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Thomas Harriot

Thomas Harriot

A contemporary of Shakespeare, Elizabeth I, Johannes Kepler, and Galilei Galileo, Thomas Harriot (1560-1621) was an English scientist and mathematician. His principal biographer, J. W. Shirley, was quoted in the website "Thomas Harriot's manuscripts," saying that in his time he was "England's most profound mathematician, most imaginative and methodical experimental scientist, and first of all Englishmen to make a telescope and turn it on the heavens." He was also an early English explorer of North America. He published very little in his life time, and the extensive scientific papers he left at his death suffered loss and then neglect until the twentieth century.

Educated at Oxford

Harriot was born in Oxfordshire, England, in 1560. Nothing is known about his parents except that his father was recorded as a plebeian when Harriot entered the University of Oxford on December 20, 1577. Of Harriot's early school years a boyhood friend, Tom Buckner, one day wrote, as quoted in Thomas Harriot: Science Pioneer, "Tom Harriot had a far greater gift for language than I had. He enjoyed reading the writings of the ancient Romans, sharpening his language abilities through disputation and debate, and writing poetry in Latin." Harriot was a good student. At Oxford he attended St. Mary's Hall with other students from the plebeian class. He became friends with two of his teachers, Richard Hakluyt, a geographer, and Thomas Allen, who had an interest in astronomy and was a suspicious figure to some because of the unusual instruments in his rooms. Harriot continued to do well in his studies and was one of only three in his class to receive a bachelor's degree in July 1580.

Sponsored by Raleigh

While Harriot was enrolled in St. Mary's Hall, Walter Raleigh had attended Oxford's Oriel College, the preserve of the gentry and nobility. Raleigh was already involved in exploration in North America when Harriot graduated. Raleigh and his half brother Sir Humphrey Gilbert had sailed with 11 ships to the Cape Verde Islands in 1578, and the ships had become badly scattered en route. Raleigh wanted someone to teach reliable navigation techniques to his ship captains. The principal at St. Mary's recommended Harriot, and Raleigh became Harriot's first patron. Harriot moved to Raleigh's London residence, Durham House.

Harriot made several investigations to prepare a course for English navigators. He interviewed ships' captains at the docks along the Thames River. His friends Allen and Hakluyt from Oxford helped him. He also read John Dee's translation of Martin Cortes' Arte de navigation. The result was a textbook he named Arcticon. Only the names of its chapters have survived; some of them were "Some Remembrances of taking the altitude of the Sonne by Astrolabe and Sea Ring," "How to find the declination of the Sonne for any time of the yeare & any place; by a speciall table called the Sonnes Regiment newly made according to late observations," and "Effect of longitude on declination."

Traveled to Virginia

When Raleigh received permission to sail to North America in 1584, Harriot may have accompanied him, but there are no records to confirm it. He is known to have sailed for the Western Hemisphere with Sir Richard Grenville in 1585. En route Harriot made many observations of the sun and stars to track his course, and he also observed a partial solar eclipse. The ship sighted Dominica in the Caribbean, then moved northward. On June 30, 1585, it anchored at Roanoke Island, off Virginia. On shore, Harriot observed the topography, flora, and fauna, making many drawings and maps, and the native people, who spoke a language the English called Algonquian. Harriot worked out a phonetic transcription of the native people's speech sounds and began to learn the language, which enabled him to converse to some extent with other natives the English encountered. Apparently Harriot favored friendly relations with the native people, but others in the party felt otherwise, and at least one of the native people was killed. At the same time, Sir Francis Drake, patrolling the Florida coast for Spanish treasure galleons to capture, heard the Spanish planned to attack the colony at Roanoke. He sailed north to warn the English and took most of them back to England in 1586. Harriot wrote his report for Raleigh and published it as A Briefe and True Report of the New Found Land of Virginia in 1588. Raleigh gave Harriot his own estate, in Ireland, and Harriot began a survey of Raleigh's Irish holdings. He also undertook a study of ballistics and ship design for Raleigh in advance of the Spanish Armada's arrival.

Security Shaken

Two events made Raleigh's and Harriot's lives stressful about this time. First, Raleigh's political situation became murky when he married Elizabeth Throckmorton, one of Queen Elizabeth's ladies in waiting, in 1587. He had been a favorite of Elizabeth, and the marriage may have displeased the queen. Second, the queen issued a proclamation on October 18, 1591, attacking Jesuits in England for trying to return the country to Catholicism. Perhaps in retaliation, Jesuit father Robert Parsons attacked Elizabeth's sometime friend Raleigh, as well as Harriot, accusing them of atheism.

Then in 1592, soon after Raleigh's son was born, Elizabeth imprisoned Raleigh and his family in the Tower of London. Coincidentally, one of Raleigh's ships captured a Spanish treasure ship, the Madre de Deus, not long after the imprisonment. With Raleigh in prison, the ship was being gradually looted. Elizabeth wanted the greater part of its fortune for England's treasury, so Raleigh and his family were released so that Raleigh could stop the looting. Harriot remained under Raleigh's patronage in Ireland, avoiding the plague that struck London in 1593.

Harriot Studied Optics, Algebra

In 1595, the Duke of Northumberland, Henry Percy, a great friend of Raleigh's, became Harriot's patron and deeded him property in Durham as well as allowing him use of a house in London. Harriot undertook a study of optics, using part of the house as a laboratory. The studies eventually led to several important discoveries concerning the refraction of light, but Harriot never published his results. He also began to analyze the forces affecting projectiles and commenced various studies in algebra. He and earlier mathematicians may have made several discoveries often credited to Rene Descartes (1596-1650). He wrote Artis Analyticae Praxis ad Aequationes Algebraicas Resolvendas, an algebra text, and left specific instructions for its publication in his will, but knowledgeable mathematicians reportedly think that the work which was eventually published represents Harriot's efforts poorly. His body of work in algebra is considerable. He advanced the notation system for algebra (although the "greater than" and "less than" symbols that have been credited to him are now thought to have been introduced by the editor of Artis Analyticae Praxis ) and did novel work on the theory of equations, including cubic equations and negative and imaginary numbers.

Queen Elizabeth died in March 1603, and James I became king. Raleigh was implicated in a plot against the new king and was arrested and charged with high treason. After a failed suicide attempt, Raleigh was sentenced to death, and Harriot, who had tried to help his former friend and patron, was mentioned in the judgment as "an atheist and an evil influence." Harriot, apparently shaken, ceased scientific work for about a year. Raleigh's death sentence was withdrawn, but he remained in the Tower of London. Then Guy Fawkes was arrested on November 4, 1604, for a plot to blow up Parliament. Henry Percy's grandson was arrested with Fawkes, and Harriot was imprisoned in a place called the Gatehouse on suspicion. Later in November, Percy was imprisoned in the Tower to remain for 16 years.

Moons, Sunspots Observed

Harriot was released by the end of 1604 and quickly resumed his study of optics, still under Percy's generous patronage. He also visited Percy and Raleigh in the Tower from time to time. Harriot was working out a theory of color, and a correspondence began between him and the German astronomer Johannes Kepler, although nothing memorable seems to have resulted. Harriot went on to observe a comet, later identified as Halley's, on September 17, 1607. With his painstaking observations, later workers were able to compute the comet's orbit. Harriot also was the first in England to use a telescope to observe the heavens. He made sketches of the moon in 1609, then developed lenses of increasing magnification. By April 1611, he had developed a lens with a magnification of 32. Between October 17, 1610, and February 26, 1612, he observed the moons of Jupiter, already discovered by Galileo. While observing Jupiter's moons, he made a discovery of his own: sunspots, which he viewed 199 times between December 8, 1610, and January 18, 1613. These observations allowed him to figure out the sun's period of rotation. After this time, his scientific work dwindled.

Cancer Diagnosed

The cause of Harriot's diminished productivity may have been a cancer discovered on his nose. A doctor he consulted in 1615 made notes in which he called Harriot "a man somewhat melancloly… . A cancerous ulcer in the left nostril eats up the septum of his nose and in proportion to its size holds the lips hard and turned upwards… . This evil the patient has suffered the last two years," quoted the "Thomas Harriot" website. Harriot lost several friends during this time, and on October 29, 1618, he witnessed the public execution of his friend Raleigh.

Three days before Harriot died, he made his will. His mind was clear. He willed Percy charts and maps and his choice of books and papers. He remembered friends, servants, and Tom Buckner, a childhood friend with whom he maintained contact all his life and who had accompanied him on Grenville's trip to America. In the will, Harriot mentioned a sister, whose son he left fifty pounds, and a cousin. Most evidence suggests they were his only family when he died; it seems he never married. He remembered his servants generously, as well as Tom Buckner's wife (in whose house he died) and the Buckners' son.

Harriot died July 1 or 2 (accounts vary), 1621, in London and was buried in Saint Christopher's Parish Church, which burned in the fire of London in 1666. According to Thomas Harriot: Science Pioneer, after the fire an inscription was incorporated in a plaque in the Bank of England of London which reads, Harriot "cultivated all the sciences And excelled in all." The plaque calls him "A most studious searcher after truth." Harriot was several times accused of atheism during his lifetime, but the plaque adds that he was "a most devout worshiper of the Triune God."

Papers Rediscovered

Harriot's story did not end with his death. What some writers describe as his "thousands upon thousands of sheets of mathematics and of scientific observations" appeared to be lost-until 1784, when they were found in Henry Percy's country estate by one of Percy's descendants. She gave them to Franz Xaver Zach, her husband's son's tutor. Zach eventually put some of the papers in the hands of the Oxford University Press, but much work was required to prepare them for publication, and it has never been done. Scholars have begun to study them, and an appreciation of Harriot's contribution began to grow in the second half of the twentieth century. Today scholars, sometimes referred to as "Harrioteers," study the details of his life and work to understand both the man and the science of his time.


Staiger, Ralph C., Thomas Harriot: Science Pioneer, Clarion Books, 1998.


Apt, Adam Jared, "Harriot, Thomas," Encyclopaedia Britannica Library,, 2003.

O'Connor, J. J., and E. F. Robertson, "Thomas Harriot," (March 1, 2003).

—, "Thomas Harriot's Manuscripts," (March 16, 2003). □

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Harriot (or Hariot), Thomas


(b. Oxford, England, c. 1560; d. London, England, 2 July 1621),

mathematics, astronomy, physics. For the original article on Harriot see DSB, vol. 6.

Harriot continues to be an important figure in the historical study of early modern science. Recent work has shed light on his ideas about atomism as well as his contributions to astronomy. Harriot’s telescopic observations (c. 1609–1612) have been overshadowed by Galilei’s rather similar ones, but may have started earlier; he had long-standing personal contacts with the Netherlands, which gave him quicker chances of access to technical developments there than were available to Galileo, and no need to act as if they were his own.

The most important new insights concern his remarkable mathematical achievements. After the death of François Viète (1603), Harriot was the leading mathematician of his time, and a notable scientist and astronomer. He was, in all his various activities, essentially a problem solver; his mathematics made no distinction between pure and applied work (as it is now called). Each arose out of the other, and extended from shipbuilding and optics to the purest geometry and algebra. He was an important part of the chain from Viète to René Descartes and beyond, which made the historic transformation of mathematics from geometric to algebraic formalism that has been the dominant mathematical development since his time, and one whose high points in the seventeenth century were the calculi of Isaac Newton and Gottfried Wilhelm Leibniz.

Harriot himself applied his algebraic notations, almost the same as the modern elementary ones, to geometry, and thence to loci in optics, projectile theory (where the work, if published, would have inaugurated the modern study of ballistics), ship design, cartography, interpolation, and impacts.

J. A. Lohne’s original article covers the main areas of Harriot’s contributions, but some of his details and emphases are misleading or unreliable. For example, the “ingenious attempts” to rectify and square the equiangular spirals were entirely successful, even extending to the rectification of the loxodromic twisted spiral. These include the first known rectifications, partly repeated by Evangelista Torricelli in the 1640s, and an extension of the classical work of Archimedes and others. Again, the “nearly finished” tables of meridional parts were in fact not only complete, but the most accurate such tables until the 1920s.

Harriot’s work would still have been notable done fifty years or more later. Many of his methods and results were rediscovered by others, such as Leibniz, Newton, Isaac Barrow, Willebrord Snel, Descartes, James Gregory, Pierre-Simon Girard, Edmond Halley, Bonaventura Cavalieri, and Thomas Simpson; later some were extended by Johann Lambert and Carl Friedrich Gauss. Particularly notable was his work on conformality and the geometry of the sphere, leading to his directly calculated tables of logarithmic tangents (meridional parts, which solve Mercator’s problem, the construction of a conformal plane map of the spherical globe; this logarithmic work was preNapierian, and more accurate). The fundamental relation here, equating an exponential of the difference of longitude to a tangent of the colatitude, is identical in form to that of the much later hyperbolic non-Euclidean geometry of Farkas Bolyai and Nikolai Lobachevsky, where the constant surface curvature is negative instead of positive. This relates directly to Harriot’s 1603 result on the area of the spherical triangle, and it is intriguing to see how this result, which gradually became known in the seventeenth century, was first modified by Lambert 150 years later for what was (in effect) the hyperbolic geometry, and then extended to more general surfaces by Gauss in the 1820s.

Harriot’s numerical methods arose from the general binomial theorem that he derived from working back from finite differences, and which also led him to the limiting exponential series. Harriot’s algebraic theory of equations is now available in translation (Steddall’s edition of 2003), and was hardly a work for “amateurs.” It starts from Viète’s work, and includes the key step of associating roots with binomial factors, the derivation of various inequalities, and extensions of Viète’s methods of obtaining numerical solutions of polynomial equations, which he applied elsewhere to problems in refraction. Moving on from Viète’s positive roots, it recognized both negative and complex roots; he called the latter “noetic,” that is, of the mind. It is no longer appropriate to judge Harriot’s algebra entirely by the posthumous and incomplete Artis Analyticae Praxis of 1631.

Harriot’s discovery (or, perhaps, confirmation) of a constant refractive index is dated in his manuscripts to 10:30 A.M. on 21 July 1601 (Old Style). John Shirley, referring to different work, dates the result to before 1597; perhaps both dates are, in some sense, correct. Both amply predate Snel (?1621) and Descartes (1637). Harriot quantified the medieval models in which rainbows were produced by refraction and reflection in spherical raindrops. He found that the maximum value of the exit arc, 2r – i, occurs when tan i = 2 tan r. This gave Harriot the “tropical” (i.e., turning) ray, which led him to the height of the primary rainbow. Armed with a constant refractive index, this result can be obtained by elementary infinitesimals, but Harriot’s own derivation is unknown.

Harriot’s cubic curve solution of Alhazen’s problem, mentioned by Lohne, not only anticipated Barrow, but turned out to be the inverse of Christiaan Huygens’s hyperbolic solution of 1660. Inversion and its related conformality are a thread in much of Harriot’s best work.

Unfortunately, one must mention recent revisionist historical trends (“the new historicism”), as they touch on modern accounts of Harriot’s life and work. His 1588 A Briefe and True Report of the New Found Land of Virginia(modern North Carolina, in and around the Outer Banks, where he was a senior member of the Roanoke Settlement [1585–1586]), which has long been recognized as a leading source on early American life and settlement, has been seen by some recently as contaminated by racial and class biases. This allegation is then used to ignore or denigrate his scientific work. However, as B. J. Sokol argues forcefully, an unbiased reading of the 1588 text shows that Harriot gave fair, if somewhat optimistic, accounts of the resources, and a sympathetic description of the native population, from whom he learned much, as he himself recognized. Granted that he was part of a settlement, he was perhaps the most open-minded and enlightened of its members. His phonetic system for the local languages, long misunderstood as a “secret code,” was a notable contribution to early phonetics.

During his life Harriot was a controversial figure and he continues to provoke lively debate amongst historians.


See also the valuable and continuing series of over forty pamphlets and lectures published by the University of Durham (U.K.) Thomas Harriot Seminar since 1983, covering many and varied aspects of Harriot’s life, work, and times. Reference: Prof. G. R. Batho, Harriot Seminar, Durham Miners Hall, Durham, U.K.


The Greate Invention of Algebra: Thomas Harriot’s Treatise on Equations. Edited by Jacqueline A. Steddall. Oxford: Oxford University Press, 2003. An edition in English translation, from the original manuscripts, with introduction and bibliography (pp. 315–320).


Chapman, Allan. “The Astronomical Work of Thomas Harriot (1560–1621).” Quarterly Journal of the Royal Astronomical Society 36 (1995): 97–107.

Fox, Robert, ed. Thomas Harriot: An Elizabethan Man of Science. Burlington, VT: Ashgate, 2000. Prints the first ten Thomas Harriot Lectures, Oriel College, Oxford, England, 1990–1999. The next ten are due out in 2010. Also contains a bibliography by Katharine D. Watson (pp. 298–303) of relevant work since the original DSB in 1974, and a note by Gordon R. Batho on possible portraits of Harriot (pp. 280–285).

Henry, John. “Thomas Harriot and Atomism: A Reappraisal.” History of Science 20 (1982): 267–296.

North, J. D. “Thomas Harriot’s Papers on the Calendar.” In Light of Nature: Essays in the History and Philosophy of Science Presented to A. C. Crombie, edited by J. D. North and J. J. Roche. Dordrecht, Netherlands: Nijhoff, 1985.

Shirley, John W. Thomas Harriot: A Biography. Oxford: Clarendon Press, 1983. Generally reliable, more complete on life than works; extensive bibliographies, pp. 476–490.

Sokol, B. J. “The Problem of Assessing Thomas Harriot’s ‘A Briefe and True Report’ of His Discoveries in North America.” Annals of Science 51, no. 1 (January 1994): 1–16.

———. Invisible Evidence: The Unfounded Attack on Thomas Harriot’s Reputation. Thomas Harriot Seminar Occasional Paper 17. Durham, U.K.: University of Durham, 1995.

Jon V. Pepper

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Harriot, Thomas (1560-1621)

Thomas Harriot (1560-1621)

English Ethnographer


Youth. Little is known about Thomas Harriots early life. He was born in Oxford in 1560, and at the age of seventeen he enrolled at university, where he studied science and mathematics. After graduation he joined Sir Walter Raleighs household staff and worked as a tutor. Raleigh was fascinated by Harriots lessons in astronomy, navigation, and math and enlisted his aid when in 1584 Raleigh received a charter to colonize the New World. At his patrons request Harriot drew up the plans for Arthur Barlowes exploratory voyage, and with a textbook he had written he taught the pilots and crewmen how to apply their nautical navigational skills to the exploration of land.

The Lane Expedition. When Barlowe returned with glowing reports of the future site of the colony, Harriot decided to join the Ralph Lane expedition. His job was to record astronomical observations, aid in navigation, and with John White observe the native inhabitants as well as their natural environment with the aim of mapping and surveying the colony. He was well prepared to undertake an ethnographical investigation of the Algonquian population because he had spent a full winter with two Indians, Manteo and Wanchese, who had been captured by Barlowe during his visit to the area. Harriot learned the Algonquian tongue spoken by the Indians while he taught his two charges English; he also began to develop a phonetic alphabet to aid in recording their speeches and vocabulary. Upon their arrival at Roanoke, Harriot spent the next several months recording his observations of Indian life while White painted what he saw.

A Briefe and True Report. Harriot published his observations upon his arrival back in England in 1588. He began A Briefe and True Report of the New Found Land of Virginia with a chapter on Virginias Marchantable Commodities. What caught his eye first were tent caterpillars he took to be silkworms. With careful cultivation of mulberry trees, the plant on which silkworms fed, Harriot predicted there will rise as great profite in time to the Virginians, as there of doth now to the Persians, Turkes, Italians and Spaniards. Other economic endeavors for which he thought the colony was well suited included the cultivation of sassafras, used as a treatment for venereal disease, and wine grapes. Cedar, a valuable wood, was plentiful, and the great walnut and oak trees provided nuts and acorns from which a good and sweete oyle could be made. The colony also held out great potential for miners and hunters. He had found iron deposits in two areas, and the copper ornaments worn by the wereowances suggested that the mineral would not be hard to find. Deer, bears, and wildcats could provide hunters with enough furs to make a good profite.

Assessment of the Natives. Having outlined where and how colonists could extract a living from the Carolina coast, Harriot went to great pains to describe the Algonquian groups already resident in the area. He first assured the readers they had nothing to fear: the Indians had no edge tooles or weapons, of yron or Steele to offend us with. They also lacked any defenses for English weapons, having only shields made of bark and armor made of woven twigs. Their towns were small, with only ten to twelve homes on average, and they were organized as chiefdoms under the command of various wereowances. In respect of us, Harriot informed his English audience, they are a people poore, and for want of skill and judgement.... And the fact that they believed their god had created woman first, Harriot implied, was further evidence of their inferiority. In conclusion he reminded readers that were it not for certain English provocations, which were nonetheless justifiable to his mind, the colony might have survived. The Indians, he asserted, gave what they got, and future settlers ought, he believed, to take the lesson into consideration.

Impact. A Briefe and True Report of the New Found Land of Virginia sold perhaps two or three hundred copies. However, it was republished two years later complete with engravings of the detailed and naturalistic paintings made by White. The second edition, undertaken by the Flemish printer and engraver Theodor de Bry, was translated into Latin, French, German, and reissued in English. With the addition of the drawings and the accessibility that different translations offered, the book became incredibly popular and was reissued for several decades. Indeed, the story of the first Roanoke colony became standard reading among a literate European population that was fascinated by the New World. One of the most avid readers was John Smith, who later governed the Jamestown colony. Not only did he prefigure his behavior based on what Harriot wrote, but also he took the volume as a model and patterned his own writings about Virginia after it. Harriots small book also transformed the way Europeans wrote about the New World. Instead of simply describing native behaviors and the flora and the fauna, those who followed Harriot began to rationalize native cultures and to develop scientifically based interpretations of the land and its human, animal, and vegetable inhabitants in order to calculate the wealth that they might extract from their colonies.

Later Years. Unlike White, Harriot did not return for the second Roanoke colony. Instead he became a favorite in the household of Henry, earl of Northumberland. Although he corresponded with Johannes Kepler, the famous German astronomer and mathematician, Harriot failed to make any further contribution to the sciences. He died of cancer of the nose in 1621.


Thomas Harriot, A Briefe and True Report of the New Found Land of Virginia: The Complete 1590 Theodor de Bry Edition (New York: Dover, 1972);

David Beers Quinn, Set Fair for Roanoke: Voyages and Colonies, 15841606 (Chapel Hill: University of North Carolina Press, 1985).

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Harriot, Thomas

Thomas Harriot (hâr´ēət), 1560–1621, English mathematician and astronomer. He was tutor to Sir Walter Raleigh, who sent him in 1585 to Virginia as surveyor with Sir Richard Grenville. Returning to England, Harriot wrote A Brief and True Report of the New Found Land of Virginia (1588), one of the earliest known large-scale statistical surveys. He made valuable contributions to algebra, introducing new symbols and notation. His Artis analyticae praxis appeared in 1631.

See biography by M. Rukeyser (1971).

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