Thomas Hariot, the Mathematician, the Philosopher and the Scholar Part 7

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 ma.n.u.script 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 pa.s.sage, 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 ma.n.u.scripts 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 a.n.a.lyticus," which is an attack on Warner for the manner in which he had edited Harriot's " Artis a.n.a.lyticae Praxis." This is a short tract, and incomplete. There is, however, another volume, A.

37-39, ent.i.tled, "Algebraica, Tabulae 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 Const.i.tute 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 doc.u.ment 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 ma.n.u.scripts, 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 circ.u.mstances 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 Ma.n.u.script 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 Ma.n.u.script 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 inst.i.tution 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 ma.n.u.scripts to the Sion Col ege Library. A complete list of about 170 books and several ma.n.u.scripts 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 ma.n.u.scripts were lost.

Torporley's ma.n.u.scripts, 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 ma.n.u.scripts relating to Hariot. The more important one comprises 116 closely-written folio leaves, or 232 pages, all in Torporley's handwriting. It bears no t.i.tle 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 Matbematic.u.m,'_ 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 tabulae 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 princ.i.p.al 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 ma.n.u.script 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 n.o.ble patron this work never bore a definite name and never saw the light of the press.

CORRECTOR a.n.a.lYTICUS Artis pofthumx THOMae HARIOTI Vt Mathematici eximij, perraro Vt Philofophi Audentes, frequentius errantis Vt Hominis evanidi, infigniter Ad Fidedigniorem refutationem Philopfeudofophiae Atomifticae;, per c.u.m Reducis, et prae caeteris eius Portentis feri corripiendae, anathematyzandaeq Compendiu Antimonitorfi, et Speciminale exanthorati ia Senioris Na: Torporley.

Vt Noverit Arbiter Caveat Emptor.

non bene Ripae Creditur, ipfe Aries etiam nunc Vellera ficcat.

_Virgil, Ecl._ iii. 94,95,]

This Second Ma.n.u.script 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 t.i.tle-page, given line for line and verbatim.

The ma.n.u.script is in small quarto, and exclusive of the t.i.tle (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 t.i.tle-page, which is here done into English, and is as follows:-

THE a.n.a.lYTICAL 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 a.n.a.lyticus' may be found printed in full (but without the quaint t.i.tles) in 'The Historical Society of Science. A Collection of Letters ill.u.s.trative of Science, edited by J. O. Halliwell,' London, 1841, 8, Appendix, pages 109-116. ForTorporley's curious paper ent.i.tled ' 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 pa.s.sed 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 lacrymae.

On the back of the above t.i.tle-page is another attempt of the same sort as follows, showing that this deed of pedantry was committed at Sion College:

CORRECTOR sive Notae in a.n.a.lyticam Novam, Novatam, Posthuma quatenus Fallacem, Defectivam, Extrariam c.u.m Apodictica refutatione Atomorum Somnij, prae caeteris Novatorum portentis corripiendi Ana- thematizandiq Ex Collegio Sion Londinenfi perfuncti Senis Artemq reponentis NT Extremu hoc munus morientis habetor : Σĸηρον προς κ 41;ντρονλ α κτρον λακτ 43;ζειν [Greek Text]

nee bene Ripae Creditur ipse Aries etia nunc Vellera ficcat.

There are one or two unimportant papers among the Torperley ma.n.u.scripts that bear marks of having belonged to the Hariot papers, and there is a ma.n.u.script by Warner, ent.i.tled, '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 ent.i.tled, '

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 d.i.c.kson, 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 a.n.a.lytica Praxis,_ no extended theory of equations was given. Harriot considered algebraical equations merely as a.n.a.lytical expressions, detached wholly from the operations by which they might be individually produced ; and, carrying all the terms over to one side, he a.s.sumed 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 Epistolae Mutuae. [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 gla.s.s). 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.