Jeremiah Horrocks

Jeremiah Horrocks hailed from Toxteth Park, Toxteth referring to a greater area than nowadays. Specifically, Horrock's home seems to be generally identified with a site latterly occupied by Otterspool Station on the Cheshire Lines Railway which was built in the 1860s.

He observed the transit of Venus from Much Hoole, east of Southport) and came to the following conclusions

His paper was published by Johannes Hevelius in Poland rather than in Britain and thisa was twenty years after the event. The relevant papers had been rescued by a friend, John Worthington, who forwarded them to a friend of his who weas involved in scientific publishing. Via the agency of Chritian Huygens, these papers reached Hevelius who had justy observed a transit of Mercury. Horrock's and Hevelius paper's were issued as one volume in 1662.

He had studied at Cambridge and distinguished himself by being seemingly the only one at Cambridge to believe in the Copernican theory.

From about 1637 onwards, the British astrionomer Jeremiah Horrocks, announced to a friend that he was attacking the problem of the Moon's motion. He soon stated that to a first approximation, the orbit was an ellipse with the Earth at a focus. This was not just a straightforward stement of Kepler's law - he did actually caqlculate the orbital constants. Jeremiah Horrocks  [Horrox],    (1618-1641), astronomer, was born in the first half of 1618 in Lancashire and grew up in Toxteth Park, then an isolated village about 3 miles from the port of Liverpool. It had been settled in the late sixteenth and early seventeenth centuries by several families of puritan sympathies. Horrocks's religious opinions reflected their outlook. His parents, who were of moderate means, were in all probability James Horrocks (d. 1641), a watchmaker, and his wife, Mary, nee Aspinwall (b. 1580). Jeremiah had a younger brother, Jonas, and relatives in New England. A passion for astronomy Horrocks was admitted sizar in Emmanuel College, Cambridge, in May 1632 and left in 1635 without taking a degree. As a sizar his tuition was remitted and he was expected to help in the college buttery or kitchen, wait on fellows at table, and act as a servant to one of the senior fellows. In a brief autobiographical sketch written when he was twenty, Horrocks tells how as a boy at Cambridge he became enamoured of astronomy and in a relatively short time, without formal instruction or the companionship of others with similar interests, mastered its principles. The intensity of his commitment to the science, he relates, was fired by ambition, pleasure in observation, contemplation of the wisdom of the Creator, and a desire to know the causes of celestial phenomena. His remarkable achievements during his short life were highly praised by the leading scientists of the seventeenth century, including Newton. By the nineteenth century the praise of astronomers and historians of astronomy had not diminished. J.-B. J. Delambre referred to him as 'a genius of the same stamp as Kepler'  (Delambre, 2.499), while John Herschel called him 'the pride and boast of British astronomy'  (Herschel, 86n). The Victorian era saw the rise of a special genre of Horrocks hagiography, emphasizing his pluck, perseverance, and moral rectitude, and the happy convergence in him of religious and scientific ideals, partially owing to the mistaken impression that he had been ordained. Horrocks came to the study of his science at a time when traditional conceptions of the heavenly bodies and the nature of the universe were breaking down and a significant increase in observational precision had become an important desideratum. At Cambridge he read as widely as he could in the works of Ptolemy, Copernicus, and Tycho Brahe as well as more recent authors. His initial textbook, however, was very likely The Strange and Dangerous Voyage of Captain James (1633), a popular account of an expedition to find the north-west passage. It contained an appendix by Henry Gellibrand (1597-1637), Gresham professor of astronomy, which seems to have provided Horrocks with an introduction to the essential literature and instrumentation of his science. Computing planetary tables Following Gellibrand's recommendation, Horrocks obtained Philip van Lansberge's Perpetual Tables, which, their author claimed, would predict accurately planetary positions for all time. When his observations made clear that Lansberge's assertions had been highly overstated, Horrocks became disenchanted, and in January 1637 concluded that Lansberge's tables should be discarded and more accurate ones created. It was presumably then that he began to compute his own, and shortly thereafter he drafted and redrafted a treatise attacking Lansberge. His annotated copy of Lansberge's book, preserved in the library of Trinity College, Cambridge, is a valuable source of information on the development of Horrocks's thought in his early period. His other early notes and manuscripts are no longer extant; those remaining were begun in the second half of 1637. They appear to be of two types: those constituting notes for his astronomical education, written in English, and several drafts in Latin of treatises begun but never completed. Among Horrocks's earliest observations, and of a kind he was to continue to make, were lunar, solar, planetary, and stellar diameters. Contrary to contemporaneous belief, Horrocks concluded that the apparent diameters of the stars were so immeasurably small as to be equivalent to points of light. He also made corrections to stellar positions in both Ptolemy's and Tycho Brahe's star tables. Determined to put astronomical theory to observational test whenever possible, he continually compared his observations of planetary positions with their places as predicted in several different astronomical tables. Horrocks's astronomical instruments included three cross-staffs, or astronomical radii-graduated rods with sliding cross-pieces for the measurement of celestial angles-which he built himself. He also constructed a 13 inch quadrant and purchased a telescope in 1637 and another the following year. Always concerned about the accuracy of his observations, he carefully noted his means of observation and frequently the weather. In the course of his career he made adjustments to his observations for atmospheric refraction, ocular parallax, or eccentricity of the eye (allowing for the slight distance of the centre of the eye from the observing end of the astronomical radius from which angular measures were taken), and redetermined terrestrial longitudes using lunar eclipses and also the latitudes of several places. Conversion to Keplerian astronomy After he left Cambridge, Horrocks presumably returned to Toxteth Park. In June 1636 he began a correspondence with William Crabtree, a clothier or draper of Broughton, near Manchester, that was to give further impetus to his studies. The two men exchanged letters frequently and they occasionally visited one another. Crabtree's observations strengthened Horrocks's conviction concerning the inadequacy of Lansberge, and Crabtree persuaded his friend to investigate the astronomy of Johannes Kepler. Horrocks then began to purchase Kepler's books, acquiring all his major works in 1636 and 1637, and immersed himself in the study of Kepler's astronomy. By the end of 1637 Horrocks had become a convinced Keplerian, accepting what would come to be called Kepler's laws-elliptical orbits, non-uniform planetary motion, and the proportionality between the squares of the planets' periods and the cubes of their distances from the sun. In Horrocks's surviving manuscripts there is no mention of Kepler's 'second law' of planetary motion, which asserts that a radius vector from the planet to the sun sweeps out equal areas in equal times. Horrocks was nevertheless familiar with it, as he would develop a geometrical solution for a means of approximating to it and used it in his theory of the moon. Horrocks fully accepted Kepler's vision of an astronomy based on physical causes, rare at the time, as well as harmonic ones, and rejected the Peripatetic division between the celestial and terrestrial regions. The causes of the motions of the planets he held with Kepler to reside in the sun. Like Kepler, he saw a great advantage in the elimination of the traditional circles, eccentrics, and epicycles from astronomy; they were fictional devices useful only for purposes of calculation. Size of the universe On dynamical and cosmological issues, however, Horrocks became partially dissatisfied with Kepler's quasi-magnetic causes of planetary motion, rejecting his concept of a periodic solar repulsion of the planets, and opting instead for a mechanical analogy with falling bodies and a conical pendulum. He also objected to Kepler's intimation that certain anomalies in the celestial motions might be due to accidental physical causes, and called attention to the doubt of some astronomers that astronomy would ever be established on certain principles, noting the number of frustrated attempts to make astronomical tables coincide with the heavens. Horrocks was persuaded, however, that, if rightly cultivated, astronomy would shortly attain the perfection sought. With his telescopes Horrocks observed the planets, the sun by projection-taking note of sunspots and recording a solar eclipse-the moon, and appulses to the moon. He took great pains to improve the accuracy of his measurements of the sun's diameter and made a considerable number, as it was important for the determination of the solar parallax, the angle subtended at the sun by the earth's radius. The effective employment of geometrical means to determine the relative distances of sun, earth, and moon had been sought from antiquity. Horrocks found the figures given for solar parallax by earlier astronomers inadequate. Since the planetary parameters depended on it, a more precise figure for it would yield more accurate predictions of planetary positions. Realizing that the parallax was negligible and outside the range of observational precision, he nevertheless thought it possible to gain a reasonable idea of it by utilizing very precise observations and making certain harmonic assumptions. Concerned with the harmonious ordering of the universe as God's creation, Horrocks, as had Kepler before him, thought that the sizes of the planets would fit a pattern. All the planets, he concluded, seem to have apparent diameters of 30 seconds of arc when seen from the sun. Horrocks derived a figure at first of 15 seconds and then 14 seconds of arc for the solar parallax, yielding a very great increase in the size of the solar system compared to those given by earlier astronomers. Horrocks's numbers gave the distance of the earth from the sun at about two-thirds its accepted value at present. Revising Kepler's tables Horrocks's revision of Kepler's figure of 1 minute of arc for the solar parallax led the young astronomer to effect improvements on Kepler's tables for the sun and planets. His comparison of his observations with the places predicted from Kepler's tables had shown Kepler to err by up to 13. Noting also that Kepler's Rudolphine Tables had the vernal equinox arriving earlier than it should have, Horrocks altered Kepler's figures for the eccentricity of the earth-the distance from the sun of the centre of the earth's elliptical orbit as a fraction of the radius along its major axis. Convinced, however, of the superiority of the Rudolphine Tables over all others, and that they alone rested on a correct theoretical foundation, Horrocks continued to work at correcting the parameters for each of the planets based on his and Crabtree's observations. His observations led Horrocks to the conclusion that Jupiter was becoming more rapid in its mean motion and Saturn slower. He seems to have recognized that these secular retardations and accelerations were periodic and may have been caused by their influence upon one another. Having noticed in 1637 significant departures in the moon's position from predicted places derived from Kepler's tables, Horrocks turned his attention to the theory of the moon. The moon was the celestial body offering the greatest difficulty in predicting its position on a consistent basis. By the end of 1638 Horrocks presented Crabtree with a rough draft of his 'new theory of the moon'. It was in his lunar theory that Horrocks created his most influential advance over Kepler. With Kepler, Horrocks accepted an elliptic orbit for the moon, but he advanced considerably beyond Kepler in accounting more accurately for certain lunar inequalities than anyone had up to that time, or indeed would for some time after him. Horrocks's lunar theory involved the adoption of a varying eccentricity for his elliptical lunar orbit and an oscillation of the lunar apsides-the line passing through its minimum and maximum distances from the earth-about its mean position, which underwent a slow rotation. He indicated that there must be some physical explanation for these variations, but offered none other than a hint that the periodically changing relationships between sun, earth, and moon must play some part. From the beginning Horrocks linked both empirical factors and physical hypotheses in his efforts to explain or account for the motions of the moon and its inequalities. His elliptical theory has in it the kernel of perturbation theory based on physical causes of the lunar inequalities. By 1640 he had changed a number of lunar parameters. The last stage of his theory is found in a letter of Crabtree to William Gascoigne in June or July 1642. In his last letter to Crabtree Horrocks had expressed the opinion that his lunar theory was the most important of his discoveries. Isaac Newton would later adopt Horrocks's variable eccentricity and oscillating apse-line, making only a small improvement in the efficacy of the theory. From the summer of 1639 to the summer of 1640 Horrocks spent a year in the village of Hoole, 20 miles north of Liverpool. His employment is unknown, but he was possibly a tutor or 'reader' to the most prominent family in the village. He may have taught in the local school or had some part in the services of the local church. Transit of Venus Horrocks continued to work at his planetary tables and, while working on the planet Venus, discovered in the autumn of 1639 that the planet would pass across the face of the sun. He computed the time of conjunction from Copernican, Tychonian, and Keplerian tables and those of Lansberge. Kepler had claimed that there would be no transit of Venus until 1761, and it was probably on his authority that no other astronomer was prepared to look for it. Having discovered an error in Venus's latitude in Kepler's tables, Horrocks realized that the planet would transit the sun on 24 November and communicated the information to Crabtree, urging that he pay particular attention to the apparent diameter of Venus. The resulting observation led Horrocks to feel it confirmed his opinion concerning the solar parallax, but required him to revise it slightly. It also permitted him to adjust the elements of the sun, and the orbits of the earth and Venus. The transit was also observed by Crabtree, who confirmed in a general way what Horrocks had observed. While the several tables Horrocks had consulted were considerably off in predicting the time of the transit-the best of them, Kepler's Rudolphine Tables, erred by almost ten hours-Horrocks's corrected tables were accurate to within two minutes. The observation also confirmed, despite the opinion of Tycho Brahe, that the planets were dark bodies and not self-luminous. Horrocks undertook to study the tides in the autumn of 1640, possibly convinced after reading Galileo's Dialogue on the Two Great World Systems that the motion of the earth could be proved by the tides. Liverpool is well situated for such observations, as there is a great difference between high and low water. Horrocks, however, held with Kepler that the tides are affected by the moon's attraction, but wondered if they could affect in turn the motion of the earth. Horrocks's achievements lay hidden from the wider scientific world for several years after his death, at Toxteth Park, on 3 January 1641. Many of his papers have been lost, but during the 1660s those that survived came to the notice of some astronomers and early fellows of the Royal Society, among whom they exerted some influence on the development of predictive astronomy and celestial mechanics. It was then that Newton learned for the first time of Kepler's third law and of Horrocks's successful test of it. Horrocks's Venus in sole visa, a draft of a treatise on the transit of Venus, and a defence of Keplerian astronomy, was published by Hevelius in 1662. Most of the remainder of his work was published under the editorship of John Wallis by the Royal Society in 1672 and 1673 as Opera posthuma. It was reissued in 1678, with an appendix by John Flamsteed describing Horrocks's mature lunar theory. In the nineteenth century a memorial tablet in Horrocks's honour was placed in Westminster Abbey near the site of Newton's burial place, and the popular astronomer Moses Holden paid for another to be set up in St Michael's Church, Toxteth. Wilbur Applebaum Sources  C. Wilson, 'Predictive astronomy in the century after Kepler', Planetary astronomy from the Renaissance to the rise of astrophysics, ed. R. Taton and C. Wilson, The general history of astronomy, ed. M. A. Hoskin (1989), 166-71, 197-201 + C. Wilson, 'On the origin of Horrocks's lunar theory', Journal for the History of Astronomy, 18 (1987), 77-94 + C. Wilson, 'Horrocks, harmonies, and the exactitude of Kepler's third law', Studia Copernicana XVI: science and history: studies in honor of Edward Rosen, ed. E. Hilfstein and others (1978), 235-59 + W. Applebaum, 'Horrocks, Jeremiah', DSB + A. Chapman, 'Jeremiah Horrocks, the transit of Venus, and the "new astronomy" in early seventeenth-century England', Quarterly Journal of the Royal Astronomical Society, 31 (1990), 333-57 + W. Applebaum, 'Between Kepler and Newton: the celestial dynamics of Jeremiah Horrocks', Proceedings of the XIIIth International Congress of the History of Science [Moscow 1971], 4 (1974), 292-9 + S. B. Gaythorpe, 'Jeremiah Horrocks: date of birth, parentage and family associations', Transactions of the Historic Society of Lancashire and Cheshire, 106 (1954), 23-33 + Memoir of the life and labours of the Rev. Jeremiah Horrox: to which is appended a translation of his discourse upon the transit of Venus across the sun, trans. A. B. Whatton (1859) + S. B. Gaythorpe, 'Jeremiah Horrocks and his "new theory of the moon"', Journal of the British Astronomical Association, 67 (1956-7), 134-44 + S. B. Gaythorpe, 'Horrocks's observations of the transit of Venus 1639 November 24 (O.S.)', Journal of the British Astronomical Association, 47 (1936-7), 60-68; 64 (1953-4), 309-15 + J. B. J. Delambre, Histoire de l'astronomie moderne, 2 (Paris, 1821), 499 + J. F. W. Herschel, Treatise on astronomy (1839), 86n. + Jeremiae Horroccii...opera posthuma, ed. J. Wallis (1673) Archives CUL, Royal Greenwich Observatory archives, papers + Trinity Cam., Horrocks's annotated copy of Philip van Lansberge's Tabulae perpetuae 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 Francois Viete (1540-1603) and Rene 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 Viete into a fully symbolic form-dropping all verbal expressions of relations and operations-and expanded considerably the problems dealt with by Viete'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 Viete's algebra a numerical rather than a geometrical interpretation. By contrast, Descartes's algebra (La geometrie, 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 (Munchen, 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