October 18, 1862. _Correspondence of Scientific Men of the Seventeenth
Century, in the Collection of the Earl of Macclesfield._[483] 2 vols.
(Oxford, University Press.)
Though the title-page of this collection bears the date 1841, it is only
just completed by the publication of its Table of Contents and Index.
Without these, a work of the kind is useless for consultation, and cannot
make its way. The reason of the delay will appear: its effect is well known
to us. We have found inquirers into the history of science singularly
ignorant of things which this collection might have taught them.
In the same year, 1841, the Historical Society of Science, which had but a
brief existence, published a collection of letters, eighty-three in number,
edited by Mr. Halliwell,[484] of English men of science, which dovetails
with the one before us, and is for the most part of a prior date. The two
should be bound up together. The smaller collection runs from 1562 to 1682;
the larger, from 1606 to past 1700. We shall speak of the two as the Museum
collection and the Macclesfield collection. And near them should be placed,
in every scientific library, the valuable collection published, by Mr.
Edleston,[485] for Trinity College, in 1850.
{297}
The history of these letters runs back to famous John Collins, the
attorney-general of the mathematics, as he has been called, who wrote to
everybody, heard from everybody, and sent copies of everybody's letter to
everybody else. He was in England what Mersenne[486] was in France: as
early as 1671, E. Bernard[487] addresses him as "the very Mersennus and
intelligence of this age." John Collins[488] was never more than accountant
to the Excise Office, to which he was promoted from teaching writing and
ciphering, at the Restoration: he died in 1682. We have had a man of the
same office in our own day, the late Prof. Schumacher,[489] who made the
little Danish Observatory of Altona the junction of all the lines by which
astronomical information was conveyed from one country to another. When the
collision took place between Denmark and the Duchies, the English
Government, moved by the Astronomical Society, instructed its diplomatic
agents to represent strongly to the Danish Government, when occasion should
arise, the great importance of the Observatory of Altona to the
astronomical communications of the whole world. But Schumacher had his own
celebrated journal, the _Astronomische Nachrichten_, by which to work out
part of his plan; private correspondence was his supplementary assistant.
Collins had only correspondence to rely on. Nothing is better known than
that it was Collins's collection which furnished the materials put forward
by the Committee of the Royal Society in 1712, as a defence of Newton
against the partisans of Leibnitz. The noted _Commercium Epistolicum_ is
but the abbreviation of a title which runs on with "D. Johannis Collins et
aliorum ..."
The whole of this collection passed into the hands of {298} William
Jones,[490] the father of the Indian Judge of the same name, who died in
1749. Jones was originally a teacher, but was presented with a valuable
sinecure by the interest of George, second Earl of Macclesfield, the mover
of the bill for the change of style in Britain, who died President of the
Royal Society. This change of style may perhaps be traced to the union of
energies which were brought into concert by the accident of a common
teacher: Lord Macclesfield and Lord Chesterfield,[491] the mover and the
seconder, and Daval,[492] who drew the bill, were pupils of De Moivre.[493]
Jones, who was a respectable mathematician though not an inventor,
collected the largest mathematical library of his day, and became possessor
of the papers of Collins, which contained those of Oughtred[494] and
others. Some of these papers passed into the custody of the Royal Society:
but the bulk was either bequeathed to, or purchased by, Lord Macclesfield;
and thus they found their way to Shirburn Castle, where they still remain.
A little before 1836, this collection attracted the attention of a
searching inquirer into points of mathematical history, the late Professor
Rigaud,[495] who died in 1839. He examined the whole collection of letters,
obtained Lord Macclesfield's consent to their publication, and induced the
Oxford Press to bear the expense. It must be particularly remembered that
there still remains at Shirburn Castle a {299} valuable mass of
non-epistolary manuscripts. So far as we can see, the best chance of a
further examination and publication lies in public encouragement of the
collection now before us: the Oxford Press might be induced to extend its
operations if it were found that the results were really of interest to the
literary and scientific world. Rigaud died before the work was completed,
and the publication was actually made by one of his sons, S. Jordan
Rigaud,[496] who died Bishop of Antigua. But this publication was little
noticed, for the reasons given. The completion now published consists of a
sufficient table of contents, of the briefest kind, by Professor De Morgan,
and an excellent index by the Rev. John Rigaud.[497] The work is now fairly
started on its career.
If we were charged to write a volume with the title "Small things in their
connection with great," we could not do better than choose the small part
of this collection of letters as our basis. The names, as well as the
contents, are both great and small: the great names, those which are known
to every mathematician who has any infusion of the history of his pursuit,
are Briggs,[498] Oughtred, Charles Cavendish,[499] Gascoigne,[500] Seth
Ward,[501] Wallis,[502] {300} Hu[y]gens,[503] Collins,[504] William
Petty,[505] Hooke,[506] Boyle,[507] Pell,[508] Oldenburg,[509]
Brancker,[510] Slusius,[511] Bertit,[512] Bernard,[513] Borelli,[514]
Mouton,[515] Pardies,[516] Fermat,[517] Towneley,[518] Auzout,[519] {301}
D. Gregory,[520] Halley,[521] Machin,[522] Montmort,[523] Cotes,[524]
Jones,[525] Saunderson,[526] Reyneau,[527] Brook Taylor,[528]
Maupertuis,[529] Bouguer,[530] La Condamine,[531] Folkes,[532]
Macclesfield,[533] {302} Baker,[534] Barrow,[535] Flamsteed,[536] Lord
Brounker,[537] J. Gregory,[538] Newton[539] and Keill.[540] To these the
Museum collection adds the names of Thomas Digges,[541] Dee,[542] Tycho
Brahe,[543] Harriot,[544] Lydyat,[545] Briggs,[546] Warner,[547] Tarporley,
Pell,[548] Lilly,[549] Oldenburg,[550] Collins,[551] Morland.[552]
{303}
The first who appears on the scene is the celebrated Oughtred, who is
related to have died of joy at the Restoration: but it should be added, by
way of excuse, that he was eighty-six years old. He is an animal of extinct
race, an Eton mathematician. Few Eton men, even of the minority which knows
what a sliding rule is, are aware that the inventor was of their own school
and college: but they may be excused, for Dr. Hutton,[553] so far as his
Dictionary bears witness, seems not to have known it any more than they. A
glance at one of his letters reminds us of a letter from the Astronomer
Royal on the discovery of Neptune, which we printed March 20, 1847. Mr.
Airy[554] there contends, and proves it both by Leverrier[555] and by
Adams,[556] that the limited publication of a private letter is more
efficient than the more general publication of a printed memoir. The same
may be true of a dead letter, as opposed to a dead book. Our eye was caught
by a letter of Oughtred (1629), containing systematic use of contractions
for the words _sine_, _cosine_, etc., prefixed to the symbol of the angle.
This is so very important a step, simple as it is, that Euler[557] is
justly held to have greatly advanced trigonometry by its introduction.
Nobody that we know of has noticed that Oughtred was master of the
improvement, and willing to have taught it, if people would have learnt.
After looking at his dead letter, we naturally turned to his dead book on
trigonometry, and there we found the abbreviations _s_, _sco_, _t_, _tco_,
_se_, _seco_, regularly established as part of the system of the work. But
not one of those who have investigated the contending claims of Euler and
Thomas {304} Simpson[558] has chanced to know of Oughtred's
"Trigonometrie": and the present revival is due to his letter, not to his
book.
A casual reader, turning over the pages, would imagine that almost all the
letters had been printed, either in the General Dictionary, or in
Birch,[559] etc.: so often does the supplementary remark begin with "this
letter has been printed in ----." For ourselves we thought, until we
counted, that a large majority of the letters had been given, either in
whole or in part. But the positive strikes the mind more forcibly than the
negative: we find that all of which any portion has been in type makes up
very little more than a quarter; the cases in which the whole letter is
given being a minority of this quarter. The person who has been best
ransacked is Flamsteed: of 36 letters from him, 34 had been previously
given in whole or in part. Of 59 letters to and from Newton, only 17 have
been culled.
The letters have been modernized in spelling, and, to some extent, in
algebraical notation; it also seems that conjectural methods of introducing
interpolations into the text have been necessary. For all this we are
sorry: the scientific value of the collection is little altered, but its
literary value is somewhat lowered. But it could not be helped: the
printers could not work from the originals, and Professor Rigaud had to
copy everything himself. A fac-simile must have been the work of more time
than he had to give: had he attempted it, his death would have cut short
the whole undertaking, instead of allowing him to prepare everything but a
preface, and to superintend the printing of one of the volumes. We may also
add, that we believe we have notices of _all_ the letters in the
Macclesfield collection. We judge this because several which are too
trivial to print are numbered and described; and those would certainly not
have been noticed if _any_ omissions had {305} been made. And we know that
every letter was removed from Shirburn Castle to Oxford.
Two persons emerge from oblivion in this series of letters. The first is
Michael Dary,[560] an obscure mathematician, who was in correspondence with
Newton and other stars. He was a gauger at Bristol, by the interest of
Collins; afterwards a candidate for the mathematical school at Christ's
Hospital, with a certificate from Newton: he was then a gunner in the
Tower, and is lastly described by Wallis as "Mr. Dary, the tobacco-cutter,
a knowing man in algebra." In 1674, Dary writes to Newton at Cambridge, as
follows:--"Although I sent you three papers yesterday, I cannot refrain
from sending you this. I have had fresh thoughts this morning." Two months
afterwards poor Newton writes to Collins, "Mr. Dary is very solicitous
about mathematics": but in spite of the persecution, he subscribes himself
to Dary "your loving friend." Dary's _problem_ is that of finding the rate
of interest of an annuity of which the value and term are given. Dary's
_theorem_, which he seems to have invented specially for the solution of
his problem, though it is of wide range, can be exhibited to mathematical
readers even in our columns. In modern language, it is that the limit of
[phi]^{_n_}_x_, when _n_ increases without limit, is a solution of [phi]_x_
= _x_. We have mentioned the I. Newton to whom Dary looked up; we add a
word about the one on whom he looked down. Dr. John Newton,[561] a sedulous
publisher of logarithms, tables of interest, etc., who began his career
before Isaac Newton, sometimes puzzles those who do not know him, when
described as I. Newton. The scientific world was of opinion that all that
was valuable in one of his works was taken from Dary's private
communications.
{306}
The second character above alluded to is one who carried mathematical
researches a far greater length than Newton himself: the assistance which
he rendered in this respect, even to Newton, has never been acknowledged in
modern times: though the work before us shows that his contemporaries were
fully aware of it, and never thought of concealing it. In his theory of
gravitation, in which, so far as he went, we have every reason to believe
he was prior to Newton, he did not extend his calculations to the distance
of the moon; his views in this matter were purely terrestrial, and led him
to charge according to weight. He was John Stiles, the London and Cambridge
carrier: his name is a household word in the Macclesfield Letters, and is
even enshrined in the depths of Birch's quartos. Dary informs Newton--let
us do his memory this justice--that he had paid John Stiles for the
carriage. At the time when the railroad to Cambridge was opened, a
correspondent recommended the directors, in our columns, to call an engine
by the name of John Stiles, and never to let that name go off the road. We
do not know whether the advice was followed: if not, we repeat it.
Little points of life and manners come out occasionally. Baker, the author
of a work on algebra much esteemed at the time, wrote to Collins that their
circumstances are alike, "having a just and equal number of chargeable
olive-branches, and being in the same predicament and blessed condemnation
with you, not more preaching than unpaid, and preaching the art of
contentment to others, am forced to practise it." But the last sentence of
his letter runs as follows: "I have sent by the bearer ... twenty
shillings, as a token to you; desiring you to accept of it, as a small
taste from Yours, Thos. Baker." In our day, men of a station to pay parish
taxes do not offer their friends hard money to buy liquor. But
Flamsteed[562] writes to Collins as follows: "Last week he sent us down the
counterpart, which {307} my father has scaled, and I return up to you by
the carrier, with 5l. to be paid to Mr. Leneve for the writing, I have
added 2s. 6d. over, which will pay the expenses and serve to drink, with
him." This would seem as odd to us as it would have seemed thirty years ago
that half-a-crown should pay carriage for a deed from Derby to London, and
leave margin for a bottle of wine: in our day, the Post-office and the
French treaty would just manage it between them. But Flamsteed does not
limit his friend to one bottle; he adds, "If you expend more than the
half-crown, I will make it good after Whitsuntide." Collins does not
remember exactly where he had met James Gregory, and mentions two equally
likely places thus: "Sir, it was once my good hap to meet with you in an
alehouse or in Sion College." There is a little proof how universally the
dinner-hour was twelve o'clock. Astronomers well know the method of finding
time by equal altitudes of the sun before and after noon: Huyghens calls it
"le moyen de deux egales hauteurs du soleil devant et apres _diner_."[563]
There is one mention of "Mr. Cocker,[564] our famous English graver and
writer, now a schoolmaster at Northampton." This is the true Cocker: his
genuine works are specimens of writing, such as engraved copy-books,
including some on arithmetic, with copper-plate questions and space for the
working; also a book of forms for law-stationers, with specimens of legal
handwriting. It is recorded somewhere that Cocker and another, whose name
we forget, competed with the Italians in the beauty of their flourishes.
This was his real fame: and in these matters he was great. The eighth
edition of his book of law forms (1675), published shortly after Cocker's
death, has a preface signed "J. H." This was John Hawkins, who became
possessed of Cocker's papers--at least he said so--and {308} subsequently
forged the famous Arithmetic,[565] a second work on Decimal Arithmetic, and
an English dictionary, all attributed to Cocker. The proofs of this are set
out in De Morgan's _Arithmetical Books_. Among many other corroborative
circumstances, the clumsy forger, after declaring that Cocker to his dying
day resisted strong solicitation to publish his Arithmetic, makes him write
in the preface _Ille ego qui quondam_[566] of this kind: "I have been
instrumental to the benefit of many, by virtue of those useful arts,
writing and engraving; and do _now_, with the same _wonted alacrity_, cast
this my arithmetical mite into the public treasury." The book itself is not
comparable in merit to at least half-a-dozen others. How then comes Cocker
to be the impersonation of Arithmetic? Unless some one can show proof,
which we have never found, that he was so before 1756, the matter is to be
accounted for thus.
Arthur Murphy,[567] the dramatist, was by taste a man of letters, and ended
by being the translator of Tacitus; though many do not know that the two
are one. His friends had tried to make him a man of business; and no doubt
he had been well plied with commercial arithmetic. His first dramatic
performance, the farce of "The Apprentice," produced in 1756, is about an
idle young man who must needs turn actor. Two of the best known books of
the day in arithmetic were those of Cocker and Wingate.[568] Murphy chooses
_Wingate_ to be the name of an old merchant who {309} delights in vulgar
fractions, and _Cocker_ to be his arithmetical catchword--"You read
Shakespeare! get Cocker's Arithmetic! you may buy it for a shilling on any
stall; best book that ever was wrote!" and so on. The farce became very
popular, and, as we believe, was the means of elevating Cocker to his
present pedestal, where Wingate would have been, if his name had had the
droller sound of the two to English ears.
A notoriety of an older day turns up, Major-General Lambert.[569] The
common story is that he was banished to Guernsey, where he passed thirty
years in confinement, rearing and painting flowers. But Baker, in 1678,
represents him as a prisoner at Plymouth, sending equations for solution as
a challenge: probably his place of confinement was varied, and his
occupation also.
[General Lambert was removed to Plymouth, probably about 1668. His daughter
captured the son of the Governor of Guernsey, who therefore probably was
reckoned an unsafe custodier thenceforward; though he assured the king that
he had turned the young couple out of doors, and had never given them a
penny. Great importance was attached to Lambert's safe detention: probably
the remaining republicans looked upon him as to be their next Cromwell, if
such a thing were to be. There were standing orders to shoot him at once on
the first appearance of any enemy before the island. See _Notes and
Queries_, 3d S. iv. 89.]
Collins informs James Gregory that "some of the Royal Academy wrote over to
Mr. Oldenburg, who was desired to impart the same to the Council of the
Royal Society, that the French King was willing to allow pensions to one or
two learned Englishmen, but they never made any answer {310} to such a
proposal." This was written in 1671, and the thing probably happened
several years before. Mr. De Morgan communicated the account of the
proposal to Lord Macaulay, who replied that he did not think that any
Englishman _received_ a literary pension from Louis; but that there is a
curious letter, about 1664, from the French Ambassador, in which he says
that he has, by his master's orders, been making inquiries as to the state
of learning in England, and that he is sorry to find that the best writer
is _the infamous Miltonus_. On two such independent testimonies it may be
held proved that the French King had attempted to buy a little adherence
from English literature and science; and the silent contempt of the Royal
Society is an honorable fact in their history.
Another little bit of politics is as follows. Oughtred is informed that
"Mr. Foster,[570] our Lecturer on Astronomy at Gresham College, is put out
because he will not kneel down at the communion-table. A Scotsman [Mungo
Murray], one that is _verbi bis minister_,[571] is now lecturer in Mr.
Foster's place." Ward in his work on the Gresham Professors,[572]
suppresses the reason, and the suppression lowers the character of his
book. Foster was expelled in 1636, and re-elected on a vacancy in 1641,
when Puritanism had gained strength.
The correspondence of Newton would require deeper sifting than could be
given in such an article as the present. The first of the letters (1669) is
curious, as presenting the {311} appearance of forms belonging to the great
calculus which, in this paragraph, we ought to call that of fluxions. We
find, of the date February 18, 1669-70, what we believe is the earliest
manifestation of that morbid part of Newton's temperament which has been so
variously represented. He had solved a problem--being that which we have
called Dary's--on which he writes as follows: "The solution of the annuity
problem, if it will be of any use, you have my leave to insert into the
_Philosophical Transactions_, so it be without my name to it. For I see not
what there is desirable in public esteem, were I able to acquire and
maintain it. It would perhaps increase my acquaintance, the thing which I
chiefly study to decline."
Three letters touch upon "the experiment of glass rubbed to cause various
motions in bits of paper underneath": they are supplements to the account
given by Newton to the Royal Society, and printed by Birch. It was Newton,
so far as appears, who added _glass_ to the substances known to be
electric. Soon afterwards we come to a little bit of the history of the
appointment to the Mint. It has appeared from the researches of late years
that Newton was long an aspirant for public employment: the only coolness
which is known to have taken place between him and Charles Montague[573]
[Halifax] arose out of his imagining that his friend was not in earnest
about getting him into the public service. March 14, 1696, Newton writes
thus to Halley: "And if the rumour of preferment for me in the Mint should
hereafter, upon the death of Mr. Hoar [the comptroller], or any other
occasion, be revived, I pray that you would {312} endeavour to obviate it
by acquainting your friends that I neither _put in_ for _any_ place in the
Mint, nor would meddle with _Mr. Hoar's place_, were it offered to me."
This means that Mr. Hoar's place had been suggested, which Newton seems to
have declined. Five days afterwards, Montague writes to Newton that he is
to have the _Wardenship_. It is fair to Newton to say that in all
probability this was not--or only in a smaller degree--a question of
personal dignity, or of salary. It must by this time have been clear to him
that the minister, though long bound to make him an object of patronage,
was actually seeking him for the Mint, because he wanted both Newton's name
and his talents for business--which he knew to be great--in the weighty and
dangerous operation of restoring the coinage. It may have been, and
probably was, the case that Newton had a tolerably accurate notion of what
he would have to do, and of what degree of power would be necessary to
enable him to do it in his own way.
We have said that the non-epistolary manuscripts are still unexamined.
There is a chance that one of them may answer a question of two centuries'
standing, which is worth answering, because it has been so often asked.
About 1640, Warner,[574] afterwards assisted by Pell,[575] commenced a
table of _antilogarithms_, of the kind which Dodson[576] afterwards
constructed anew and published. In the Museum collection there is inquiry
after inquiry from Charles Cavendish,[577] first, as to when the
_Analogics_, as he called them, would be finished; next, when they would be
printed. Pell answers, in 1644, that Warner left his papers to a kinsman,
who had become bankrupt, and proceeds thus:
"I am not a little afraid that all Mr. Warner's papers, {313} and no small
share of my labours therein, are seazed upon, and most unmathematically
divided between the sequestrators and creditors, who (not being able to
ballance the account where there appeare so many numbers, and much troubled
at the sight of so many crosses and circles in the superstitious Algebra
and that black art of Geometry) will, no doubt, determine once in their
lives to become figure-casters, and so vote them all to be throwen into the
fire, if some good body doe not reprieve them for pye-bottoms, for which
purposes you know analogicall numbers are incomparably apt, if they be
accurately calculated."
Pell afterwards told Wallis[578] that the papers had fallen into the hands
of Dr. Busby,[579] and Collins[580] writes that they were left in the hands
of Dr. Thorndike,[581] a prebendary of Westminster; whence Rigaud[582]
seems to say that Thorndike had left them to Dr. Busby. Birch[583] says
that he procured for the Royal Society four boxes from Busby's trustees,
containing papers of Warner and Pell: but there is no other tradition of
such things in the Society. But in the Birch manuscripts at the British
Museum, there turns up, as printed in what we call the Museum collection, a
list of Warner's papers, with _Collins's_ receipt to Dr. Thorndike at the
bottom, and engagement to restore them on demand. The date is December 14,
1667; Wallis's statement being in 1693. It is possible that Busby may be a
mistake altogether: he was very unlikely to have had charge of any
mathematical papers: there may have been a confusion between the Prebendary
of Westminster and the Head Master of Westminster School. If so, in all
probability Thorndike handed {314} the cumbrous lot over to the notorious
collector of mathematical papers, blessing himself that he got rid of them
in a manner which would insure their return if he were called upon by the
owners to restore them. It is much against this hypothesis that Dodson, who
certainly recalculated, can say nothing more about Warner than a repetition
of Wallis's story: though, had Collins kept the papers, they would probably
have been in Jones's possession at the very time when Dodson, who was a
friend of Jones and a user of his library, was engaged on his own
computations. But even books, and still more manuscripts, are often
singularly overlooked; and it remains not very improbable that Warner's
table is now at Shirburn Castle, among the unexamined manuscripts.