It is not without good reason that, of all Thomas Harriot’s
Mathematical writings, this on Analysis has been published first. For
whereas all his remaining works, remarkable for their manifold
novelties of discovery, are written precisely in the same, hitherto
unusual, logical style as this treatise (which consists entirely of
varied specimens of beautiful reasoning); this was certainly done that
this preliminary treatise, besides its own inestimable utility, might
suitably serve as a necessary preparation or introduction to the study
of Harriot’s remaining works, the publication of which is now under
serious consideration. Of this accessory use of this treatise we have
thought it worth while to remind mathematical students in these brief
remarks.
From this it appears that Hariot’s system of Analytics or Algebra was
based on that of his friend and correspondent Francois Vieta, as
Vieta’s was avowedly based on that of the ancients. There appears to
have been no attempt whatever on the part of the Englishman to
appropriate the honors of the Frenchman, as many foreign writers have
charged. Full credit was given by Hariot and his friends to the
distinguished French mathematician.
But Hariot’s modifications, improvements, and simplifications were so
distinct and marked that from the first, and long before publication,
they were called among his students and correspondents ‘Hariot’s
Method,’ meaning thereby only Hariot’s peculiarities, without reference
to the great merits of Vieta’s restoration, modification, adaptation,
and improvement of the old analyses from the times of the Greeks.
Vieta’s’ Canon Mathematicus’ was published at Paris in 1579, and was
reissued in London with a new title in 1589 as his ‘Opera Mathematica.’
But this work does not contain the Algebra. That was first published in
1591 under the following title :
‘Francisci Vietæ/InArtem Analyticam/Isagoge/Seorfim excuffa ab Opere
reftitutæ Mathematicæ/Analyfeos, seu, Algebraicâ nouâ. / Tvronis,/ Apud
Iametivm Mettayer Typographium Regium. / Anno 1591.’ / folio. A
Supplement appeared in 1593. Seven years later there came out under the
auspices of Ghetaldi, a young Italian nobleman of mathematical tastes,
who had been studying in Paris, the following:—‘De Nvmerosa Potestatvm
/ Ad Exegefum / Resolvtione. / Ex Opere reftitutæ Mathematicæ
Analyfeos, / feu, Algebrà nouà / Francisci Vietæ. / Parisiis, /
Excudebat David le Clerc. / 1600.’ / folio. On the last page of this
book is an interesting letter from Marino Ghetaldi to his preceptor
Michele Coignetto, dated at Paris the I5th of February 1600.
These three thin folio volumes of great rarity are models of
typographic beauty. They manifestly served as the model for printing
Hariot’s Algebra in 1631. The set here described (the three bound in
one volume), Prince Henry’s own copies, bearing his arms and the Prince
of Wales’ feathers, is preserved in the British Museum, press-marked
530, m. 10.
Thus Vieta’s method appears to have been given to the world in three
instalments between 1591 and 1600, while the author himself died in
1603. It was probably in reference to one or both of these works that
Lower gently reproached Hariot for having allowed himself to be
anticipated in the public announcement of his discoveries in Algebra by
Vieta. It has already been seen, on page 101 above, what Torperley, the
friend of Vieta, wrote of his two masters in 1602, and also, on page
121, what Lower wrote to Hariot in 1610.
One is forced, therefore, to the conclusion that by 1600, if not some
time before, Hariot had completed his method in Algebra, and
distributed his well known problems to his admiring scholars. It has
also been seen how, from 1603 to the day of his death, he was occupied
in many other absorbing matters connected with Raleigh and Percy. Yet
he may have felt, as Lower expressed it, that when he surveyed his
storehouse of inventions this one of Algebra might seem in ‘comparison
of manie others smal or of no value.’ The matter is introduced here
mainly because certain foreign writers,rebutting Wallis’s patriotic
claims in behalf of Hariot, have not only accused Hariot of
appropriating Vieta’s rights, but they even describe the distinguished
English mathematician as working on the ‘Cartesian Method.’ While the
truth appears to be that Hariot’s method in Algebra, though not
published for more than thirty years after its invention, must date
from a time when Descartes was scarcely four years old.
On the other hand, on looking into Descartes’ great and original work
on geometry, first published in 1637, six years after Hariot’s Algebra
first saw the light in print, one is not disposed to accuse the great
philosopher of plagiarism because in working out his problems of great
novelty in reference to geometrical curves he employed any systems of
notation and calculation in algebra (Hariot’s among the others) that
happened to be before the world. The point or essence of Descartes’
work was geometry and not algebra. Therefore, in climbing to his loft,
he was perfectly justified in using the ladder which Hariot had left,
as it was then in general use, and was only an incidental aid in his
independent calculations, especially as the fame of his great
mathematical brother was well established, and he had been already
sixteen years in St Christopher’s. Vieta therefore had manifestly no
just reason to complain, and Descartes stands acquitted.
The history of Hariot’s _Praxis_ has attracted a great deal of
attention for more than two centuries and has long been obscured by
many misconceptions and erroneous statements. In the first place it has
been always said from the days of Collins that it was edited by Walter
Warner, and Wood adds that Warner was to have his pension continued by
Algernon Percy, for that scientific labor. There is evidence that
Warner, though employed on the work by Sir Thomas Aylesbury, was not
the sole editor. See Aylesbury’s Letter to the Earl on page 189.
The book led to a great deal of international or patriotic controversy,
and with great injustice to Hariot was treated by the English advocates
as his masterpiece in science. Wallis in 1685 in his History of
Algebra, after much correspondence with Collins and others on the
subject between 1667 and 1676, became Hariot’s English champion. The
controversy respecting the Methods of Hariot and of Descartes became as
warm as that respecting the discoveries of Leibnitz and of Newton.
Wallis ranked Oughtred’s _Clavis_ and Hariot’s _Praxis_ very high, and
because both were first printed in 1631, treated them as productions or
inventions of that year, whereas Hariot’s method, as we have seen, had
been long practically before his disciples; and was, ten years after
the author’s death, given to the world avowedly as an’ accessory’ only,
or preliminary treatise, that it ‘might suitably serve as a necessary
preparation or introduction to the study of Hariot’s remaining works,
the publication of which is now under serious consideration.’
Unfortunately this excellent scheme fell through, probably in
consequence of the death of the Earl of Northumberland, and perhaps
partly because of the death of Nathaniel Torporley who had long been
engaged in ‘penning the doctrine’ of Hariot’s mathematical papers. They
both died in 1632, shortly after the publication of the Praxis.
Wallis’s charge had a basis of truth, but it was narrow and petty. As
an Algebraist he seems to have lost sight of the main point, that
Descartes’ great work was on Geometry and not on Algebra, and that
Hariot’s method, though first printed in 1631, was almost as old as
Descartes himself. Montucla the French mathematician, near the close of
the last century, in his History of Mathematics, summed up the
controversy raised by Wallis including the minor one raised by Dr Zach
in 1785, clearing Descartes of Wallis’s charges and relegating Hariot
to the respectability of a second-rate mathematician. If Montucla’s
verdict be based on mathematical reasoning as loose and slipshod as is
his statement of the historical points of the case, to say nothing of
his utter ignorance of Hariot’s biography and true position as an
English man of science, one feels justified in rejecting it as
worthless : as one also is compelled to do the vapid conclusions drawn
from Montucla which have since found their way into many recent
biographical dictionaries and into many pretentious articles in learned
encyclopædias respecting Hariot and his works. The truth seems to be
that Hariot was unlucky and fell into oblivion accidentally. He was a
man of immense industry and great mental power, but perhaps careless of
his scientific and literary reputation. As has been seen, he always had
many irons in the fire, and was overtaken by death in the prime of
life, leaving, as his will shows, many things unfinished, and none of
his papers in a state ready for publication. He was surrounded by the
best of friends, but time and opportunity, as so often happens in the
affairs of busy men, worked against him, and he was well nigh consigned
to forgetfulness.
However, after a half century’s slumber, when the great fire of London
had destroyed his monument, and too late many scholars were minded to
attempt the recovery and preservation of memorials of the past, John
Collins the mathematician began soundings in the pool of oblivion for
Hariot and his papers. He and his correspondents fished up a great deal
of truth and history, but so mixed with error and conjecture that the
results, though interesting, are misleading.
In the ‘Correspondence of Scientific Men of the Seventeenth Century,
Edited by Professor S.J. Rigaud, 2 volumes, Oxford 1841,’ 8°, are found
the following instructive and amusing passages :
As for Geysius, he published an Algebra and Stereometria divers years
before the first edition of the Clavis [of Oughtred, 1631] was extant
in Mr. Harriot’s method, out of which Alsted took what he published of
algebra in his Encylopasdia printed in 1630, the year before the Clavis
was first extant (see Christmannus and Raymarus). Mr. Harriot’s method
is now more used than Oughtred’s, and himself in the esteem of Dr.
Wallis not beneath Des Cartes. Dr. Hakewill, in his Apology, tells you
Harriot was the first that squared the area of a spherical triangle;
and I can tell you, by the perusal of some papers of Torporley’s it
appears that Harriot could make the sign of any arch at demand, and the
converse, and apply a table of sines to solve all equations, and
treated largely of figurate arithmetic. His papers fell into the hands
of Sir Thomas Aylesbury, father to the Lord Chancellor’s lady, where I
hope they still are, unless they had the hard fate to be lent out,
before the fire, and be burned, as some have said.
_Collins to Wallis, no date, circa_ 1670, _vol. ii, page_ 478.
As to Harriot, he was so learned, saith Dr. Pell, that had he published
all he knew in algebra, he would have left little of the chief
mysteries of that art unhandled. His papers fell into the hands of Sir
Thomas Aylesbury, who was father to the late Lord Chancellor’s
[Clarendon] Lady,by which means they fell into the Lord Chancellor’s
hands, to whom application was made by the members of the Royal Society
to obtain them: his lordship (then in the height of his dignity and
employments) gave order for a search to be made, and in result the
answer was, they could not be found. I am afraid the search was but
perfunctory, and that, if his lordship (now at leisure) were solicited
for them, he might write to his son the Lord Cornbury to make a
diligent search for them. One Mr. Protheroe, in Wales, was executor to
Mr. Harriot, and from him the Lord Vaughan, the Earl of Carbery’s son,
received more than a quire of Mr. Harriot’s Analytics. The Lord
Brounker has about two sheets of Harriot de Motu et Collisione
Corporum, and more of his I know not of: there is nothing of Harriot’s
extant but that piece which Mons. Garibal hath.
_Collint to Vernon, not dated but circa_ 1671, _vol. i, page_ 153.
Upon this passage Professor Rigaud makes the following note, written at
Oxford in 1841:
Harriot’s will is not to be found, but Camden says that he left his
property to Viscount Lisle and Sir Thomas Aylesbury. Lord Lisle’s share
of the papers appear to have been given up to his father-in-law, Henry
earl of Northumberland, who had been Harriot’s munificent patron, and
they descended with the family property to the E. of Egremont, by whom
a large portion has been given to the British Museum, and the remainder
are still preserved at Petworth. Sir Thomas Aylesbury’s share became
the property of his son-in-law Lord Chancellor Clarendon, to whom the
Royal Society applied, but, as it appears, without obtaining them. (See
Birch, Hist. Royal Society, vol. ii, pp. 120, 116, 309.)—_Vol. i, page_
153.
Here seems to be the germ of Professor Wallis’s charge of plagiarism
against Descartes, written to Collins twelve years before it appeared
in thefirst editionof his History of Algebra in English in 1685. It
subsequently took a wider range, and was strenuously defended by Wallis
when opposed:
That which I most valued in his [Des Cartes] method, and which pleased
me best, was the way of bringing over the whole equations to one side,
making it equal to nothing, and thereby forming his compound equations
by the multiplication of simples, from thence also determining the
number of roots, real or imaginary, in each. This artifice, on which
all the rest of his doctrine is grounded, was that which most made me
to set a value on him, presuming it had been properly his own; but
afterwards I perceived that he had it from Hariot, whose Algebra was
published after his death in the year 1631, six years before Des
Cartes’ Geometry in French in the year 1637 : and yet Des Cartes makes
no mention at all of Harriot, whom he follows in designing his species
by small letters, and the power: of them by the number of dimensions,
without the characters of _j, c, qq, &c._
_Walla to Collins, Oxford,_ 12 _April_ 1673, _vol, ii, page_ 573.
And had I but known of any precedent, (as since in Harriot I find one,
and I think but one √_—dddddd,)_ I should not have scrupled to follow
it; but I was then too young an algebraist to innovate without example.
Since that time I have been more venturous, and I find now that others
do not scruple to use it as well as I. [Just what Descartes did. He
‘innovated’ prior to 1637, when he took Hariot’s well recognized
notation in algebra to work out his problems in geometry for which
Hariot himself would have thanked him.]
_Wallis to Collins, May 6,_ 1673, _vol. ii, page_ 578.
One Torporley, long since, left a manuscript treatise in Latin in Sion
College, wherein is a much more copious table of figurate numbers,
which I have caused to be transcribed, with what he says de
combinationibus, to send to Mr. Strode.
On this passage, extracted from a letter from Collins to Baker, dated
the 19th of August, 1676, Professor Rigaud has the following note,
written in 1841, vol. ii, page 5 :
Nath. Torporley left his manuscripts to Sion College, where he spent
the latter years of his life ; but the greater part of them was
destroyed by the fire of London. Reading, in his catalogue of the
library, mentions only one, “Corrector Analyticus,” which is an attack
on Warner for the manner in which he had edited Harriot’s “Artis
Analyticæ Praxis.” This is a short tract, and incomplete. There is,
however, another volume, A. 37-39, entitled, “Algebraica, Tabulæ
Sinuum,&c.” in which Torporley’s hand may be certainly recognized.
Wood, in the list of his works, speaks of "Congestor opus
Mathematicam,— imperfect." A perfect copy of this treatise is in Lord
Maccles-field’s possession, and probably once belonged to Collins.
Perhaps the best comment that one can make on the wild and
extraordinary statements contained in the above extracts is to ask the
reader to read over Hariot’s Will,given entire on pages 193-203, and
especially this _Item_ respecting his Mathematical and other Writings,
and the Rev. Nathaniel Torporley, from which it will appear that all
his valued papers were bequeathed with great care to the Earl of
Northumberland, to be deposited in his library in a trunk with lock and
key, after they had been looked over and perused, by Mr Torporley, and
(the waste papers having been weeded out) the whole arranged by him ‘to
the end that _after hee doth vnderstand them_ he may make use in
penning such doctrine that belongs unto them for publique use.’ This,
of course, was to be done under the supervision of the four Executors,
who were persons of no less distinction than Sir Robert Sidney Knight
Viscount Lisle, John Protheroe Esquire, Thomas Aylesbury Esquire, and
Thomas Buckner Mercer.
ITEM I ordayne and Constitute the aforesaid Nathaniel Thorperley first
to be Overseer of my Mathematical Writings to be received of my
Executors to peruse and order and to separate the Chiefe of them from
my waste papers, to the end that after hee doth vnderstand them hee may
make use in penninge such doctrine that belongs vnto them for publique
vses as it shall be thought Convenient by my Executors and him selfe.
And if it happen that some manner of Notacions or writings of the said
papers shall not be understood by him then my desire is that it will
please him to confer with Mr Warner or Mr Hughes Attendants on the
afore said Earle Concerning the aforesaid double. And if hee be not
resolued by either of them That then hee Conferre with ihe aforesaid
John Protheroe Esquier or the aforesaid Thomas Alesbury Esquior. (I
hopeing that some or other of the aforesaid fower last nominated can
resolve him). And when hee hath had the use of the said papers soe
longe as my Executors and hee have agreed for the use afore said That
then he deliver them againe unto my Executors to be putt into a
Convenient Truncke with a locke and key and to be placed in my Lord of
Northumberlandes Library and the key thereof to be delivered into his
Lordshipps hands. And if at anie tyme after my Executors or the afore
said Nathaniell Thorperley shall agayne desire the use of some or all
of the said Mathematicall papers That then it will please the said
Earle to lett anie of the aforesaid to have them for theire use soe
long as shall be thought Convenient, and afterwards to be restored
agayne unto the Truncke in the afore said Earles Library. Secondly my
will and desire is that the said Nathaniell Thorperley be alsoe
Overseere of other written bookes and papers as my Executors and hee
shall thincke Convenient.
This will, of extraordinary interest, has fallen to our lot to exhume,
after many antiquaries and scholars had long sought it in vain. It was
recently discovered in the Archdeaconry Court of London, just the place
where one would least expect to find it. One has only to read the
document to read the character of the man—good, learned,affectionate,
charitable and just. He was carried off by a terrible disease, away
from home, but among friends. He left his affairs and fame in loving
hands. His will was proved on the 4th day after his death by two of the
Executors, Sir Thomas Aylesbury and Mr Buckner, with the right reserved
to the other two to act subsequently. It is found by papers in the
British Museum that Sir John Protheroe did act, for there is a very
long list of manuscripts, copied from Protheroe’s list of papers
delivered to Mr Torporley, which served as a receipt for them, and
which was returned with the papers.
Mr Torporley then, it is manifest, had in hand the papers and returned
them, but it is not apparent what amount of labor he bestowed upon
them. They do not appear to be properly arranged, nor have the waste
papers been weeded out. From Protheroe’s list and other circumstances
it is likely that nothing has been destroyed, except perhaps the
Raleigh accounts and the Irish papers in the ‘canvas baggs.’ The papers
were at Sion, and were placed in a trunk and delivered to the Earl, who
left the Tower only sixteen days after Hariot’s death. They
subsequently found their way to Petworth, another seat of the Earl,
where the trunk and half of the papers still remain, in the possession
of the Earl of Leconsfield, a branch of the Northumberland family. They
are briefly described in this manner by Mr Alfred J. Horwood in the
Sixth Report of the Historical Manuscript Commission for 1877, page
319, folio.
A black leather box containing several hundred leaves of figures and
calculations by Hariot.
A large bundle of Hariot’s papers. They are arranged in packets by
Professor Rigaud. Spots on the Sun. Comets of 1607 and 1618. The Moon.
Jupiter’s Satellites. Projectiles, Centre of Gravity, Reflection of
bodies. Triangles. Snell’s Eratosthenes Batavus. Geometry. Calendar.
Conic Sections. De Stella Martis. Drawings of Constellations, papers on
Chemistry and Miscellaneous Calculations. Collections from Observations
of Hannelius, Warner, Copernicus, Tycho Brahe. On the vernal and
autumnal equinoxes, the solstices, orbit of the Earth, length of the
year, &c. Algebra.
A similar collection, but not yet arranged, catalogued, numbered or
bound, is carefully preserved in the Manuscript Department of the
British Museum (Additional, 6782-6789), in eight thick Solander cases,
probably as much in bulk as the Petworth papers. They were presented to
the Museum by the Earl of Egremont in 1810. Why the two collections
were separated does not appear. The Museum papers contain much that is
waste, but much also that is of importance equal probably to those at
Petworth. Mr Torporley was in effect appointed by Hariot his literary
and scientific editor under the direction of the Executors. No papers
were left ready for publication. It must have required great study and
labor to master them sufficiently to pen for public use such doctrine
or science as belonged to them. Torporley lived in Shropshire, but a
few years after Hariot’s death he retired from his rectorship and
removed to London,taking rooms in 1630 at Sion College in London Wall,
when that institution was first founded. It contained then as now a
library for the use of the Clergy, and a few suites of apartments for
those who desired to reside on the premises. It never was a College or
place of instruction, but a sort of guild or Clergyman’s Club. At this
time Mr Torporley was about seventy years old. He died in his chambers
at Sion College in April 1632, and was buried on the 17th of that month
in the Church of St Alphage, close by. In a nuncupative will spoken the
14th ofApril, a copy of which is before the writer, he left his books
and manuscripts to the Sion Col ege Library. A complete list of about
170 books and several manuscripts is preserved in the ‘Donors’ Book.’ A
few of the books are said to have been destroyed by the fire of London,
but probably none of the manuscripts were lost.
Torporley’s manuscripts, as has been stated, have often been referred
to, and sometimes copied, but their true history and character is
explained by Hariot’sWill. There are really but two manuscripts
relating to Hariot. The more important one comprises 116
closely-written folio leaves, or 232 pages, all in Torporley’s
handwriting. It bears no title or designation. Hence various writers
who have seen it, from Collins, Wood, and Dr Zach, have given it
different names, such as, _‘Ephemeris Chysometria,’ ‘Congestor opus
Matbematicum,’_ etc. but it appears to be nothing more nor less than
Torporley’s attempt to pen out such doctrine as he found in Hariot’s
papers. The leaves are numbered, 1 to 16 containing a Treatise on
Hariot’s Theory of Numbers. Leaves 17 to 25 are tables of the divisors
of odd numbers up to 20,300. On the verso of leaf 25 the Theory of
Numbers is resumed, extending to the recto of 27. On the verso of leaf
27 begins the treatise on the properties of Triangles and ends on leaf
34. Leaves 35 to 55 comprise examples of Algebraical processes, and
leaves 56 to 116 contain Tables (probably tabulæ sinuum ?) up to 180°.
On the second leaf the Author speaks of himself as working out, or
working on Hariot’s principles, and also as making use of the writings
of Vieta. He adds:
‘And since it is our principal design to explain the improvement in
this science[the Properties of Numbers and Triangles] discovered by our
friend Thomas Hariot; but he neither completely reformed it (which
indeed was not necessary) nor gave a full account of it, but only
strengthened it where it was defective, and by treating in his own way
the points of the science which were heretofore more difficult,
rendered them clear and easy.’
This manuscript was probably intended for another printed volume of
Hariot’s mathematical works, but owing to the deaths about the same
time, 1632, of the venerable editor and the noble patron this work
never bore a definite name and never saw the light of the press.
CORRECTOR ANALYTICUS
Artis pofthumx THOMÆ HARIOTI
Vt Mathematici eximij, perraro
Vt Philofophi Audentes, frequentius errantis
Vt Hominis evanidi, infigniter
Ad
Fidedigniorem refutationem Philopfeudofophiæ
Atomifticæ;, per cum Reducis, et præ
cæteris eius Portentis
feriò
corripiendæ, anathematyzandæq
Compendiu Antimonitorfi, et Speciminale
exanthorati ia Senioris
Na: Torporley.
Vt
Noverit Arbiter Caveat Emptor.
non bene Ripæ
Creditur, ipfe Aries etiam nunc Vellera ficcat.
_Virgil, Ecl._ iii. 94,95,]
This Second Manuscript is a pretentious but small affair. It was
manifestly written at Sion College after the _Praxis_ appeared in 1631.
It is only the preface or the opening of a growl of envy or
disappointment. It shows clearly that Torporley himself was not the
editor of the Algebra or Praxis. The above is the pedantic title-page,
given line for line and verbatim.
The manuscript is in small quarto, and exclusive of the title (which,
indeed, is the nub of the achievement) contains only nine pages,
breaking off abruptly in the middle of a sentence. He criticises the
editors of Hariot’s Algebra, the executors Aylesbury and Protheroe,
aided by Warner, who were all eminent mathematicians. He speaks of the
administrators or editors as if more than one, and does not mention
Warner, or lead us to believe that he was sole editor. Only a small
portion of this projected criticism seems ever to have been written. It
appears to have been begun in senile peevishness, containing only a few
prefatory remarks and discussing some algebraical questions with the
fancied errors of the editors. No mention is made of the’Atomic
Theory,’as promised on the title-page, which is here done into English,
and is as follows:—
THE ANALYTICAL CORRECTOR
of the posthumous scientific writings
of THOMAS HARRIOT.
As an excellent Mathematician one who very seldom
erred
As a bold Philosopher one who occasionally erred,
As a frail Man one who notably erred
For
the more trustworthy refutation of the pseudo-philosophic
atomic theory, revived by him and, outside his
other strange notions, deserving of
reprehension and anathema.
A Compendious Warning with specimens by the aged
and retired-from-active-life
Na: Torporley.
So that
The critic may know
The buyer may beware.
It is not safe to trust to the bank,
The bell-wether himself is drying his fleece.
The ‘Corrector Analyticus’ may be found printed in full (but without
the quaint titles) in ‘The Historical Society of Science. A Collection
of Letters illustrative of Science, edited by J. O. Halliwell,’ London,
1841, 8°, Appendix, pages 109-116. ForTorporley’s curious paper
entitled ‘A Synopsis of the Controversie of Atoms,’ see Brit. Mus. Mss,
Birch 4458, 2.
Mr Torporley informs us, and the papers appear to bear him out in the
statement, that Hariot wrote memoranda, problems, etc. on loose pieces
of paper, and then arranged them in sets fastened together according to
the subjects treated of. He adds, ‘First then let me speak of Hariot’s
method, of which frequent mention will have to be made in the following
pages; so that the reader may understand why some things are stated and
some passed over: here I cannot but complain, that I find it a serious
defect that his Commentators have so completely transformed it [the
Praxis] that they not only do not retain his orderbut not evenhis
language.’ Again he writes, ‘But not even those well-thought-out and
necessary to be known matters, which have been delivered to us, have
been handed down to posterity by his administrators with the fidelity
and accuracy promised.’ The suspicion is raised that Torporley’s age
and dilatoriness compelled the accomplished executors to take the
editorial matter in hand themselves and hinc iliae lacrymæ.
On the back of the above title-page is another attempt of the same sort
as follows, showing that this deed of pedantry was committed at Sion
College:
CORRECTOR
sive
Notæ in Analyticam
Novam, Novatam, Posthuma
quatenus
Fallacem, Defectivam, Extrariam
cum
Apodictica refutatione Atomorum
Somnij, præ cæteris Novatorum
portentis corripiendi Ana-
thematizandiq
Ex Collegio Sion Londinenfi
perfuncti Senis Artemq reponentis
NT
Extremu hoc munus morientis
habetor :
Σĸηρον προς κέντρονλ α κτρον λακτίζειν
[Greek Text]
nee bene Ripæ
Creditur ipse Aries etia nunc Vellera ficcat.
There are one or two unimportant papers among the Torperley manuscripts
that bear marks of having belonged to the Hariot papers, and there is a
manuscript by Warner, entitled, ‘Certayne Definitions of the
Planisphere.’ Any one curious in the history of Torperley may find in
the Calendar of State Papers, Domestic Series, 1636, page 364, how his
property was purloined by Mr Spencer, the first Librarian of Sion
College. He was sued by Mistress Payne the administratrix and was
compelled to disgorge _£4.0_ in money, eleven diamond rings, eight gold
rings, two bracelets, etc. Then Archbishop Laud took away Spencer’s
librarianship, and let him drop.
Mr William Spence of Greenock published in Nov. 1814, a work entitled,
‘Outlines of a Theory of Algebraical Equations deduced from the
Principles of Harriott, and extended to the Fluxional or differential
Calculus. By William Spence. London, for the Author, by Davis and
Dickson, 1814, 8°, _iv and 80 pages._ Privately printed, intended
‘exclusively for the perusal of those gentlemen to whom it is
addressed.’ He says in his prefatory note that—
‘As the principles are drawn from that theory of equations, by which
Harriott has so far advanced the science of algebra.’ The author says,
page I,’ Until the publication of Harriot’s _Artis Analytica Praxis,_
no extended theory of equations was given. Harriot considered
algebraical equations merely as analytical expressions, detached wholly
from the operations by which they might be individually produced ; and,
carrying all the terms over to one side, he assumed the hypothesis,
that, as in that state the equation was equal to nothing, it could
always be reduced to as many simple factors as there were units in the
index of its highest power.’
Between 1606 and 1609 a very interesting and historically instructive
correspondence took place between Kepler and Hariot upon several
important scientific subjects. Five of the letters are given in full in
‘Joannis Keppleri Alio-rumque Epistolæ Mutuæ. [Frankfort] 1718,’ folio,
to which the reader is referred, but a brief abstract of them may not
be out of place here. The letters are numbered from 222 to 226 and fill
pages 373 to 382. The correspondence was begun by Kepler:
_Letter_ 122, _dated Prague,_ 11 _October,_ 1606, _from John Kepler_
_to Thomas Hariot,_
Kepler had heard of Hariot’s acquirements in Natural Philosophy from
his friend John Eriksen. Would be glad to know Hariot’s views as to the
origin and essential differences of colours; also on the question of
refraction of rays of light; and the causes of the Rainbow; and of
haloes round the sun.
_Letter_ 223, _dated London,_ 11 _December, 1606,from_
_Thomas Hariot to John Kepler,_
Had received with pleasure Kepler’s letter; but should not be able to
answer it at length, being in indifferent health, so that it was not
easy to write or even carefully to reflect. Sends a table of the
results of experiments on equal bulks of various liquids and
transparent solids (thirteen in number, including spring, rain, and
salt water; Spanish and Rhenish wine; vinegar; spirits of wine; oils
and glass). The angle of incidence is 30° in each case; also the
specific gravity of each substance is given. Then he discusses the
reason why refraction takes place. Promises to write on the Rainbow;
but will merely say at present that it is to be explained by the
reflection on the concave superficies and the refraction at the convex
superficies of each separate drop.
_Letter_ 224 _is from John Kepler to Thomas Hariot, dated at Prague,_
11 _August,_ 1607.
Thanks Hariot for his table, which supplies matter for serious
consideration. Asks questions as to how he defines the angles of
incidence and refraction; and goes on to discuss the reasons of
refraction. Agrees with Hariot as to his views about the Rainbow; but
will be very glad to receive his treatises on Colours and the Rainbow.
_Letter_ 225 _is from Thomas Hariot to John Kepler, dated at Syon,_
_near London,_ 13 _July_ (o.s.), 1608.
The departure of Eriksen and other matters do not allow leisure to
write at length. The turpentine (oleum terebinth inum) was not the same
as that experimented on by Kepler but a purer and lighter article (Sp.
grav. ’87). The angle of incidence is understood as defined by Alhazen
and Vitellio [first published 1572]. Points out some errors in
Vitellio’s second table of refractions. As to the causes of refraction,
Hariot believes in the theory of the vacuum; ‘where we still stick in
the mud’. Hopes God (Deum optimum maximum) will soon put an end to
this. Wishes for Kepler’s meteorological records for the last two
years, and will send his own notes in return. Gilbert, author of a work
on the magnet, had recently died, leaving in his brother’s hands a book
entitled ‘De Globo et Mundo nostro sub lunari Philosophia nova contra
Peripateticos, lib. 5." [A treatise, in five books, on Natural
Philosophy, in answer to the Peripatetics.] The book is likely to be
published before the end of the year. Hariot had read some chapters;
and saw that Gilbert defends the doctrine of a vacuum. Not to leave a
vacuum on this page (says Hariot), it is remarkable that though gold is
both heavy and opaque, when beaten out into gold-leaf the light of a
candle can be seen through it, though it appears of a green colour.
_Letter 226, from John Kepler to Thomas Hariot, it dated from_
_Prague, September,_ 1609.
Excuses himself for not having replied sooner; having been very busy;
but would not lose the present opportunity of writing. Discusses the
questions of refraction and the vacuum. Commentaries on Mars entitled
‘Astronomia Nova [Greek Text] or Physica Cælestis,’ have been published
at Frankfort; has not a copy by him. Regrets to hear of the death of
Gilbert. Hopes his work on Magnetism will also be published; and that
Erikson will bring a copy with him. Promises to send a copy of his own
meteorological observations; and hopes to receive Hariot’s.
These studies in optics and this correspondence with the learned Kepler
indicate Hariot’s great advancement in natural philosophy as early as
1606 to 1609 and give an earnest of his inventive genius and scientific
enterprise with his telescope in the astronomical discoveries which
immediately followed in 1609 to 1613. Before awarding all the prizes
for discoveries and inventions in mathematics, philosophy and natural
science to claimants throughout the wide Republic of Letters, let
modest Hariot be heard and examined. Let his papers and all his
credentials be laid out before the high court of science, not in the
light of today, but contemporaneously with those of Tycho, Kepler,
Galileo, Snell, Vieta and Descartes. Hariot himself has claimed
nothing, but Justice and Historical Truth are bound to assign him a
niche appropriate to his merits.
To show that Hariot, like his friends Hakluyt and Purchas, was alive to
everything geographical as well as mathematical going on, the following
is given from the original manuscript among the Hariot papers in the
British Museum (Add. 6789):
Three reasons to prove that there is a passage from the North’ west
into the South-sea.
1. The tydes in Port Nelson (where Sr. Tho : Button did winter, were
constantly, 15, or, 18, foote ; wc is not found in any Bay Throughout
the world but in such seas as lie open att both ends to the mayne
Ocean.
2. Every strong Westerne winde did bring into the Harbor where he
wintered, soe much water, that the Neap-tydes were equall to the
Spring-tydes, notwtstanding yt the harbor was open only to ye E.N.E.
3. In comming out of the harbor, shaping his course directly North,
about, 60, degrees, he found a stronge race of a tyde, set-ting dueEast
and West, wc in probabilitie could be noe other thing, than the tyde
comming from the West, and retourning from the East,
Among the manuscripts in the handwriting of Hariot in the British
Museum (Add. 6789) are these samples of ingenious trifling. No evidence
is forthcoming that he was ever a married man, but that he occasionally
let himself down from pure mathematics and high philosophy and amused
himself with anagrams is plain enough. Here are a few specimens on his
own name.