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HARRIOT, THOMAS (1560–1621), mathematician and astronomer, was born at Oxford, probably in the parish of St. Mary, in 1560. Ashmole believed that he came of a Lancashire family. He entered St. Mary's Hall, Oxford, and graduated B. A. on 12 Feb. 1580. Sir Walter Raleigh then engaged him to reside with him as his mathematical tutor, and sent him out to Virginia as a surveyor with Sir Richard Grenville's expedition in 1585. Harriot returned to England at the end of the following year, and published at London in 1588 'A Brief and True Report of the new-found Land of Virginia,' a work 'remarkable for the large views it contains in regard to the extension of industry and commerce,' and one of the earliest examples of a statistical survey on a large scale (Edinburgh Review, lxxi. 11). It excited much notice, appeared in Latin in De Bry's 'Arnericae Descriptio' (Frankfort, 1590), and was included in the third volume of Hakluyt's 'Voyages' (London, 1600). Among the mathematical instruments by which the wonder of the Indians was excited, Harriot mentions 'a perspective glass whereby was showed many strange sights.'

About this time Raleigh introduced him to Henry, earl of Northumberland, who admired his affability and learning, and allowed him to the end of his life a pension of 300l. a year. After his committal to the Tower in 1606, the earl kept a handsome table there for Harriot and his mathematical friends, Walter Warner and Thomas Hughes, who became known as the 'three magi' of the Earl of Northumberland. The company was often joined by Raleigh. The earl assigned to Harriot in 1607 a residence at Sion House, near Isleworth, where he continued to study and observe until his death, on 2 July 1621, of a cancer in the nose. His case is mentioned by Dr. Alexander Reid, the physician who attended him (Chirurgtcall Lectures, p. 307). His body was removed with much ceremony to St. Christopher's Church in London, where a monument, destroyed in the great fire, was erected to him by his executors, Robert Sidney, Viscount Lisle, and Sir Thomas Aylesbury [q. v.] The inscription, preserved by Stow (Survey of London, i. ii. 123, ed. Strype), celebrates his successful pursuit of all the sciences, and calls him 'Dei Triniunius cultor piissimus.' In his 'Report of Virginia' Harriot speaks with reverence of the Christian religion, and the lines in Dr. Corbet's poem on the comet of 1618, referring to

deep Harriot's mine,
In which there is no dross, but all refine,

have been interpreted in favour of his orthodoxy. Wood, however, asserts that he 'made a philosophical theology, wherein he cast off the Old Testament.' It is possible that reference is made to Harriot and to his popular reputation as a rationalist in the 'opinion' ascribed to Christopher Marlowe, 'that Moyses was but a Juggler, and that one Heriots can do more than hee '(cf. Harl. MS. 6853, f. 320).

Harriot's health was long weak. He complained to Kepler on 2 Dec. 1606 of inability to write or even think accurately upon any subject, which may explain his failure to complete and publish his discoveries. Sir William Lower warned him in 1609 that his procrastination might lead to the anticipation of some of his ' rarest inventions and speculations.' Among Harriot's anticipated discoveries Lower mentions the ellipticity of the planetary orbits, a ' curious way to observe weights in water,' and ' the great invention of algebra,' the ' garland ' for which had been snatched by Viete. Lower adds that these were small discoveries in comparison with others in Harriot's 'storehouse.'

The posthumous publication of Harriot's ' Artis Analyticae Praxis ad JEquationes Algebraicas resolvendas ' (London, 1631) was due to Sir Thomas Aylesbury, who induced Warner, by the promise of the continuance of his pension from the Earl of Northumberland, to 'draw out some piece fit to be published' from his friend's manuscripts. This work embodies the inventions by which Harriot virtually gave to algebra its modern form. The important principle was introduced by him that every equation results from the continual multiplication of as many simple ones as there are units in the index of its highest power, and has consequently as many roots as it has dimensions. He first brought over to one side, and thus equated to zero all the terms of an equation; he adverted to the existence of negative roots, improved algebraical notation, and invented the signs of inequality > and <. Dr. Wallis's claim on behalf of the 'incomparable' author to have laid the foundation, 'without which the whole superstructure of Descartes had never been' (A Treatise of Algebra, p. 126, 1685), raised a sharp controversy, scarcely yet extinct, between French and English mathematicians. Dr. Pell remarked that had Harriot 'published all he knew in algebra, he would have left little of the chief mysteries of that art unhandled.' But Warner's promise (Epilogue to Harriott's Praxis, p. 180) of continuing his editorial labours remained unfulfilled.

Harriot's will was not found, but Camden states that he divided his papers between Sir Thomas Aylesbury and Viscount Lisle. Aylesbury's share, transmitted to his son-in-law, the Earl of Clarendon, never came to light, though diligently inquired for in 1662-3 by the Royal Society (Birch, Hist. R. Society, i. 120, 309). The remainder, handed over by Lord Lisle to his father-in-law, the Earl of Northumberland, descended from him to the Earl of Egremont, and were discovered at Petworth Castle by Baron von Zach in 1784, buried beneath a pile of old stable accounts. His account of the contents published in the Berlin 'Ephemeris' for 1788, and translated into English, was disfigured by some inaccuracies corrected later by Professor Rigaud. Von Zach designed to write from these new materials a biography of Harriot, and in 1786 made a proposal to the university of Oxford for its publication, but he merely transmitted in 1794, without any illustrative text, the selected original manuscripts which it should have accompanied. These were submitted to Dr. Robertson, the Savilian professor of astronomy, who reported in 1802 that their publication would show Harriot to have been very assiduous in his studies and observations, but could not contribute to advance science (Edinburgh Philosophical Journal, vi. 314). They are now at Petworth Castle, having been restored to Lord Egremont, by whom the remaining papers, being seven-eighths of the entire, were presented to the British Museum.

Harriot was known only as a mathematician until Von Zach's disclosures showed him to have been an astronomer as well. He applied the telescope to celestial purposes almost simultaneously with Galileo. In July 1609 he is said to have made with its help two sketches of the moon (Encycl. Brit. xvl. 528, 8th ed.), and he commenced on 17 Oct. 1610 a series of observations on ' the new-found planets about Jupiter,' continued until 26 Feb. 1612, and accompanied by calculations of I their orbits, and graphical notes of their configurations. He made 199 observations of sun-spots from 8 Dec. 1610 to 18 Jan. 1613, and determined from them the sun's axial rotation. His telescopes magnified up to fifty times. He first saw the comet of 1607 (Halley's) from Ilfracombe on 17 Sept. His observations upon it were made with a 'cross-staff' giving the distances of the nucleus from various stars. They were published by Von Zach (Berlin Astr. Jahrbuch, 1793, l ter Suppl. Band), and reduced by Bessel, who computed an orbit from them (Monatliche Correspondenz, x. 425). Harriot observed the third comet of 1618 from Sion House nine times between 30 Nov. and 25 Dec. He stated the length of its tail on 11 Dec. at forty degrees.

Harriot corresponded on optical subjects with Kepler, 1606-9 (Kepleri Opera Omnia, ii. 67-74). In one letter he refuted experimentally the opinion that refraction varies with density ; others show him to have been a systematic meteorological observer, and to have prepared a treatise on the rainbow and colours. A tract by him, 'De Motuet Collisione Corporum,' was in Lord Brouncker's hands about 1670 ; his 'Ephemeris Chrysometria' is preserved in manuscript at Sion House. The Egremont collection of his papers in the British Museum is bound in eight large volumes (Addit. MSS. 6782-9), filled chiefly with miscellaneous calculations. The seventh volume contains, besides fragments on mechanics, hydrostatics, specific gravity, and magnetism, a letter from Nathaniel Torporley (f. 117), and the eighth includes letters from Sir William Lower and one from Sir Thomas Aylesbury. A further deposit of Harriot's mathematical papers forms part of the Harleian MSS. (6001-2, 6083). Among them are tracts on harmony, solid geometry, infinite series, extracts from the gospel of St. Matthew translated into French, a short phoranomical treatise (6083, f. 236), and a 'Traité d'Algebre' (in French), in which ad- vances are made towards the application of algebra to geometry. Harriot was designated by Wood 'the universal philosopher' (Athenæ Oxon. ii. 230), and a wide contemporary admiration is attested by Kepler's expressions towards him. His 'Report of Virginia' was published in German at Leipzig in 1607.

[Biog. Brit. iv. (1757); Wood's Athenae Oxon. ii. 299; Wood's Fasti Oxon. i. 212 (Bliss); Von Zach, Astr. Jahrbuch fur 1 788, p. 1 52 ; Monatliche Correspondenz, viii. 30 (1803) ; Correspondance Astronomique, vii. 105 (1822); Kigaud, Proceedings K. Society, iii. 125 ; Report British Association, i. 602 ; Journal Royal Institution, ii. 267 ; Bradley's Miscellaneous Works, App. p. oil ; Robertson's Edinburgh Phil. Journal, vi. 314 (1822) ; Aubrey's Lives of Eminent Men, ii. 418, 578 (information from Dr. Pell and Isaac Walton) ; Thomson's Hist. R. Society, p. 259 ; Hutton's Mathematical Dict. (1815), i. 94, and art. Harriot; ' Montucla's Hist, des Mathematiques, ii. 105; Marie's Hist, des Sciences, iii. 92, v. 140; Poggendorff's Hist, de la Physique pp 100, 114, 119 ; Wilde's Geschichte der Optik i. 190; Wolf's Gesch. der Astr. pp. 318, 402; Ersch und Gruber's Allgemeine Encyklopadie', sect. ii. Th. iii. ; Hakluyt Society's Publications, iii. (1848), Introduction, p. xxix.]

A. M. C.