholium from the ' ' Principia " (first edition). 
" In letters which passed between me and that most 
skilful geometer G. G. Leibnitz ten years ago, 
when I signified that I had a method of determining 
maxima and minima, of drawing tangents to curves, 
and the like, which would apply equally to irrational 
as to rational quantities, and concealed it under trans- 
posed letters which would form the following sentence 
'Data aequatione quotcunque fluentes quantitates 

1 [De Morgan wrote a biography of Leibniz, an extract from which is 
given in the first Appendix to this Essay.] 



"MEMOIRS OF NEWTON" 



149 



involvente, fluxiones invenire, et vice versa ' that 
eminent man wrote back that he had fallen upon a 
method of the same kind, and communicated his 
method, which hardly differed from mine in any- 
thing except language and symbols. The founda- 
tion of both is contained in the preceding Lemma. " 



Newton's explanation^ left 
in manuscript. 



"After seven years, viz. 
in October 1684, he pub- 
lished the elements of this 
method as his own, without 
referring to the correspon- 
dence 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 Principles, 
lest it should be thought that 
I borrowed that Lemma from 
Mr Leibnitz," 



Newton's explanation circu- 
lated in writing, and printed 
in Raphson's "Fluxions" 
(1716, date of title 1715) 
after Leibniz's death. 

P. 115. "He pretends 
that in my book of Principles, 
PP- 2 S3> 2 54> I allowed him 
the invention of the Calculus 
Differential independently 
of my own ; and that to at- 
tribute this invention to my- 
self, is contrary to my know- 
ledge. But in the paragraph 
there referred unto, I do not 
find one word to this purpose. 
On the contrary, I there re- 
present that I sent notice of 
my method to Mr Leibnitz 
before he sent notice of his 
method to me : and left him 
to make it appear that he 
had found his method before 
the date of my letter; that 
is, eight months at least 
before the date of his own. 
And by referring to the letters 
which passed between Mr 
Leibnitz and me ten years 
before, I left the reader to con- 
sult these letters, and inter- 
pret the paragraph thereby." 



150 REVIEW OF BREWS TER'S 

The first explanation is from a manuscript supple- 
ment to that printed answer to Leibniz of which 
the second explanation is part. We think better of 
Newton in 1687 than to believe either, though we 
do not doubt that Newton in 1716 saw his former 
self through the clouds of 1712. Though the 
morbid suspicion of others, which was the worst 
fault of temperament, the fault alluded to by Locke, 
did act to some extent throughout his whole life, 
yet we do not believe that it was in 1687 what it 
afterwards became when he had sat on the throne of 
science for many years, the object of every form of 
admiration, and every form of flattery. Could we 
believe his first explanation, could we think that 
in 1687 hi s hidden anagrams, answered by Leibniz's 
candid revelations, produced no effect except a 
diseased feeling that perhaps Leibniz would rob 
him, instead of a generous confidence that Leibniz 
would not suspect him, we should turn from him 
with pity. We must now change our position, and 
defend him from his biographer. Sir D. Brewster 
does not quote the second explanation ; he only 
cites the page, and quotes a few words occurring 
further on, which are much less to the purpose, and 
which he says ' ' fortunately " give us Newton's 
opinion. Now we say that the second explanation, 
as quoted by us, fortunately saves Newton from 
his own imputation upon himself. The two ex- 
planations cannot stand together : according to the 



"MEMOIRS OF NEWTON" 151 

first Newton was guarding himself from a charge of 
plagiarism ; according to the second, he was putting 
upon Leibniz the onus of averting a similar charge 
from himself. Both motives might have been simul- 
taneous ; but both could not be so much the chief 
motives as to be separately worthy of standing alone. 
But the most precious inference in Newton's favour is 
that the second explanation l is demonstrably not the 
true one, and the disorder of mind which perverted 
the best-known facts may as easily, and more easily, 
have perverted the memory of impressions. Those 
letters which Newton referred to that the reader 
might consult them, for interpretation of his printed 
paragraph, had never been published, had never 
been announced, were not then likely to be published, 
and in fact never were published till 1699, thirteen 

1 In reference to both explanations, the following is remarkable. 
Just after Leibniz made his publication of 1684, a young Scotchman, 
Craig, then of Cambridge, took it up, and published a short tract upon 
the quadrature of curves, in which he uses, with high praise, the 
differential calculus of Leibniz. He had been in communication with 
Newton, had asked for help in this very subject of quadrature, and had 
received the binomial theorem, then unprinted. But not one word 
did Newton drop to the effect that he also had a method like that of 
Leibniz, and that he and Leibniz had communicated seven or eight 
years before. Craig says, long after, in 1718, that Newton examined 
the manuscript : it is clear, however, that his memory is at fault here, 
and that it was the second edition (1693) which Newton examined. Are 
we to believe that Newton was brooding over the matter of the two 
explanations, at a time when he allowed his young friend to proclaim 
Leibniz as the author of the new calculus, with that negation of himself 
which was implied in acknowledgment of assistance on another point '? 
We rather suspect that, at the time, when the geometrical form which 
is so prominent in the Principia, then on the anvil, was in his mind, 
he greatly undervalued his own fluxions. And we think they never 
would have been heard of if the mighty force which the calculus had 
developed by 1693 had not shown him how much there was to contend 
for. 



152 REVIEW OF BREWS TER'S 

years afterwards. Moreover, the letters were not 
written by Leibniz and Newton to one another, but 
by both to Oldenburg : how could the readers of 
the Principia have known what to go to ; or how 
could they have gone to the letters, if they had 
known ? The truth we suspect to be as follows : 
In 1712, when those letters were first republished, 
the second edition of the Principia was in preparation, 
and the battle of fluxions was raging : we believe 
that in 1716, all that Newton said of himself in 
reference to the first edition of the Principia must 
be referred to the Newton of the second edition. 
On any other supposition, except morbid confusion 
of ideas, Newton must be charged with worse than 
we ever believed of him. What well-read and 
practised investigator, with his mind in its normal 
state, and all his books before him, ever mistakes 
the date of first publication of any of his own works 
by thirteen years, in a deliberate answer to an 
acute opponent ? Again, Newton is quite wrong 
as to the eight months which he gives Leibniz to 
execute his alleged fraud in. His own Commercium 
Epistolicum would have taught him better. Though 
his second letter to Oldenburg (the one in question) 
was dated October the 24th, 1676, and Leibniz's 
answer June the 2ist, 1677, yet Collins informs 
Newton that the copy intended for Leibniz was in 
his hands on March the 5th, 1677, but that in a week 
it would be despatched to Hanover by a private hand. 



" MEMOIRS OF NEWTON" 153 

We are of opinion that the moral intellect of 
Newton -not his moral intention, but his power of 
judging underwent a gradual deterioration from 
the time when he settled in London. We see the 
faint traces of it in his manner of repudiation of the 
infinitesimal view of fluxions, in 1704. A man of 
sound judgment as to what is right does not 
abandon a view which he has held in common with 
a great rival, and this just at a time when the 
world is beginning to ask which came first in their 
common discovery, without a clear admission of the 
abandonment : he does not imply that some have 
held that view, and declare against the opinion of 
those some> without a distinct statement that he 
himself had been one of them : still less does he 
quietly and secretly alter what he had previously 
published, or allowed to be published, so as to 
turn the old view into the new one, and to 
leave the reader to understand that he had never 
changed his opinion. The Newton of the mytho- 
logists would have felt to his fingers' ends that 
such a proceeding had a tendency to give false 
impressions as to the case, and to throw suspicion 
on his own motives. This is a small matter, but it 
is a commencement of worse. We come to the 
Commercium Epistolicum, the name given to the 
collection of letters, accompanied by notes and a 
decision of the question, on the part of a Com- 
mittee of the Royal Society. To this well-known 



154 REVIEW OF BREWSTERS 

part of the history Sir D. Brewster has a very 
important addition to make ; and he makes it 
fairly, though we confess we wish he had given us 
what they call chapter and verse. "It is due 
to historical truth to state that Newton supplied 
all the materials for the Commercium Epistolicum, 
and that though Keill was its editor, and the Com- 
mittee of the Royal Society the authors of the 
Report, Newton was virtually responsible for its 
contents. 1 

Before we proceed further, we must address a 
respectful word to Lord Portsmouth, the descendant 
of Newton's niece, the representative of his blood, 
and the possessor of these valuable papers, to whose 
liberality and judgment the permission to publish 
their contents is due, after long concealment from 
fear of hurting Newton's reputation, and long 
abeyance from family circumstances. We submit 
to him that either too much is done, or not enough. 
Great harm arose out of the rumours which circulated 
during the period in which the papers were con- 
cealed : both the opponents and the defenders of 
Newton's conduct were, without any fault of their 
own, put in a wrong position as to interpretation of 
facts and appreciation of probabilities. Much more 

1 [See Brewster, Memoirs, 1855, vol. ii, p. 75. From a study of the 
"Portsmouth Papers," Brewster was enabled to confirm De Morgan's 
contention of 1852 that Newton wrote the anonymous preface to the 
second edition of the Commercium Epistolicum. On De Morgan's 
rather later view of Newton's character, see the second Appendix to 
this Essay.] 



"MEMOIRS OF NEWTON" 155 

harm will be done if the regretful admissions of so 
warm a partisan as Sir D. Brewster be allowed to 
stand instead of these rumours. The papers cannot 
possibly contain anything from which any such 
injury would arise as unquestionably will arise from 
the above substitution, which, to all the indefinite- 
ness of mere rumour, adds all the authority of a 
judicial decision. For when Sir D. Brewster declares 
against Newton, it is as if a counsel threw up his 
brief: we mean nothing disrespectful, for we re- 
member when we ourselves would have held it, on 
such retainers as the Principia, the fluxions, and 
the optics. Why should not these papers be 
published ? It must come to this at last. We 
have little doubt that the Government would defray 
the expense, which would be considerable : and the 
Admiralty publication of the Flamsteed papers 
would be a precedent of a peculiarly appropriate 
character. Those who were scandalised at the idea 
of the nation paying for the printing of an attack 
upon Newton would take it as reparation : while 
those who entirely approved of the proceeding would 
as heartily approve of the new measure. It is im- 
possible that the matter should rest here. Sir 
D. Brewster himself will probably desire, for his 
own sake, for that of Newton, and for that of truth, 
that these documents should undergo public scrutiny. 
And we have no delicacy in saying that they ought 
to come under the eyes of persons familiar with the 



156 REVIEW OF BREWS TER'S 

higher parts of mathematics, which Sir D. Brewster 
neither is, nor pretends to be. 1 

The Committee of the Royal Society was always 
considered in England as judicial, not as expressly 
defensive of Newton. A few years ago, Professor 
De Morgan, a decided opposer of Newton and the 
Committee in the fluxional dispute and one whose 
views Sir D. Brewster states himself to have con- 
firmed on several points rescued the objects of his 
censure from the inferences which this notion would 
lead to, and showed that the Royal Society intended 
its Committee for purposes of advocacy, and that 
the members of the Committee had no other idea 
of their own function. Sir D. Brewster says that 
Newton himself asserted this also : he does not say 
where, and this is only one of several obiter dicta 
which ought to have been supported by reference ; 
we remember no such statement. It is now of 
course perfectly settled that the Committee was not 
judicial ; and we find Newton to have been the real 
source of the materials of the Commercium Epistoli- 
cum y and answerable for all the running notes which 
accompany the published correspondence. We 
might easily proceed to justify our assertion that 
his moral intellect was undergoing deterioration : 
but, for want of space, we shall pass on to 1716, 
and shall make one extract from his letter to Conti, 

1 [For a later utterance of De Morgan's about the necessity of 
publishing the " Portsmouth Papers," see Newton ; his Friend : and his 
Niece, London, 1885, pp. 148-149.] 



"MEMOIRS OF NEWTON" 157 

in which, in his own name, he makes the assertion 
that Leibniz had stolen from him. He says that 
he had explained his ' ' method " to Leibniz, ' ' partly 
in plain words and partly in cyphers," and that 
Leibniz "disguised it by a new notation pretending 
that it was his own." His statement contains two 
untruths, which we impute to the forgetfulness of 
irritation. He did not describe part of his method 
in plain words : all that he described in plain words 
was the species of problems which he could solve. 
When Glendower said, " I can call spirits from the 
vasty deep," no one ever supposed that he "partly 
described" the "method" of doing it. Secondly, 
he did not describe the rest in cypher : he put the 
letters of his sentences into alphabetical order, and 
gave what was called an anagram. There are many 
good decypherers in the country, and the task is 
one for a mathematician : Wallis in past times, and 
Mr Babbage now, may be cited as instances. But 
no one will undertake to say what the sentence is 
which we have decomposed into the following string 
of letters : 6a 2c $d 196 2f sh $ij $kl 6n 50 8r 93 9t 
3u 2vw 3y ; ninety-three letters in all, six of which 
are a's, two are c's, etc. 

Yet a few years more, and the deterioration is 
more decided. In 1722, Newton himself wrote a 
preface and an Ad Lectorem to the reprint of the 
Commercium Epistolicum, and caused to be prefixed 
a Latin version of the account of that work which 



158 REVIEW OF BREWS TER'S 

he had inserted anonymously in the Philosophical 
Transactions for 1715. His authorship of this 
paper, constantly denied, and for very cogent 
reasons, by his partisans, but proved from evidence 
internal and external, is now admitted by Sir D. 
Brewster. Much is to be got from those documents, 
but we shall only add that a few years ago Mr De 
Morgan discovered that some alterations, one in 
particular of great importance, had been made in 
this reprint, without notice. Of .this Sir D. Brewster 
says not one word. He calls the reprint a new 
edition, which it was not : so completely doesut pro- 
fess to be only a reprint, that the old title-page, and 
the old date, are reprinted after the new title, and 
the avowedly new matter at the beginning. We 
now believe that Newton was privy to the altera- 
tions, and especially to the most important of all : 
we believe it independently of what may possibly 
arise from further scrutiny ; and we suppose from 
Sir D. Brewster's silence that he has no means of 
contradicting this natural inference. The famous 
letter of Newton to Collins, on which the Committee 
(very absurdly) made the whole point turn, was 
asserted to have been sent to Leibniz, but no date of 
transmission was given with the letter, though the 
report of the Committee affirmed a rough date of 
which nothing was said in their evidence. A date of 
transmission was smuggled into the reprint. Where 
does this date first appear ? Who first gave it ? 



"MEMOIRS OF NEWTON" 159 

Newton himself in the Philosophical Transactions, 
anonymously, and without stating any authority. 

Lastly, in the third edition of the Principia, 
Newton struck out the scholium in which he had 
recognised the rights of Leibniz. It has been 
supposed that Pemberton, who assisted him, was 
the real agent in this ' ' perhaps unwise " step : but 
it appears distinctly that Newton alone is responsible. 
He struck out this scholium ; did he state openly 
why, and let his reader know what had been done ? 
He supplied it by another scholium, beginning and 
ending in words similar to the old one, but describ- 
ing, not the correspondence with Leibniz, but the 
celebrated letter to Collins. If the old scholium 
had been misunderstood, as Newton affirms it was, 
nothing would have been more easy than to annex 
an explanation : if the suppression were done openly. 
Newton, in the second edition of the Principia, had 
revenged himself on Flamsteed by omitting Flam- 
steed's name in every place in which he could 
possibly do without it : the omission of his candid 
and proper acknowledgment of what had passed 
between himself and Leibniz was but a repetition 
of the same conduct under more aggravated circum- 
stances. Of this letter to Collins, asserted to have 
been sent to Leibniz, and falsely, as proved in our 
own day both from what was sent to Leibniz, now 
in the Library at Hanover, and from the draught 
which has turned up in the archives of the Royal 



160 REVIEW OF BREWS TER'S 

Society, we shall only say that it proved that 
Newton was more indebted to Hudde than Leibniz 
would have been to him if he had seen the letter. 
But the relations of Hudde to the two inventors 
of the differential calculus would be matter for a 
paper apart. 

VII 

To discuss every subject would require volumes ; 
and we shall therefore now pass on to Sir D. 
Brewster's treatment of the curious question of the 
relation which existed between Newton's half niece, 
Catherine Barton, and his friend and patron, 
Charles Montague, Earl of Halifax. Sir D. Brew- 
ster declares that for a century and a half no stain 
has been cast on the memory of Mrs C. Barton, and 
then proceeds to quote Voltaire's insinuation as 
scarcely deserving notice; so that by "no stain" 
we are to understand no stain which he thinks 
worthy of notice. Now the fact is that, though 
respect for Newton has kept the matter quiet, there 
has always been a general impression that it was a 
doubtful question, a thing to be discussed, whether 
or no Mrs C. Barton was the mistress of Lord 
Halifax. Mr De Morgan took up this subject in 
the Notes and Queries (No. 210), and, perfectly 
satisfied that she was either a wife or a mistress, 
came to a balanced conclusion that, as he says, 
* * the supposition of a private marriage, generally 



"MEMOIRS OF NEWTON" 161 

understood among the friends of the parties, seems 
to me to make all the circumstances take an air of 
likelihood which no other hypothesis will give them : 
and this is all my conclusion." Sir D. Brewster, 
whose mind admits no such balance, makes this 
the * ' inference " of a private marriage. The grounds 
of the alternative are that she was publicly declared, 
by the writer of the Life of Halifax, to have lived, 
when very young, and she herself distinguished by 
beauty and wit, in the house of Lord Halifax as 
"superintendent of his domestic affairs ": and this 
not in attack, but defensively, with a declaration 
that she was a virtuous woman, though " those that 
were given to censure passed a judgment upon her 
which she no ways merited." Further, Lord Halifax 
held in trust an annuity for her of 200 a year, 
bought in Newton's name : besides which he left her 
5000, with Bushy Park and a manor for life : 
while neither she nor any one of her friends con- 
tradicted the admission made in the Life of Halifax, 
which came out at the time when the legacies and 
the annuity would have turned public attention 
upon Miss Barton. This is a subject unconnected 
with mathematics ; and we dwell upon it more than 
its intrinsic importance deserves, because it will 
enable us to show to every reader the kind of 
reasoning which can be pressed into the service of 
biography, when biography herself has been tempted 

into the service of partisanship. We may judge 

u 



162 REVIEW OF BREWSTERS 

from the arguments which Sir David is driven to 
employ, that he would have followed the example 
of other biographers in slurring this subject, if Mr 
De Morgan's closing words had not reminded him 
that the day for such a suppression was past : " such 
points, relating to such men as Newton, will not 
remain in abeyance for ever, let biographers be as 
timid as they will." And we may also judge from 
these arguments why it is that the subject has been 
allowed to remain in abeyance. 

And first, as to the annuity. Halifax holds in 
trust an annuity for Miss Barton, and directs his 
executor to give her all aid in the transfer : this 
annuity was bought in Newton's name. Sir D. 
Brewster declares that "an annuity purchased in 
Sir Isaac Newton's name can mean nothing else than 
an annuity purchased by Sir Isaac Newton." This 
is an assertion of desperation it could have meant, 
not thereby saying that it did mean, a settlement 
by Halifax on Miss Barton, done in Newton's name, 
with or without Newton's knowledge ; and done in 
Newton's name purposely that people might think it 
was made by Newton, or, at least, not by Halifax. 
This may appear impossible to Sir D. Brewster in 
1855, and yet it may have been done in 1706. We 
may fairly infer that Halifax did not draw his will with 
the intention of giving colour to those reports against 
which his biographer protests, or with the intention of 
exciting such reports : if the annuity were bought by 



"MEMOIRS OF NEWTON" 163 

Newton, what more easy than to have said so? In 
spite of Sir D. Brewster, who is neither lawyer nor 
actuary, we affirm positively that the description of 
an annuity upon the life of A B as bought in the 
name of C D, does not imply that C D paid for 
it, and that so far as it implies anything on the 
point, which is little enough, it is the very contrary. 
Again, Conduitt does not mention this annuity in 
his list of the benefactions which Newton, who was 
very generous to his family, bestowed on his poorer 
relations. For this Sir D. Brewster has to find a 
reason ; Conduitt was the husband of Catherine 
Barton, knew of the assertions in Halifax's bio- 
graphy, had read Halifax's will, and must have been 
cognisant of the fact that the existence of a scandal 
had been asserted in print. And he finds a curious 
reason. 

' ' But the annuity was not a benefaction like 
those contained in Conduitt's list. It was virtually 
a debt due to his favourite niece whom he had 
educated, and who had for twenty years kept his 
house ; and if she had not received it from Sir Isaac, 
his conduct would have been very unjust, as, owing 
to his not having made a will, she got only the 
eighth part of his personal estate along with his 
four nephews and (three other) nieces." 

Let us first take Sir D. Brewster's statement, as 
here given, erroneous as it is. When a single man 
educates a favourite niece, thereby distinguishing her 
from his other nieces, and gives her shelter and main- 



1 64 REVIEW OF BREWSTER'S 

tenance until she marries (for we must here take Sir 
D. Brewster's assertion that she did not leave him to 
live with Lord Halifax), all the world knows that the 
least that favourite niece can do is to keep house for 
him, and that the idea of her services in looking after 
the dinner, which he pays for and gives her share of, 
running him into debt, actual or virtual (oh, the 
virtue of this word !), is an absurdity. No doubt a 
man ought to provide for such a niece after his 
death : but if he should leave her, as Newton did to 
Miss Barton, the eighth part of ,32,000, producing 
an income of more than 200 a year, he treats her 
very handsomely : especially if a friend of his should 
have left her a large fortune, and his introduction 
should have married her to a member of Parliament. 
Now to Sir D. Brewster's statement. Just before our 
quotation begins, he informs us that by the act of 
transference it appears that this trust was created in 
1706, so that he seems to say that Miss Barton, aged 
six years, began to keep Newton's rooms in Trinity 
College, when he was writing the Principia : for he 
says she * ' had " kept his house for twenty * years. 
He does not mean this : but here and elsewhere he 

1 Conduitt tells us that his wife lived with her uncle nearly twenty 
years, before and after her marriage : it is believed that the Conduitts 
resided with Newton from the very marriage. Newton lived in London 
thirty years ; therefore, ten or more of those years his niece did not 
live with him. The annuity was bought in 1706 and Halifax died in 
1715. Miss Barton, being sixteen years old when Newton came to 
London, must have finished her school education shortly afterwards. 
Either Newton did not invite his favourite niece, whom he had educated, 
to live with him for ten years afterwards, or there is a gap which tallies 
most remarkably with the hypothesis of her residence under the roof of 



"MEMOIRS OF NEWTON" 165 

heaps circumstances together without sufficient atten- 
tion to consistency. We very much doubt if Newton 
could have afforded the price of that annuity in 1 706. 
He came to London with very little in 1696 : by 
1 706 he had enjoyed 600 a year for four years, and 
;i 500 a year for six years. An annuity of 200 on 
a life of twenty-six, money making five per cent, 
now costs about 3000 : if we say, which is straining 
the point to the utmost, that Miss Barton's annuity 
cost 2000, we confess we think it not very 
likely that Newton could have bought it, or that he 
would have held it just to his other relatives to have 
bought so large an annuity. But we are quite sure 
that Conduitt, under all the circumstances, would 
never have held this annuity as payment of a debt 
due to his wife ; he would not have made the twenty 
years end with 1706, to speak of nothing else. 

Next, we come to the way in which Sir D. Brewster 
treats the assertions of Halifax's biographer. Those 
assertions are not in attack, but in defence ; the 
witness is a friendly one, and the publication was 
made at the very time when Halifax's will had just 
drawn public attention to the legacies. 

Halifax. But, as a presumption against the first supposition, there is 
extant a short letter from Newton to his niece, written in 1700, which 
by the contents seems written to an inmate of his house, absent for 
change of air. 

Newton has been charged with avarice ; of which there is really no 
proof, unless his dying worth more than ^"30,000 be one. But Conduitt 
was in easy circumstances, and his wife also: their daughter was said 
to have had ,60,000. Supposing, as is probable, that they bore their 
fair share of the joint expenses, Newton might have saved nearly all his 
income for the last ten years of his life. 



1 66 REVIEW OF BREWS TER'S 

"I am likewise to account for another Omission 
in the Course of this History, which is that of the 
Death of the Lord Halifax's Lady ; upon whose 
Decease his Lordship took a Resolution of living 
single thence forward, and cast his Eye upon the 
Widow of one Colonel Barton, and Neice to the 
famous Sir Isaac Newton, to be Superintendent of 
his domestic Affairs. But as this Lady was young, 
beautiful and gay, so those that were given to censure, 
pass'd a Judgment upon her which she no Ways 
merited, since she was a Woman of strict Honour and 
Virtue ; and tho' she might be agreeable to his Lord- 
ship in every Particular, that noble Peer's Com- 
plaisance to her, proceeded wholly from the great 
Esteem he had for her Wit and most exquisite 
Understanding, as will appear from what relates to 
her in his Will at the Close of these Memoirs." 

Now Sir D. Brewster is so far biased by the 
necessities of his case, as to affirm that it is not 
here stated that Miss Barton (that she had been 
married is a mistake) lived under Halifax's roof. 
" His biographer makes no such statement. . . . 
How could any person contradict the cast of an eye 
the only act ascribed to Halifax by his bio- 
grapher ? " The writer of * ' Newton " in the Bio- 
graphia Britannica as strong a partisan as Sir 
David could not get so far as this ingenious 
solution : for he makes Halifax's continuance in 
his widowed state "the less to be regretted" on 
account of this ' ' cast of an eye. " We are to infer, 
according to Sir David, that this friendly biographer, 
wishing to defend Miss Barton from censure she no 



"MEMOIRS OF NEWTON" 167 

ways deserved, and alluding to rumours which had 
no source except a "plan or a wish" of Lord 
Halifax, omitted to state that the plan was all 
Montague's eye ; and forgot to assert the very 
material circumstance that she did not accede to the 
plan, that she did not live in the house of her earnest 
admirer. We make no doubt, on the other hand, 
that the apologist means to say that she did live 
there, and made her a widow to give some colour 
of respectability to it. Her noble admirer left his 
large legacy "as a token," he writes, "of the 
sincere love, affection, and esteem, I have long had 
for her person, and as a small recompence for the 
pleasure and happiness I have had in her conversa- 
tion. " Sir D. Brewster appends a note to prove 
that love and affection "had not, in Halifax's day, 
the same meaning which they have now." Does 
he really think that they mean nothing now except 
conjugal love and its imitations ? Does not a man 
still love his friends, and might not Pope write to 
H. Cromwell now, as then, of his affection and 
esteem ? If we come to old meanings, we might 
remember that conversation did not always mean 
colloquy.^- If Miss Barton did live with Halifax 
under one roof, and if Halifax did buy the annuity, 
these words are to be interpreted accordingly. And 
they must be looked at jointly with the other things. 

1 [On the old meaning of the word "conversation," see De Morgan, 
Newton: his Friend: and his Niece, London, 1885, pp. 58-64.] 



1 68 REVIEW OF BREWSTER'S 

There Is a fallacy which has no name in books of 
logic, but is of most frequent occurrence. It is that 
because neither A, nor B, nor C, will separately 
give moral conviction of D, that therefore they do 
not give it when taken together. 

We have seen that Sir D. Brewster can omit, as 
in the case of the secret alterations in the reprint 
above mentioned : we shall now see that he can 
omit when he distinctly declares he has not omitted. 
We are far from charging him with any unfair in- 
tention : we know the effect of bias, and nothing 
disgusts us more than the readiness with which 
suppressions and misrepresentations are set down 
to deliberate intention of foul play. Sir D. Brewster 
informs us that he has given in an appendix ' ' all 
the passages " in which Swift mentions Miss Barton 
or Halifax. He has not given all. When he wrote 
this (vol. ii, p. 278), he intended to give all ; but 
when he came to the appendix, he altered his mind, 
omitted two, and forgot his previous announcement. 
It was not oversight, because Mr De Morgan had 
particularly mentioned these curious passages, in 
which Swift quotes to Stella some of Miss Barton's 
conversation, which has the freedom of a married 
woman (we mean of that day ; our matrons are 
more particular). Either the Professor, who de- 
clines to repeat the stories, is overfastidious, or is 
unskilful in rendering the license of the seventeenth 
century into the decorums of the nineteenth : we 



"MEMOIRS OF NEWTON* 169 

think we can convey an idea of the good joke over 
which Catherine Barton, aged 31, and Jonathan 
Swift, aged 43, enjoyed a hearty laugh. A man 
had died, leaving small legacies to those who should 
bear him to the grave, who were to be an equal 
number of males and females : provided always that 
each bearer, male or female, should take a declara- 
tion that he or she had always been a strict votary 
of Diana. The joke was, that there lay the poor 
man, unburied, and likely to remain so : and this 
was the joke which Miss Barton introduced, in a 
tete-a-tete with Swift ; at least so says Swift him- 
self. Mr De Morgan thinks that ' c Swift's tone 
with respect to the stories, combined with his 
obvious respect for Mrs Barton, may make any one 
lean to the supposition that he believed himself to 
be talking to a married woman." Certainly it can 
hardly be credited that the maiden niece of Newton 
(then living in Newton's house, according to Sir D. 
Brewster) would bring up such a joke for the enter- 
tainment of a bachelor friend : and Swift's great and 
obvious respect for Catherine Barton will justify us 
in thinking that he never would have invented such 
a story as coming from her. 

We do not intend to decide the question whether 
the lady was the platonic friend, the mistress, or the 
secretly married wife, of Lord Halifax : in conse- 
quence of the reserve of biographers, it has never 
been fully put forward until our own day. Further 



1 70 REVIEW OF BREWS TER'S 

research may settle it : what we have to do with is 
our biographer's mode of dealing with his case. Sir 
D. Brewster certainly handles the phenomena of 
mind and conduct as if they were phenomena of 
matter : he requires that any conclusion shall be a 
theory, which is to explain how all the circumstances 
arose. No such thing is possible in grappling with 
circumstantial evidence as to the dealings of human 
beings with one another. Never a day passes 
without the prisoner's counsel triumphantly bringing 
to notice a circumstance which is perfectly inexpli- 
cable on the supposition of his client's guilt. So 
says the judge too, and so feel the jury : and both 
parties are in a difficulty. If it were a question 
about an explanatory theory, as of light, an obstinate 
dark band or coloured fringe might put the undula- 
tions out of the question, till further showing. But 
the court asks the jury, not for their theory, but for 
their verdict : that verdict is guilty, and the prisoner 
generally confirms it, at least in capital cases, and 
explains the difficulty. The matter we have been 
discussing has two counts : the first opens the 
question whether, under the circumstances, the con- 
clusion that Miss Barton lived with Halifax can be 
avoided ; the second, on the supposition that it 
cannot be avoided, opens the question whether she 
lived with him as a mistress or as a secretly married 
wife. Sir D. Brewster works hard against the 
supposition of the marriage, and, by an ignoratio 



"MEMOIRS OF NEWTON" 171 

elenchi, believes himself to be forwarding his own 
alternative ; but we strongly suspect that his reasons 
against the marriage, be their force what it may, 
will not avail against the other alternatives of our 
second count. 1 

VIII 

We will now take the vexed question of Newton's 
religious opinions, a vexed question no more, for 
the papers so long, and, in the first instance, so un- 
worthily suppressed, are now before the world. Sir 
D. Brewster, in his former Life, followed his pre- 
decessors in stoutly maintaining orthodoxy, by which, 

1 [De Morgan made many further investigations on this subject. An 
article on Catherine Barton and Halifax was written by him in 1858 for 
The Companion to the Almanac, This article was rejected by Charles 
Knight, the editor, who thought that the question discussed in it would 
not be held generally interesting (see also Mrs De Morgan's Memoir, 
1882, p. 264). The original manuscript was revised, and received some 
additions in the years 1864-6. And, later still, on the accession of new 
evidence, it was enlarged again. It was published posthumously, under 
the editorship of his widow and his pupil A. C. Ranyard, under the 
title Newton: his Friend: andliis Niece (London, 1885). This book 
contains many digressions, most of which are interesting and some of 
which are amusing ; and De Morgan concluded that a private marriage 
between Halifax and Catherine Barton was contracted in 1706. The 
most important piece of evidence is a letter in Newton's handwriting, 
dated in May 1715, bought by De Morgan's friend Guglielmo Libri 
who was accused and proceeded against by the French government, 
unjustly it seems, of having stolen books from public libraries in France 
in 1856, which contains the sentence : " The concern I am in for the 
loss of my Lord Halifax, and the circumstances in which I stand related 
to his family, will not suffer me to go abroad till his funeral is over." 
See also Mrs De Morgan's Memoir, p. 288. Macaulay's view of the 
question was (Newton : his Friend: and his Niece, p. 70) that Catherine 
Barton was neither Halifax's mistress nor his wife, and that the relation 
between them was of the same sort as that between Congreve and Mrs 
Bracegirdle, as that between Swift and Stella, as that between Pope 
and Martha Blount, and as that between Cowper and Mrs Unwin. For 
De Morgan's view of Brewster's treatment of the Halifax case, see ibid. , 
pp. 107-130 ; the case is discussed in Brewster's Memoirs, 1855, vol. ii, 
pp. 270-281.] 



REVIEW OF BREWS TER'S 

in this article, we mean a belief of at least as much 
as the churches of England and Scotland hold in 
* common. But many circumstances seemed to point 
the other way. There was a strong and universal 
impression that Horsley had recommended the con- 
cealment of some of the "Portsmouth Papers," as 
heterodox : and here and there was to be found, in 
every generation, a person who had been allowed to 
see them, and who called them dubious, at least. 
Newton was the friend of the heretics Locke and 
Clarke, and sent abroad, for publication, writings 
on the critical correction of texts on which Trini- 
tarians relied, without a word against the conclusion 
which might be drawn respecting himself. Nay, he 
spoke of the Trinity in a manner which Sir D. 
Brewster admits would make any one suspect his 
orthodoxy. Whiston, always indiscreet, but always 
honest, declared from his own conversation with 
Newton, that Newton was an Arian ; Haynes, 
Newton's subordinate at the Mint, declared to Baron, 
a Unitarian minister, that Newton was what we now 
call a Unitarian. He himself, in the Principia, 
allowed himself a definition of the word * ' God " 
which would have permitted him to maintain the 
Deity of the second and third persons of the Trinity. 
He said that every spiritual being having dominion 
is God : Dominatio entis spiritualis Deuni constituit. 
And he enforces his definition by so many exempli- 
fications that it is beyond question he means that, 



"MEMOIRS OF NEWTON* 173 

if the Almighty were to grant some power, for only 
five minutes, to a disembodied spirit, that spirit 
would be, for that time, a God. 

In the papers now produced for the first time, 
we have certain paradoxical questions (the word 
"paradox" then meant an unusual opinion) con- 
cerning Athanasius and his followers, in which many 
historical opinions of a suspicious character are 
maintained ; but no matters of doctrine are touched 
upon. In (( A Short Scheme of the True Religion," 
the purpose is rather to describe religion as opposed 
to irreligion, and all who are conversant with opinion 
know that a Trinitarian and a Unitarian use the 
same phrases against atheism and idolatry. Hence, 
some language which in controversy would be 
heterodox, may be counted orthodox. But in 
another manuscript, "On our Religion to God, to 
Christ, and the Church," there is an articulate 
account of Newton's creed, in formal and dogmatical 
terms. This we shall give entire : and it is to be 
remembered that Newton destroyed many papers 
before his death, which adds to those he left behind 
him additional meaning and force. 

"Art. i. There is one God the Father, ever 
living, omnipresent, omniscient, almighty, the maker 
of heaven and earth, and one Mediator between God 
and man, the man Christ Jesus. 

* * Art. 2. The Father is the invisible God whom 
no eye hath seen, nor can see. All other beings 
are sometimes visible. 



174 REVIEW OF BREWS TER'S 



1 1 



Art. 3. The Father hath life in himself, and 
hath given the Son to have life in himself. 

' ' Art. 4. The Father is omniscient, and hath all 
knowledge originally in his own breast, and com- 
municates knowledge of future things to Jesus 
Christ ; and none in heaven or earth, or under the 
earth, is worthy to receive knowledge of future things 
immediately from the Father, but the Lamb. And, 
therefore, the testimony of Jesus is the spirit of 
prophecy, and Jesus is the Word or Prophet of 
God. 

"Art. 5. The Father is immovable, no place 
being capable of becoming emptier or fuller of him 
than it is by the eternal necessity of nature. All 
other beings are movable from place to place. 

"Art. 6. All the worship (whether of prayer, 
praise, or thanksgiving), which was due to the 
Father before the coming of Christ, is still due to 
him. Christ came not to diminish the worship of his 
Father. 

' * Art. 7. Prayers are most prevalent when 
directed to the Father in the name of the Son. 

' ' Art. 8. We are to return thanks to the Father 
alone for creating us, and giving us food and raiment 
and other blessings of this life, and whatsoever we 
are to thank him for, or desire that he would do for 
us, we ask of him immediately in the name of 
Christ. 

' ' Art. 9. We need not pray to Christ to intercede 
for us. If we pray the Father aright he will 
intercede. 

"Art. 10. It is not necessary to salvation to 
direct our prayers to any other than the Father in 
the name of the Son. 

"Art. ii. To give the name of God to angels or 
kings, is not against the First Commandment. To 
give the worship of the God of the Jews to angels 



"MEMOIRS OF NEWTON" 175 

or kings is against it. The meaning of the com- 
mandment is, Thou shalt worship no other God 
but me. 

' ' Art. 12. To us there is but one God, the Father, 
of whom are all things, and one Lord Jesus Christ, 
by whom are all things, and we by him. That is, 
we are to worship the Father alone as God Almighty, 
and Jesus alone as the Lord, the Messiah, the Great 
King, the Lamb of God who was slain, and hath 
redeemed us with his blood, and made us kings and 
priests. " 



In a paper called " Irenicum," or " Ecclesiastical 
Polity tending to Peace," are many remarks on 
church-government, but on doctrine only as follows. 
After insisting, in one place, that those who intro- 
duce any article of communion not imposed from 
the beginning are teaching another gospel, he gives, 
in another place, the fundamentals, by which he 
means the terms of communion imposed from the 
beginning. 

' * The fundamentals or first principles of religion 
are the articles of communion taught from the be- 
ginning of the Gospel in catechising men in order to 
baptism and admission into communion ; namely, 
that the catechumen is to repent and forsake covet- 
ousness, ambition, and all inordinate desires of the 
things of this world, the flesh, and false gods called 
the devil, and to be baptized in the name of one 
God, the Father, Almighty, Maker of Heaven and 
Earth, and of one Lord Jesus Christ, the Son of 



1 76 REVIEW OF BREWS TER'S 

God, and of the Holy Ghost. See Heb. v. 12, 13, 
14, and vi. i, 2, 3." 

In some queries on the word O/ULOOVO-LOS, Newton 
asks, among many questions of a similar tendency, 
whether unius substanticz ought not to be consubstan- 
tialis whether hypostasis did not signify substance 
whether Athanasius, etc., did not acknowledge 
three substances whether the worship of the Holy 
Ghost was not ' ' set on foot " after the Council of 
Sardica whether Athanasius, etc. , were not Papists. 
We prefer giving the reader Newton's opinions in full 
to arguing on them ourselves. It would be difficult, 
we think, to bring him so near to orthodoxy as 
Arianism. Though his exposition of his own 
opinions goes far beyond the simple terms of com- 
munion, there is not a direct word on the divinity 
of Christ, on his pre-existence, on the miraculous 
conception, on the resurrection, on the personality 
of the Holy Ghost, or on the authority of Scripture. 
Those who think that some of these points (as we 
think of the fourth and sixth) must be implied, will 
perhaps bring in the rest : but those who look at the 
emphatic first article of the twelve, unmodified and 
unqualified by the rest, though enforced by the 
eighth and ninth, will, we think, give up the point, 
and will class Newton, as Haynes did, with the 
Humanitarians, and not, as Whiston did, with the 
Arians. Sir D. Brewster leaves it to be implied 
that he does not any longer dispute the heterodoxy 



"MEMOIRS OF NEWTON" 177 

of Newton's creed ; that is, its departure from the 
creed most commonly believed by Christians. Of 
this we have no doubt, that in his theological 
opinions, Newton was as uncompromising and as 
honest as in his philosophical ones. And he was 
no dabbler in the subject, having in truth much 
reading, both as a scholar and a theologian. 1 

IX 

We cannot easily credit the story of Newton in 
love at sixty years of age. In Conduitt's hand- 
writing is a letter entitled "Copy of a letter to 
Lady Norris by . . . ," docketed, in another hand, 
"A letter from Sir I. N. to . . . ." The letter is 
amusing. After informing the lady that her grief 
for her late husband is a proof she has no objection 
to live with a husband, he advises her, among other 
things, that a widow's dress is not acceptable in 
company, and that it will always remind her of her 
loss : and that ' * the proper remedy for all these 
mischiefs is a new husband " ; the question being 
whether she ' * should go constantly in the melancholy 
dress of a widow, or flourish once more among the 
ladies." Sir D. Brewster seems rather staggered 
by this letter : but there is no authority for it 
coming from Newton, and surely we may rather 

1 [On Newton's religious opinions, see, besides XI. of the first 
Essay, above, De Morgan, Newton: his Friend: and his Niece, London, 
1885, p. 107.] 

12 



1 78 REVIEW OF BREWS TER'S 

suspect that his friend, Lady Norris, sent him, or 
perhaps Miss Barton, a copy of a letter from some 
coxcomb of a suitor. 1 Newton was always a man 
of feeling, right or wrong, and, though perhaps he 
would have been awkward at the expression of it, 
he never would have addressed a woman for whom 
he experienced a revival of what he once felt for 
Miss Storey, in such terms as the young bucks in 
the Spectator address rich widows. The letter 
reminds us much more of Addison's play, and of the 
puppy who was drummed away from the widow by 
the ghost, than of Newton. 

X 

To us it has always been matter of regret that 
Newton accepted office under the Crown. Sir D. 
Brewster thinks otherwise. " At the age of fifty, 
the high-priest of science found himself the inmate 
of a college, and, but for the generous patronage of 
a friend, he would have died within its walls. " And 
where should a high-priest of science have lived and 
died ? At the Mint ? Very few sacrifices were 
made to science after Newton came to London. 
One year of his Cambridge life was worth more to 
his philosophical reputation and utility than all his 
long official career. If, after having piloted the 

1 The original letter, written shortly after 1702, is copied in the 
handwriting of Conduitt, who did not become a member of Newton's 
family till 1717. Say that Lady Norris sent it to Mrs Conduitt, to 
amuse her, and that Conduitt copied it. 



"MEMOIRS OF NEWTON" 179 

country safely through the very difficult, and as 
some thought, impossible, operation on the coinage, 
he had returned to the University with a handsome 
pension, and his mind free to make up again to the 
"litigious lady," he would, to use his own words, 
have taken "another pull at the moon," and we 
suspect Clairaut would have had to begin at the 
point from which Laplace afterwards began. Newton 
was removed, the high-priest of science was trans- 
lated to the temple of Mammon, at the time when 
the differential calculus was, in the hands of Leibniz 
and the Bernoullis, beginning to rise into higher 
stories. Had Newton remained at hi % s post, coining 
nothing but ideas, the mathematical science might 
have gained a century of advance. 



XI 

We now approach the end of our task, and, in 
in spite of our battle with the biographer, we cannot 
express the pleasure with which we have read his 
work. It is very much superior, new information 
apart, to the smaller Life which he published long 
ago. Homer's heroes are very dry automatons so long 
as they are only godlike men : but when they get 
into a quarrel with one another, out come the points 
on which we like and dislike. Newton always right, 
and all who would say otherwise excathedrally re- 
proved is a case for ostracism ; we are tired of hear- 



1 8o REVIEW OF BREWSTERS 

ing Aristides always called the just. But Newton 
of whom wrong may be admitted, Newton who must 
be defended like other men, and who cannot always 
be defended, is a man in whom to feel interest even 
when we are obliged to dissent from his eulogist. 
As we have said before, it is the defence which pro- 
vokes the attack. Newton, with the weak points 
exposed and unprotected, is not and cannot be an 
object of assault : our blow is on the shield which 
the biographers attempt to hold before him. A 
great predecessor was guilty of delinquencies before 
which the worst error of Newton is virtue itself : he 
sold justice for bribes, so committing wilful perjury 
for who may dare to deny that the oath of the 
false judge rose before his mind when he fingered 
the price of his conscience that the perjury itself 
is forgotten in the enormity of the mode of commit- 
ting it. But how often is this remembered when 
we think of Bacon ? The bruised reed is not broken, 
because even biographers admit that it is a bruised 
reed : let them hold it up for a sturdy oak, and the 
plain truth shall be spoken whenever the name is 
mentioned. And so, in its degree, must it be with 
the author of the Principia. 

All Newton's faults were those of a temperament 
which observers of the human mind know to be in- 
capable of alteration, though strong self-control may 
suppress its effects. The jealous, the suspicious 
nature, is a part of the man's essence, when it exists 



"MEMOIRS OF NEWTON" 181 

at all : it is no local sore, but a plague in the blood. 
Think of this morbid feeling as the constant attend- 
ant of the whole life, and then say, putting all 
Newton's known exhibitions of it at their very 
worst, how much they will amount to, as scattered 
through twenty years of controversy with his equals, 
and thirty years of kingly power over those who 
delighted to call themselves his inferiors. Newton's 
period of living fame is longer than that of Welling- 
ton : it is easy to talk of sixty years, but think of 
the time between 1795 and 1855, and we form a 
better image of the duration. In all this life, we 
know of some cases in which the worst nature con- 
quered the better : in how many cases did victory, 
that victory which itself conceals the battle, declare 
for the right side ? Scott claims this allowance even 
for Napoleon ; how much more may it be asked for 
Newton ? But it can only be asked by a biographer 
who has done for the opponents of his hero what he 
desires that his readers should do for the hero him- 
self. When once the necessary admissions are made, 
so soon as it can be done on a basis which compro- 
mises no truth, and affords no example, we look 
on the errors of great men as straws preserved in 
the pure amber of their services to mankind. If we 
could but know the real history of a flaw in a 
diamond, we might be made aware that it was a 
necessary result of the combination of circumstances 
which determined that the product should be a 



1 82 "MEMOIRS OF NEWTON" 

diamond, and not a bit of rotten wood. Let a flaw 
be a flaw, because it is a flaw : Newton is not the 
less Newton ; and without the smallest rebellion 
against Locke's maxim whatever it is nobis 
gratulamur tale tantumque extitisse humani generis 
decus. 



APPENDIX I. TO THE THIRD ESSAY 
(See note i on p. 148.) 

DE MORGAN'S VIEW OF LEIBNIZ'S CHARACTER 1 

THE Leibniz of our day is either the mathematician or the 
metaphysician. 

In the first of these two characters he is coupled in the 
mind of the reader with Newton, as the co-inventor of what 
was called by himself the Differential Calculus, and by 
Newton the Method of Fluxions. Much might be instanced 
which was done by him for the pure sciences in other 
respects ; but this one service, from its magnitude as a 

1 [The following is from a biographical sketch entitled "Leibnitz" 
which appeared anonymously in the Gallery of Portraits : with Memoirs 
(vol. vi, 1836, pp. 132-136) which was published by Charles Knight 
at London under the superintendence of the Society for the Diffusion 
of Useful Knowledge. We know from Mrs De Morgan's Memoir 
(p. 108), that this article was by De Morgan. "The Life of Maske- 
lyne," she says, " is one of a series of lives of Astronomers written by him 
for the Gallery of Portraits , published by C. Knight two or three years 
before this time (1839). They are those of Bradley, Delambre, Descartes, 
Dollond, Euler, Halley, Harrison, W. Herschel, Lagrange, Laplace, 
Leibnitz, and Maskelyne. They are bound up together, and illustrated 
in his own way, under the title of ' Mathematical Biography, extracted 
from the Gallery of Portraits, by Augustus De Morgan, H.O.M.O. 
P.A.U.C.A.R.U.M. L.I.T.E.R.A.R.U.M.' The letters of his literary 
tail were only B.A., F.R.A.S., besides those expressing membership 
of one or two lesser scientific societies. On account of the declaration 
of belief at that time required by the University, he never took his M. A. 
degree." On the reference to Halley, cf. note 2 on p. 21. The extract 
printed above is on pp. 134-136 of the Gallery. The portrait of 
Leibniz given in this article is an engraving after the well-known 
picture in the Florence Gallery, which is reproduced in the Open Court 
Company's series of portraits of philosophers. ] 

183 



1 84 CHARACTER 

discovery, and its notoriety as the cause of a great con- 
troversy, has swallowed up all the rest. 

Leibniz was in London in 1673, an d from that time 
began to pay particular attention to mathematics. He was 
in correspondence with Newton, Oldenburg, and others, on 
questions connected with infinite series, and continued so 
more or less till 1684, when he published his first ideas on 
the Differential Calculus in the Leipsic Acts. But it is 
certain that Newton had been in possession of the same 
powers under a different name, from about 1665. The 
English philosopher drops various hints of his being in 
possession of a new method, but without explaining what 
it was, except in one letter of 1672, of which it was after- 
wards asserted that a copy had been forwarded to Leibniz 
in 1676. Leibniz published both on the Differential and 
Integral Calculus before the appearance of Newton's 
Principia in 1687 ; and indeed, before 1711, the era of the 
dispute, this new calculus had been so far extended by 
Leibniz and the Bernoullis, that it began to assume a shape 
something like that in which it exists at the present day. 
In the first edition of the Principia^ Newton expressly avows 
that he had, ten years before (namely, about 1677), in- 
formed Leibniz that he had a method of drawing tangents, 
finding maxima and minima, etc. ; and that Leibniz had, in 
reply, actually communicated his own method, and that he 
(Newton) found it only differed from his own in symbols. 
This passage was, n5t very fairly, suppressed in the third 
edition of the Principia^ which appeared in 1726, after the 
dispute ; and the space was filled up by an account of 
other matters. It was obvious that, on the supposition of 
plagiarism, it only gave Leibniz a year to infer, from a hint 
or two, his method, notation, and results. 

Some discussion about priority of invention led Dr 
Keill to maintain Newton's title to be considered the sole 
inventor of the fluxional calculus. Leibniz had asserted 
that he had been in possession of the method eight years 



OF LEIBNIZ 185 

before he communicated it to Newton. He appealed to 
the Royal Society, of which Newton was President, and that 
body gave judgment on the question in 1712. Their 
decision is now worth nothing ; firstly, because it only 
determined that Newton was the first inventor, which was 
not the whole point, and left out the question whether 
Leibniz had or had not stolen from Newton; secondly, 
because the charge of plagiarism is insinuated in the 
assertion that a copy of Newton's letter, as above mentioned, 
had been sent to Leibniz. Now they neither prove that he 
had received this letter in time sufficient to enable him to 
communicate with Newton as above described, or, if he had 
received it, that there was in it a sufficient hint of the 
method of fluxions. The decision of posterity is, that 
Leibniz fairly invented his own method; and though 
English writers give no strong opinion as to the fairness 
with which the dispute was carried on, we imagine that 
there are few who would now defend the conduct of their 
predecessors. Whoever may have had priority of invention, 
it is clear that to Leibniz and the Bernoullis belongs the 
principal part of the superstructure, by aid of which their 
immediate successors were enabled to extend the theory of 
Newton ; and thus Leibniz is placed in the highest rank of 
mathematical inventors. 

The metaphysics of Leibniz have now become a by-word. 
He is pre-eminent, among modern philosophers, for his 
extraordinary fancies. His monads, his pre-established 
harmony, and his best of all possible worlds, are hardly 
caricatured in the well-known philosophical novel of 
Voltaire. If any thinking monad should find that the pre- 
established harmony between his soul and body would 
make the former desire to see more of Leibniz as a meta- 
physician, and the latter able to second him, we can inform 
him that it was necessary, for the best of all possible 
universes, that Michael Hansch should in 1728 publish the 
whole system at Frankfort and Leipsic, under the title, 



1 86 CHARACTER OF LEIBNIZ 

Leibnitii Prindpia philosophica more geometrico demonstrate* ; 
and also that M. Tenneman should give an account of this 
system, and M. Victor Cousin translate the same. It is 
not easy to give any short description of the contents, nor 
would it be useful. A school of metaphysicians of the sect 
of Leibniz continued to exist for some time in Germany, 
but it has long been extinct. 

The mathematical works of Leibniz were collected and 
published at Geneva in 1768. His correspondence with 
John Bernoulli was also published in 1745, at Lausanne 
and Geneva. It is an interesting record, and exhibits him 
in an amiable light. He gives his friend a check for his 
manner of speaking of Newton, at the time when the 
partisans of the latter were attacking his own character, 
both as a man and a discoverer. He says, 1 " I thank you 
for the animadversions which you have sent me on Newton's 
works ; I wish you had time to examine the whole, which 
I know would not be unpleasant even to himself. But in 
so beautiful a structure, non ego paucis offendar maculis." 
He also says that he has been informed by a friend in 
England, that hatred of the Hanoverian connexion had 
something to do with the bitterness with which he was 
assailed; "Non ab omni veri specie abest, eos qui parum 
Domui Hanoveranae favent, etiam me lacerare voluisse; 
nam amicus Anglus ad me scribet, videri aliquibus non tarn 
ut mathematicos et Societatis Regise Socios in socium, sed 
ut Toryos in Whigium quosdam egisse." 2 

1 Ibid., vol. ii, p. 234. 

2 Ibid., p. 321. 



APPENDIX II. TO THE THIRD ESSAY 

(See note I on p. 154.) 

NOTE BY DE MORGAN ON THE CHARACTER OF NEWTON 
AND ON THE ACTIONS OF THE ROYAL SOCIETY. 1 

RECENT knowledge has recoloured the mythical portrait of 
Newton's character. He was not a simple-minded man in 
the sense propounded : he was not like the old philosopher 
who knocked his foot against a stone while he was looking 
at the stars. Though not learned in human nature, he was 
very much the man of the world. He stuck to the main 
chance, and knew how to make a cast. He took good care 
of his money, and left a large fortune, though very even 
magnificently liberal on suitable occasions, especially to 
his family. He was observant of small things, as are all 
men of suspicious temperament; and he had a strong 
hatred of immorality, whether in word or deed, which no 
doubt would have turned his acuteness of observation, and 
his tendency to suspicion, upon anything from which infer- 
ence could have been drawn. Those who imagine that 
Newton was always thinking of gravitation might just as 
well imagine that Wellington was always thinking of 
strategy. The following description applies to both. After 
this (the Prindpia or Waterloo, according to the person 
thought of), he lived about forty years, during which his 
attention to what had been his main pursuit was inter- 

1 [This Appendix is extracted from De Morgan's book, Newton : 
his Friend: and his Niece (London, 1885, the first paragraph on 
pp. 70-71, and the rest on pp. 130-136), which was, for the most part, 
written in 1858 (see note I on p. 171).] 

187 



1 88 ON NEWTON AND 

mittent and casual, and rather directive of others than 
executive. He had a new career before him, in which 
again he was eminently successful ; and in the last years of 
his life he was of all his contemporaries the most famous 
and the most respected. 

It was in Britain the temper of the age, before Baily's 
Life of Flamsteed rudely broke in upon the illusion, to take 
for granted that Newton was human perfection. There is 
a class in this country which has a perennial 1 existence 
among all that is middle, from nobility down to handicraft ; 
into both of which it throws its shoots. It is a respectable 
class : it can truly be described as so respectable, you can't 
think ! It is a useful class ; it is part of the ballast of our 
good ship ; and though our middle ranks furnish a much 
larger percentage of that which is ballast and cargo, both, 
yet no ballast is useless. Who does not know the smug 
individual of this species, as he sees him picking his way 
through the world ? His highest model is aristocracy ; his 
social life is silver-forkery ; his main pursuit is money- 
grubbery ; and his whole religion is Sunday-prayery. This 
is the complete specimen, fit for the museum ; but the 
characteristics are variously interfused through an immense 
mass, often lost in other and better features, except to a 
close observer. This class is, in every case in which its 
members knew the name of Newton, the one in which you 
were safe to be reckoned as in the broad way if you imputed 
anything wrong to the man who bore that name at the 
Mint a position which was mysteriously connected with 
wonderful discoveries in the heavens. 

" And, so you think that Newton told a lie ; 
Where do you hope to go to when you die ? " 

By help of this class, without which the man of science 
could not have put Newton on the pedestal which had been 
made for him, it was practicable to allow what had the 

1 [" Percential '' is misprinted in the original.] 



THE ROYAL SOCIETY 189 

clearest appearance of a direct and deliberate falsehood on 
Newton's part to stand unexamined for more than a century. 
Newton, in his final conflict with Leibniz, declared that the 
decision at the Royal Society against Leibniz had been 
voted by a " numerous committee of gentlemen of different 
nations." The world was never told of more than six, all 
British subjects of English mother-tongue; no list of the 
committee was published with the decision. Here was, to 
all appearance, if not a falsehood, worse the evasion of 
calling the English, Scotch, etc., different nations in refer- 
ence to a dispute between Britain and the Continent. If 
the faith in Newton had been anything but a formula, some 
would have reasoned thus: " Newton could not be false : 
he says the committee had members of different nations ; 
let us look at the minute-books of the Royal Society, and 
find them out." But this was not thought necessary. I 
had long been puzzled with this statement of Newton's ; 
though I knew him to be capable of being betrayed by the 
necessities of his case into that culpable evasion in which 
self-love finds excuse, I did not believe that his principles 
would allow him directly and wilfully to falsify a fact ; or 
that his acuteness would allow him to do it on so small a 
matter and to so little purpose. It chanced to me, in 
1845, to look at a Life of De Moivre of the rarest character, 
by his friend Dr Matthew Maty, Sec., R.S. I never saw 
more than one separate copy ; but I long afterwards found 
it in the Journal Britannique for 1755 a French journal, 
published in England by the "little black dog," as Sam 
Johnson called him Maty himself. Here I found eleven 
members named, two of them aliens De Moivre himself 
and Bonet the Prussian minister. And though they were 
the only two foreigners, yet De Moivre was a host: the 
only one among the rest who was fit to stand up against 
him for one moment on a mathematical question was 
Halley. On application to the Royal Society, the facts 
were verified immediately : the six who have passed for the 



190 ON NEWTON AND 

whole were those first appointed ; the remaining five were 
added piecemeal in the five weeks following the first 
nomination. 

I drew up a few words on this discovery, and sent them 
to the Royal Society. I thought they would be a charta 
volans for the Proceedings, etc. To my very great surprise 
they were printed in all the dignity of the Philosophical 
Transactions, in which no historical paper has ever appeared, 
that I know of certainly none within the century. But 
the matter concerned the character of Newton. The little 
bit of two and three-quarter pages, with the facts about the 
Committee and some anecdote as how, for instance, 
Newton said nothing but his age prevented him from 
having "another pull at the moon" looks curious among 
the elaborate mathematical and physical papers. This is so 
far a mere anecdote : it takes meaning in connexion with 
what follows. 

About a year after the preceding paper was sent, some of 
those accidents, by which those who are prepared can snap 
surmises, as well as facts, led me to a surmise that perhaps 
the reprint (1722) of the Commercium Epistolicum (1712) 
as the work containing the reasons and decisions of the 
above-named Committee is called had not been quite 
fairly made. I say reprint, not second edition ; for the very 
title-page was reprinted with the old date, after the avowedly 
new matter and a new title over all, which amounted to the 
most positive declaration that not a comma was intentionally 
changed. I had no copy of the first edition, so I applied to 
the Council of the Royal Society for the loan of their copy, 
stating why I wanted it The request was instantly granttd ; 
and I found, on examination, that some alterations had been 
made, of which some were decidedly unfair in matter, all 
being of course unjustifiable under the old date and without 
notice. The worst among them was, that whereas the old 
Committee did not -say precisely, in the evidence, when the 
letter on which the most depended was forwarded to Leibniz, 



THE ROYAL SOCIETY \gi 

a date for this transmission was foisted into the reprint. It 
ought to be said that the notions of the literary world, 1 in 
that day, about the sanctity of documents were by no means 
so rigid as they are now ; so that what, done by one of us, 
would be sheer rascality, may be let off with a much softer 
name. I drew up an account of the alterations, and sent 
it to the Royal Society ; to have sent it elsewhere would 
have been to say, in effect, that though I knew the Society 
would go out of the way to clear the fame of Newton, I 
could not trust them to clear their own wrong to Leibniz. 
That they had some hand in it was clear from the reprint 
having cuts from the old wood blocks which were the 
property of the Society. The Society proved itself worthy 
of the reflection which I could not venture to cast; it 
declined to print the second paper. I gathered that the 
council thought it would be necessary to submit my paper 
and the documents to a special committee of examination. 
The documents were two printed books, and the question 
was whether certain passages in one book were accurate 
reprints of certain passages in the other ; and if not, how 
they differed. I have no doubt the real reason was, that in 
the paper was seen danger of danger to Newton's character. 
I afterwards saw a published reason, of which I was not 
cognisant at the time, for .thinking that Newton himseli 
was the editor of this reprint, and the writer of the preface 
which preceded the old title. Sir D. Brewster, from the 
" Portsmouth Papers," found that I was quite right. When 
I made this last discovery, it crossed my mind for one 
moment that the fact was known in the Council of the 
Royal Society, and the refusal to investigate the question 
was in part the consequence of disinclination to bring it 
out. But this notion took no root; I soon felt satisfied 
that, whatever unconscious bias might do, there was no 
reason to fear a definite intention to suppress a definite 
fact. And further, so small and so inexact is the know- 
1 ["Word" is misprinted in the original.] 



192 ON NEWTON AND 

ledge of the history of science among scientific men, that 
I could easily imagine not one single person on the council 
knew so much as that there had been a reprint, much less 
that Newton's active share in the reprint had been matter 
of discussion, of affirmation, and denial. 

I applied for permission to withdraw the paper, hoping 
thus to nullify the proceedings in form at least. But the 
laws of the Society prevent the withdrawal of any communi- 
cation which has undergone adjudication ; hence this little 
matter must have its little place in the history of the 
Society, and its somewhat larger place in mine. A copy 
would have been allowed me if I had requested it ; but I 
preferred to write another paper, and to request its insertion 
in the Philosophical Magazine (June, 1848). 

One testimony to the significance of the variantes is that 
of Sir D. Brewster, who holds it wise to omit all mention of 
them. After my paper, which I took care he should have, 
and with full knowledge of the new work being reprinted 
under the old date> he calls it " a new edition with notes, a 
general review of it and a preface of some length." x He 
did not even give the true date (1722), but sticks by that 
of the second title-page (1725). This is of some conse- 
quence; for three years, at Newton's age, then made a 
difference in the palliation which years and infirmity may 
be made to give. But it must be remembered that persons 
unused to bibliography are often not even aware of the 
distinction between a reprint and a new edition. 

I freely and unreservedly blame the Council of the Royal 
Society collectively, of course for not printing the account 
of the variations mentioned above ; they missed a golden 
opportunity. They might have shown that the beautiful 
edition of the Commercium Epistolicum, published in 1856, 
by Biot and Lefort, at the expense of the French Govern- 
ment, "avec 1'indication des variantes de 1'edition de 1722," 
would have recorded that these variantes were first made 
1 [Brewster, Memoir s> 1855, vol. ii, p. 75.] 



THE ROYAL SOCIETY 193 

\ 

known by the Royal Society itself, the body which was 
most concerned in the publication of them. Considered as 
an act of reparation, the opportunity is lost, and the revela- 
tions of the "Portsmouth Papers" and of those of Leibniz 
have left little chance of another. The Royal Society, in 
this matter, reminds one much of those old managers of the 
impeachment, who, when Warren Hastings, many and 
many a year after his acquittal, appeared before a House 
of Commons, the members of which rose and uncovered at 
his retirement, remained sitting with their hats on, to show 
their sullen consistency. As a question of curiosity, I 
asked myself whether Leibniz ever found as stubborn an 
adherent in spite of all that could be learnt? I could not 
remember such a thing in real life, but the optimist of 
Voltaire's fiction hits the case exactly : " * Eh bien ! mon 
cher Pangloss,' lui dit Candide, 'quand vous avez e*te 
pendu, disseque, roue de coups, et que vous avez rame aux 
galeres, avez-vous toujours pense que tout allait le mieux du 
monde?' 'Je suis toujours de mon premier sentiment,' 
repondit Pangloss ; 'car enfin je suis philosophe; il ne me 
convient pas de me dedire. Leibnitz ne pouvant pas avoir 
tort. , 



1.3 



INDEX 



Achilles, 120. 
Adams, J. C., 6, 21, 105. 
Addison, 178. 
Anne, Queen, 35. 
Antitrinitarian, 55, 58, 59. 
Arabians, 107. 
Arbuthnot, 27. 
Archimedes, 23, 107, 121. 
Ariam'sm, 54, 55, 57, 176. 
Arians, vii, 53, 56, 172, 176. 
Aristides, 180. 
Aristotle, 48. 

Arithmetic, universal, 13, 16. 
Aston, Francis, 27, 132, 134. 
Athanasius, 176. 
Atticus, 122. 

Babbage, Charles, 157. 
Bacon, Francis, 128, 180. 
Baily, Francis, v, 40, 143, 188. 
Ball, W. W. Rouse, 4, 7, 13, 19, 

20, 23, 103. 
Baptists, 55. 

Barbara (syllogism), 130. 
Baron, Richard, 55, 58, 172. 
Barrow, Isaac, 9, II, 12, 24, 29, 

73, 83, 104, 107, 109, 1 10, 

112, 131. 
Barton, Catherine, 6, 34, 160 ff., 

178. 

Colonel, 6, 166. 
Robert, 6. 

Beman, W. W., 103. 
Bentley, Richard, 15, 1 6. 
Bernoulli, James, 72. 
John, 28, 30, 32, 33, 72, 101, 

112, 186. 
Nicolaus, 72. 
Bernoullis, the, 26, 72, 88, 107, 

179, 184. 



Binomial Theorem, 24, 25. 
Biot, Jean Baptiste, ix, 3, 58, 

123, 192. 

Blount, Martha, 171. 
Bohn, Henry G , v. 
Bonet, 27, 189. 
Boreili, 18. 
Boswell, James, 133. 
Bouillaud, 18, 52. 
Boyle, Robert, 15. 
Bracegirdle, Mrs, 171. 
Bradley, James, 183. 
Brahe, Tycho, 18. 
Brewster, Sir David, ix, xiii, 3, 5, 

6, 7, 8, 10, n, 12, 15, 17, is. 

34, 43, 44, 56, 58, 68, 85, 

104, 107, 108, 109, no, 115, 

117, 119, 122, 124, 125, 127, 
128, 131, 132, 134, 135, 138, 
139, 141, 142, 143, 144, 146, 
147, 148, ISO, 154, 155, 156, 

158, 160, 161, 162, 163, 164, 
165, 166, 167, 168, 169, 170, 
171, 172, 176, 177, 178, 191, 
192. 

Brill, A., 109. 

Brougham, Lord, 3. 

Brunschvicg, Leon, 106. 

Burgess, Bishop, 60. 

Burnet, 27. 

Csenopolis, 121. 
Cajeti (syllogism), 130. 
Calculus, differential, 23 ff., 71, 

94, 95 ff- 
Cambridge, University of, 6, 9, 

10, 13. 

Candide, 193. 
Cantor, Moritz, viii, 103, 107, 

109, no, 112, 114. 



194 






INDEX 



195 



Cassini, 42. 

Cavalieri, Bonaventura, 96, 107, 

121, 146. 

Cdarent (syllogism), 130. 
Chalmers, Dr, 57. 
Chamberlayne, 86. 
Charles II., 13. 
Cheyne, Dr, 89, 96. 
Christianity. Newton and, vii, 

53 ff- 
Cipher, Newton's fluxional, 25 fF., 

93, 157- 

Clairaut, Alexis Claude, 61, 179. 
Clarke, Samuel, 43, 55, 59. 
Cobbett, 128. 
Collins, John, 12, 24, 28, 29, 31, 

70, 7i, 72, 73 74, 75, 78, 

79, 80, 82, 83, 8 4} 85, 87, 
106, 109, no, in, 152, 158, 

159- 

Colson, John, 1 10. 
Commerchtm Epistolicum, viii, 

28, 39, 68, 71, 75, 78, 79, 

80, 82, 87, 115, 152, 153, 

154, I5 6 > J 57, 190, 192. 
Committee of Royal Society, 27, 

68, 100, 153 ff., 190. 
Conduitt, 5, 6, 130, 131, 141, 163, 

164, 165, 177, 178. 
Mrs, 178. 
Congreve, 171. 
Conti, Abbe, 30, 31, 33, 77, 106, 

156. 

Copernicus, 139. 
Cotes, Roger, 3, 6, 35, 73, 74, 

96, 104. 

Cousin, Victor, 186. 
Covel, Dr, 133. 
Cowper, 171. 

Craig, John, 88, 89, 96, 151. 
Crompton, Samuel, xi. 
Cromwell, H., 167. 

Oliver, 129. 
Curvity, radius of, 1 1. 
Cyprian, 58. 



Dafenes (syllogism), 130. 
Daniel, prophecies of, 16, 53. 
Dary, Michael, no. 
Delambre, 183. 



I De Moivre, Abraham, 27, 50, 89, 

96, 189. 
J De Morgan, Augustus, v, vi, vii, 

viii, ix, x, xiii, 3, II, 21, 34, 

48, 63, 68, 96, 101, 102, 104, 

108, 154, 156, 158, 160, 162, 

167, 1 68, 169, 171, 177, 183, 

187. 
Mrs, v, vi, vii, ix, 21, 37, 104, 

148, 171, 183. 
Descartes, Rene, 10, 11, 18, 24, 

37, 61, 107, 112, 113, 128, 

I3i> 183. 

Diamond, Newton's dog, 14. 
Diana, 169. 
Differential Calculus (see Calculus 

and Fluxions). 
Dollond, 183. 
Duillier, Fatio de, 27, 96, 112. 

Edleston, J., 3, 7. 9, 12, 13, 35, 
42, 73> 77, 78, 104, 108, 109, 

IIO, III, 112, 114, 131. 

Ekins, Dr, 16. 

Erasmus, 58. 

Euclid, 9, 10, n, 107, 127, 128. 

Euler, Leonhard, 107, 183. 



Fecana (syllogism), 130. 
Fermat, Pierre de, 29, 107, 112, 

121, 146. 
Fink, Karl, 103. 
"Firstrede, Prof.," 121. 
Flamsteed, John, v, 39, 40, 41, 

42, 43, 104, 143, 141, 155, 

159, 1 88. 
Fluxional controversy, viii, xiii, 

27 ff., 67 ff., U4ff., 144 ff. 
Fluxions, vii, n, 16, 23 ff., 67 ff. , 

89, 130, 149. 
Fontenelle, 3, 5, 6. 
French Academy, 78. 



Gadaco (syllogism), 1 30. 
Galileo, 18, 123. 
Galloys, 72. 
George I., 31, 35. 
George II., 35. 
George, Prince, 143. 



INDEX 



Gerhardt, Carl Immanuel, vii, 67, 

71,72,96,97, 102, 105, 106, 

114, 115. 

Giordano, Vitale, 72. 
Glendower, 157. 
Gordon, Thomas, 55. 
Grandi, Guido, 72. 
Gravitation, Newton's theory of 

universal, 18 ff, 51-53, 138 ff. 
Gray, G. J., x, 3, 7, 16, 103, 105, 

109, no, 115. 
Gregory, James, 5, 29, 70, 72, 73, 

74, 75, 78, 79, 83, 1 10. 
Guhrauer, G. E., 106. 

Hales, 95. 

Halifax, Earl of, 6, 34, 160 ff. 

Halley, Edmund, 21, 22, 23, 27, 

38, 41, 48, 50, 96, 138, 139, 

141, 183, 189. 
Hansch, Michael, 185. 
Harris, John, 90, 96. 
Harrison, 183. 
Hastings, Warren, 193. 
Hayes, Charles, 90, 91, 96. 
Haynes, Hopton, 55, 57, 58, 172, 

176. 

Hebare (syllogism), 130. 
Hector, 122. 
Hercules, 120. 
Herschel, W., 183. 
Hill, 27. 
Homer, 179. 
Hooke, Robert, 17, 18, 20, 22, 

23. 139- 

Hopital, de 1', 48, 72, 88, 89, 90, 

91. 

Horace, 125. 
Horsley, Samuel, 15, 16, 54, 57, 

58, 108, 109, 172. 
Hudde, 73, 85, 87, 107, 146, 160. 
Humanitarians, vii, 53, 55, 176. 
Hutton, Charles, 69, 95. 
Huygens, Christian, x, 15, 18, 19, 

72, 107. 

Infinite Series, Method of, n. 
Infinitesimal Calculus (see also 

Calculus and Fluxions), vii. 
Infinitesimal view of fluxions, 

89 ff. 



Jacobites, 30. 
James I., 5. 
James II. , 13, 133. 
Jerome, 57. 
Johnson, Samuel, 189. 
Jones, Sir W., 27, 108, 
Jupiter, 123. 
Juvenal, 125. 

Kaleidoscope, 123. 

Keill, John, vii, 27, 28, 79, 87, 

154- 

Kepler, 9, 18, 19, 107. 
Kinckhuysen, 107, 109, in. 
Kirmansegger, Baron, 30. 
Knight, Charles, v, 67, 171, 183. 
Kowalewski, Gerhard, no, 114. 

Lagrange, Joseph Louis, 107, 183. 

Laplace, 179, 183. 

Le Clerc, 58, 60. 

Lefort, 192. 

Leibniz's character, 151, 183 ff. 

Leibniz, Gottfried Wilhelm, v, 
vii, viii, ix, x, xiii, 24, 25, 26, 
27,28,29, 30.31,32,34,35, 
39, 40, 44, 49, 68,69,70,71, 
72, 73, 74, 75,76,77,78, 79, 
80, 81, 82, 84,85, 86,87, 88, 

89, 9i, 92, 93, 94, 95, 96, 97, 
98, 99, 100, 101, 102, 103, 
106, 107, in, 112, 113, 114, 

115, 121, 143, 144, 145, I 4 6, 

147, 148, 149, 150, 151, 152, 

157, 159, 160, 179, 183, 184, 
185, 186, 189, 190, 191, 193. 

manuscripts of, 67, 96 ff., 1 12 ff. 

metaphysics of, 185. 
Le Verrier, U. J. J., 21. 
Liveing, G. D., 6, 105. 
Locke, John, 35, 46, 58, 59, 182. 
Lowthorp, J., 84. 
Luard, H. R., 6, 105. 
Lymington, Viscount, 6. 
Lynn, W. T., 3. 

Macaulay, Thomas ] Babington, 

8^171. 

Macclesfield, Earl of, 83, 104. 
Mach, Ernst, 4, 19. 
Machin, 27. 



INDEX 



197 



Maclaurin, 107. 
Martin, Benjamin, 3. 
Mary, Queen, 133. 
Maskelyne, 183. 
Maty, Matthew, 189. 
M'Cormack, T. J., 4. 
Mercator, Nicolas, 107. 
Middle Ages, 107. 
Montague, Charles {see also Hali- 
fax), 34, 1 60, 167. 
Motte, Andrew, 16. 
Mouton, Gabriel, 69. 

Napoleon, 181. 

Newton, Sir Isaac, v, vi, vii, viii, 

ix, x, xi, xiii, 68, 69, 70, 72, 

73, 74, 75, 77,' 78, 79, 80, 

81, 82, 83, 84, 85, 87, 88, 

89, 90, 91, 92, 93, 94, 96, 

97, 100, 102, 103, 104, 105, 

106, 1 08, 109, no, in, 112, 

113, 114, 115, 184, 185, 186. 

biography of, 3-63, 119-182. 

character of, 4, 36 ff., 134, 

156 ff., i8off., 187 ff. 
Isaac, his father, 4. 
John, 5. 

manuscripts of, viii, 7, 67, 107 ff. 
religious beliefs of, vi, 171 ff. 
theological writings of, 53 ff. 
Nieuwentiit, 107. 
Noether, M., 109. 
Norris, Lady, 177, 178. 

Oldenburg, Henry, 24, 25, 27, 

29, 3 2 > 70, 71, 73, 74, 78, 
79, 81, 89, 92, 100, 106, 
no, in, 152, 184. 
Optics, Newton's work on, 16 ff., 
43, 137- 

Paget, 22. 

Pangloss, 193. 

Pappus, 107. 

Pascal, Blaise, 107, 112. 

Peacock, George, 138. 

Pemberton, Henry, 36, 40, 43, 

1 10, 131, 159. 
Pepys, Samuel, 133. 
Pericles, 122. 
Pertz, G. H., 72. 



Picard, 26. 
Pilkington, 6. 
Pope, Alexander, 167, 171. 
Portsmouth, Earl of, 6, 105, 154. 
Portsmouth Papers, 6, 54, 125, 
126, 135, 154, 156, 172, 191, 

193- 
Pound, 43. 
Priestley, Joseph, 57. 
Principia, Newton's, 9, 15, 16, 

18, 22, 23, 26, 31, 32, 33, 

34, 35, 36, 39, 4i, 43, 5, 
60, 61, 88, 89, 96, 104, 128, 
13, 13 1 . !3 2 , 138, 140, 148, 
IS 1 . !52, 155, 159, 164, 172, 
1 80, 187. 
Pryme, de la, 14. 

Ranyard, A. C., 171. 

Raphson, Joseph, 31, 69, 93, 102, 
103, 108, 109, 149. 

Renascence, 107. 

Ricci, 83. 

Rigaud, Stephen Jordan, 104. 
Stephen Peter, 4, 20, 94, 96, 
97, 102, 103, 104, 108. 

Robarts, 27. 

Roberval, G. P., 107. 

Robins, 109. 

Romulus, 122. 

Rosenberger, Ferdinand, 4, 15, 
17, 18, 27, 105, 107, 109, 
no, 112, 114. 

Royal Society, vii, ix, x, xiii, 7, 
15, 16, 17, 20, 22, 24, 27, 
28, 35, 38, 41, 44, 47, 54, 
56, 68, 70, 71, 74, 75, 77, 
81, 84, 86, 89, 100, 112, 

135, i3 6 ' !39, H7, 153, 156, 
160, 186, 187, 189, 190, 191, 
192, 193. 

Sanderson, 9, 129. 
Sangrado, 132. 
Sardica, Council of, 176. 
Schooten, F. van, n, 107. 
Scott, Sir Walter, 181. 
Scriven, E., x. 
Shakspere, 119. 
Sharp, Abraham, v. 
Sherlock, 59. 



198 



INDEX 



Sloman, H., 115. 

Sluse, 73, 81, 82, 83, 84, 85, 87, 

98, 107, no. 
Smith, Barnabas, 5. 

David Eugene, 103. 

Hannah, 6. 
Socinians, vii, 53. 
South, Sir James, 59. 
Stella, 1 68. 

Stewart, John, 109, 1 10. 
Stokes, G. G., 6, 105. 
Storey, Miss, 7, 22, 178. 
Stourbridge fair, q. 
St. Vincent, Gregory of, 107, 112. 
Subsizar, 8. 
Suisset, 130. 
Swift, Jonathan, 43, 168, 169. 

Tangents, drawing of, n. 
Taylor, Brook, 107. 
Teignmouth, Lord, 108. 
Tenneman, 186. 
Thomson, Dr, 54. 
Torricelli, E., 107. 
Tracts, Unitarian, 54. 
Trinitarians, vii, 53, 57, 58, 59. 
Trinity College, Cambridge, 6, 8, 

121, 127, 164. 
Tschirnhaus, E. W. von, 72, 74, 

79, 1 06, in, 113. 
Tumor, Edmund, 5, 7. 



Unitarians, 53, 55, 57, 59, 172, 

173- 

Unwin, Mrs, 171. 
Uranus, 21. 
Uvedale, Robert, 11. 

Valerius, 107. 
Vanderbank, x. 
Varignon, Pierre, 72. 
Vieta, ii. 
Vincent, Dr, 22. 
Voltaire, 160, 185, 193. 

Wallis, John, n, 12, 24, 26, 59, 
72, 82, 85, 89, 90, 91, 92 tf., 
104, 107, 1 10, in, 121, 157. 

Wallop, 6. 

Ward, Seth, 13. 

Weissenborn, Hermann, 105, ii_). 

Weld, 68, 86. 

Wellington, Duke of, 181, 187. 

Wetstein, 58. 

Whiston, William, v, 13, 35, 39, 
44, 55, 56, 57, 59, 172, 176. 

William III., King, 43, 53, 133. 

Wilson, 109. 



Young, Thomas, 137, 138. 
Zendrini, J2. 



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