by J. J. Roche
© Oxford University Press 2004 All rights reserved
Harriot, Thomas (c.1560-1621), mathematician and natural philosopher, was born in the city or county of Oxford. All that is known for certain of his family is that his father was a commoner, he had a married sister, he had relatives in Berkshire, and he did not marry. He matriculated at Oxford on 29 December 1577 as a member of St Mary Hall, and was awarded a BA degree at Easter 1580.
The art of navigation
Harriot soon developed a high reputation for the mathematical and instrumental skills necessary for astronomical navigation, stimulated in these studies, perhaps, by the prevailing enthusiasm for exploration and colonies in America. By 1584 at the latest he was employed 'at a most liberal salary' by the queen's favourite, Sir Walter Ralegh (c.1552-1618), to teach Ralegh and his sea captains at Durham House in London the sciences of navigation, and to serve him in various other capacities, in preparation for Ralegh's first enterprise to establish a settlement in America. Harriot--but not Ralegh--was a member of the short-lived colony which landed on Roanoke Island, Virginia, in June 1585 and returned to England with Sir Francis Drake in June 1586. Before the voyage Harriot had studied the local language from two Algonquian Indians who had been taken to England in 1584 by a reconnaissance expedition. He even invented a phonetic alphabet to represent the language, and used his knowledge in Virginia to study local social and religious customs, together with plants, animals, and produce. Harriot published a summary of his survey, largely to defend Ralegh's enterprise, as a pamphlet in 1588 entitled A Brief and True Report of the New Found Land of Virginia. At a time of brutal violence between colonists and native inhabitants the text is remarkable for its sympathy towards Algonquian beliefs and customs. It also contains what may be the first printed promotional literature in English for tobacco by an English writer, and Harriot and Ralegh were subsequently credited with the introduction of pipe tobacco smoking into England from Virginia. The Report was much published subsequently.
Following his return from Virginia, Harriot participated in Ralegh's colonizing enterprise in Munster and was granted title to Molanna Abbey near Youghal. He was definitely living there in August, 1589, although by early 1590 he was back in Durham House. From at least 1591 Harriot became increasingly involved in the circle of another controversial figure, Henry Percy (1564-1632), the ninth and so-called 'Wizard' earl of Northumberland, a close friend of Ralegh. In 1590 Harriot is reported as being at work examining existing navigational tables for Ralegh. He discovered that 'eclipses happen an houre and sometimes more out and sometimes little less, after the time they are foretold' (Roche, 251). To reform these tables Harriot constructed the largest astronomical instrument in sixteenth-century England, a 12 foot device which may have been an astronomer's cross-staff. The observations and calculations which he carried out between 1590 and 1594, his lost navigational manuscript 'Arcticon', his innovations in mathematical cartography, and his improved instruments and observing practices provided Ralegh with the best navigational expertise then available in Europe, which he made use of during his voyage in 1596 to Guiana in search of El Dorado. Perhaps Harriot's most advanced achievement in map theory during this period was his construction of a table which allowed a navigator to set a fixed compass course when sailing between two ports--offering a solution to the so-called 'Mercator problem'. He completed this work by 1614, developing very sophisticated mathematical techniques in the process.
Political misfortunes
Ralegh's star began to wane at court in 1592 following the queen's discovery of his secret marriage to Elizabeth Throckmorton. He was also accused in print in the same year of maintaining a school of atheism led by Harriot. Both men were mentioned in the evidence gathered to prove the 'scorn of Gods word' by the free-thinking playwright Christopher Marlowe (1564-1593), who was murdered in 1593 (Shirley, Biography, 181-3). This led to hearings on atheism in Dorset by an ecclesiastical commission which met in 1594 at Cerne Abbas, near where Ralegh then lived. Although much hearsay evidence was presented against Ralegh and Harriot the investigation went no further. Indeed, Harriot's published papers and manuscripts reveal an intelligent piety and contain little which might be interpreted as irreligion; even so, he acquired a damaging reputation for impiety, which was reinforced by his support for atomism--long associated with atheism--and his phrase ex nihilo nihil fit ('from nothing, nothing is made') echoing the ancient atomists. However, soon after, he found a powerful new patron: during the mid-1590s Henry Percy granted him rents from an estate in co. Durham, the use of an estate house in the grounds of Syon House, Isleworth, and a pension of £80 a year which he received for the rest of his life. Harriot maintained a library and a research workshop at Syon, and was looked after by three servants and craftsman. He appears to have had no formal duties, was able to pursue his theoretical and practical researches in a most encouraging environment, and maintained a close involvement with Ralegh and with navigational matters. Harriot's most important achievement during his early years at Syon was his discovery in 1601 of the correct mathematical law according to which light is refracted when it passes from one transparent medium into another--the sine law of refraction. He also recognized that red, yellow, and blue light are refracted differently and measured their refractions. Johann Kepler (1571-1630) heard of Harriot's discovery and wrote to him in 1606 for information. Harriot sent Kepler some refraction data but did not reveal the law, hoping, perhaps, to achieve proper recognition in print: perplexingly, however, Harriot never published a discovery which would have secured his reputation in the history of science, nor was any of his work in optics, mechanics, astronomy, mathematics, navigation, or cartography published in his lifetime--causing considerable distress to his friends. Harriot's other interests during this period included the study of ordnance, and chemical experiments. The former studies seem to have led him to an advanced mathematical treatment of falling bodies and projectiles, and of collisions between bodies. He also read widely in the learned literature of his day.
Harriot must have felt very secure in June 1603, when King James visited Syon House as part of his progress through the realm and showed clear marks of favour to Northumberland. In July, however, Ralegh was arrested on suspicion of involvement in a plot to kill the king and taken to the Tower, where he attempted suicide. Harriot assisted Ralegh's preparation for his trial and was mentioned by Lord Chief Justice Popham as an atheist and evil influence when passing a judgment of treason on Ralegh. Although the king stayed the execution, Ralegh was not pardoned: after his release in 1616 he undertook a disastrous voyage to Guiana and on his return was beheaded in 1618, an event witnessed by Harriot. Misfortune also struck Harriot's second patron, Henry Percy, who was rumoured to be aware of the Gunpowder Plot of 1605. He was interrogated and imprisoned in the Tower. In November 1605 Harriot was incarcerated in the Gatehouse prison for at least three weeks, his house at Syon was searched, and he and his close friends Nathaniel Torporley (1564-1632) and Sir William Lower (c.1570-1615) were interrogated. In a controversial trial of 1606 Northumberland was convicted of various offences connected with the Gunpowder Plot, stripped of offices, fined £30,000 and imprisoned in the Tower at the king's pleasure. Until his release in 1621 he lived in the Tower, from where he managed his estates and continued to support Harriot at Syon. Harriot, of course, saw his situation as precarious and, in a letter to Kepler in 1608, stated that 'we still stick in the mud' (Kepler, 15.172).
A tradition developed in the early seventeenth century that Ralegh and the earl maintained a kind of academy (the 'School of Night') in the Tower, with Harriot as its master and including the mathematicians Walter Warner (d. before 1644) and Robert Hues (1553-1632). The antiquary John Aubrey (1626-1697) in his Brief Lives reports that 'these 3 were usually called the earle of Northumberland's three Magi' (Brief Lives, 1.286). Although Warner and Hues were connected with the earl of Northumberland there is no evidence for any such association based in the Tower. Nevertheless, during the first two decades of the seventeenth century Harriot was the leading figure in a network of scholars which, together with Percy, Ralegh, Warner, and Hues, included the poet and scholar George Chapman (1557-1634), Sir William Lower, member of parliament for Lostwithiel in Cornwall, Thomas Aylesbury (d. 1658), secretary to the earl of Nottingham, Torporley, mathematician and clergyman, and Lord Harrington (1592-1614).
Mathematics and astronomy
Harriot's will and surviving manuscripts make it clear that he thought of himself primarily as a mathematician. He was, perhaps, the most able mathematician in Europe between François Viète (1540-1603) and René Descartes (1596-1650), but he failed to publish any mathematics in his lifetime. In 1631 Walter Warner edited and published posthumously a limited selection of Harriot's papers dealing with algebra, with the title Artis analyticae praxis. The mathematician John Wallis (1616-1703) was so impressed by this text that, in a publication of 1685, he accused Descartes of failing to acknowledge Harriot as the source of most of his innovations in algebra, provoking a long dispute with French mathematicians. It seems unlikely that Harriot had found Descartes's 'rule of signs' about the positive and negative zeroes of a polynomial, but Wallis claimed it for him, and his name was and is often associated with it. A more sober assessment of Harriot's Artis analyticae praxis shows that it developed the algebra of Viète into a fully symbolic form--dropping all verbal expressions of relations and operations--and expanded considerably the problems dealt with by Viète's methods. This was an achievement of the first importance. The text also introduced inequality symbols for the first time in print, it used italic lower-case notation systematically for the first time to represent algebraic equations, and it gave Viète's algebra a numerical rather than a geometrical interpretation. By contrast, Descartes's algebra (La géometrie, published in 1637) was interpreted geometrically.
By 1610 Harriot was a Copernican and rejected the crystalline spheres of the ancients. He anticipated Kepler by conjecturing that the motions of planets were not perfect circles and he immediately accepted Kepler's theory of elliptical orbits. He also anticipated Galileo in conjecturing that other planets besides the earth have satellites. Speculations, however, are not discoveries, and Harriot was not a dedicated theoretical or observational astronomer, although he made astronomical observations for some thirty years. He used a cross-staff to measure the angular distances to neighbouring stars of Halley's comet during its return in 1607, and Friedrich Bessel (1784-1846) found his data sufficiently accurate to calculate its orbit. Harriot also observed the comet of 1618. On 26 July 1609 Harriot observed the moon through his telescope--the first was possibly bought in the Low Countries, though lenses were subsequently apparently ground and constructed by himself and his craftsman Christopher Tooke (1572-1630)--and sketched the lunar surface. Harriot's first recorded observation of sunspots was on 28 November 1610. Although this was undoubtedly an independent observation, Harriot may not have observed them before Galileo. Harriot's most sustained programme of observations contains some 100 nightly logs of Jupiter's satellites between 17 October 1610 and 26 February 1612. These led him to a remarkably accurate value for the period of Io, the first satellite. Harriot's papers contain records of various observations of lesser importance, including the determination of planetary positions, the exact moment of occurrence of the first quarter of the moon, and the study of the phases of Venus.
In his day Harriot had something of a European reputation but his failure to publish meant that his positive contributions to European science, which may have been transmitted through his personal contacts, are difficult to establish. The commitment to publication often brings a scholar's work to maturity. This failure was in part due to Harriot's reputation for impiety and his close association with Ralegh and Northumberland, but it is difficult to see how publications in navigational science or of maps, mathematics, optics, mechanics, or astronomy could have been other than beneficial to his position. It is difficult, also, to form a clear picture of Harriot the person. His friend Sir William Lower speaks of his 'too great reservednesse' (Shirley, Biography, 400). In 1615 the king's physician Theodore de Mayerne examined Harriot for a cancerous tumour of the nose and describes him as 'a man somewhat melancholy' (ibid., 433). There are indications, however, that he had a restrained, scholarly humour. Also, he had many loyal friends and showed considerable loyalty himself in dangerous circumstances.
Death and revaluation
Harriot died of his tumour at a house in Threadneedle Street, London, on 2 July 1621, a month before Henry Percy was released from the Tower, and he was buried in the nearby church of St Christopher-le-Stocks. His will, dictated three days previously, reveals that, although Harriot owned no landed property, he possessed a substantial library, much scientific equipment, including many telescopes and alchemical furnaces, and savings of about £300. He bequeathed his papers to the earl, which explains why so many have survived. The memorial plaque erected to Harriot in the church was destroyed in the great fire of 1666 but its wording was preserved. In 1971 a bronze plaque with the same Latin inscription was unveiled on a wall in the Bank of England, as close to the site of Harriot's grave as could be determined.
Many volumes of Harriot's working mathematical papers survive. An examination of them shows that he made other important innovations in mathematics, including the application of algebra to the analysis of conic sections, a study of binary numbers, the discovery of an algorithm for computing the area of a spherical triangle, and the development of logarithmic tangents.
Harriot's astronomical papers received considerable publicity following the rediscovery by Frans Xavier Zach (later Baron von Zach; 1754-1832) in 1784 of Harriot's manuscripts at Petworth House, Sussex, where they had remained since the death of Henry Percy in 1632. Von Zach, who was particularly interested in astronomy, claimed priority for Harriot over Galileo in the discovery of sunspots and Jupiter's satellites. This caused considerable controversy until a systematic study of Harriot's astronomical papers was undertaken and published in 1833 by Stephen Peter Rigaud (1774-1839), Savilian professor of astronomy at Oxford. Rigaud attempted to refute von Zach's claims for Harriot's priority but, as he himself admitted, he had not the opportunity to study all of Harriot's manuscripts bearing on this subject. Nor did Rigaud have access to Harriot's will which sheds significant light on his astronomy. The latter was discovered before 1885 by Henry Stevens (1819-1886) of Vermont. Except for von Zach's selection of papers and some others which remain at Petworth--a total of more than 1000 folios--the bulk of the Harriot manuscripts--more than 4000 folios--were deposited in 1810 in the British Museum by Lord Egremont, who held title to Petworth House. The Harriot manuscripts received considerable scholarly attention in the twentieth century, mainly as a result of some forty years of pioneering historical research by John W. Shirley of the University of Delaware and owing to the scholarship, stimulus, and financial support of Cecily Young Tanner of Imperial College, London.
J. J. ROCHE
Sources
J. W. Shirley, Thomas Harriot: a biography (1983) [incl. bibliography]
D. B. Quinn, ed., The Roanoke voyages, 1584-1590: documents to illustrate the English voyages to North America under the patent granted to Walter Raleigh in 1584, 2 vols., Hakluyt Society, 2nd ser., 104, 105 (1955)
J. Jacquot, 'Thomas Harriot's reputation for impiety', Notes and Records of the Royal Society, 9 (1951-2), 164-87
R. C. H. Tanner, 'Thomas Harriot as mathematician: a legacy of hearsay', Physis, 9 (1967), 235-92 [includes Harriot's will]
J. Wallis, A treatise of algebra both historical and practical (1685)
J. A. Lohne, 'Thomas Harriot, 1560-1621: the Tycho Brahe of optics', Centaurus, 6 (1959), 113-21
J. W. Shirley, 'Thomas Harriot's lunar observations', Science and history: studies in honor of Edward Rosen, ed. E. Hilfstein and others (1978), 283-308
J. W. Shirley, ed., A source book for the study of Thomas Harriot (1981)
T. Harriot, A briefe and true report of the new found land of Virginia (1588)
Petworth House, Harriot MSS, MS HMC, 240 i-v; 241 i-x
BL, Add. MSS 6782-6789
Johannes Kepler: Gesammelte Werke, ed. W. von Dyck and M. Caspar, 15-17 (München, 1951-9)
J. J. Roche, 'Harriot's "Regiment of the sun" and its background in sixteenth-century navigation', British Journal for the History of Science, 14 (1981), 245-61
Brief lives, chiefly of contemporaries, set down by John Aubrey, between the years 1669 and 1696, ed. A. Clark, 2 vols. (1898)
J. W. Shirley, ed., Thomas Harriot: Renaissance scientist (1974)
matriculation register, Oxford
Archives
BL, corresp. and mathematical calculations, Harley MS 6083; Add. MSS 6782-6789
Petworth House, West Sussex, astronomical and mathematical notes, MS HMC 240 i-v and 241 i-x | BL, Sloane MS 2292
Wealth at death
approx. £300: will, Archdeaconry court of London
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