SPECIAL ARTICLE Perish, Then Publish Thomas Harriot and the Sine Law of Refraction

Ronald S. Fishman, MD

talented young scientist, Thomas Harriot, wrote the first English account of the New World, “A Briefe and True Report of the New Found Land of ,” distinguished by its serious effort to describe and understand the American Indian. Harriot went on to make innovations in and was one of the first astronomers to use the Atelescope. His largely unappreciated contribution to the history of ophthalmology was the first for- mulation of the sine law of refraction of light, found in his unpublished papers long after his death in 1621. Willebrord Snell discovered the sine law in Holland in 1621 but also died without for- mally publishing it. Rene´ Descartes first published the sine law in 1637. The sine law of refraction became not only the prime law of all lens systems but ushered in a new world of physical laws. Arch Ophthalmol. 2000;118:405-409 THE VIRGINIA EXPEDITION In that party were 2 unusual men. One was John White, an artist whose wa- In 1584, Sir Walter Ralegh (or Raleigh) re- tercolor paintings of the Indians and the ceived a monopoly charter from Queen land with its flora and fauna are still pre- Elizabeth I “to discover, search, find out, cious historical documents themselves. and view such remote heathen and bar- White’s maps remained the best available barous lands, countries, and territories, not of the area for most of the 17th century. actually possessed by any Christian prince, The other unusual man in the party nor inhabited by Christian people.”1,2(p5) was 25 years old and a recent graduate of Elizabeth did not commit government University, Oxford, : Tho- funds herself since she was well aware that mas Harriot. No portrait of him has been Crown funds were usually abused by these found. Harriot was a naturalist (the word adventurers. She also wanted to avoid an scientist did not yet exist). He made notes official confrontation with Spain, but her of his observations on Roanoke and in name was enough to get Ralegh some pri- 1588—the year of the Armada— vate backing. published them in Latin in a small edi- With the Spanish in Florida and tion of which only 6 copies remain. In Georgia and the French in Canada, there 1590, an English version was published, was still unclaimed coastline between which included engravings made from them. In 1584, Ralegh sent a small 2-ship John White’s paintings. Harriot’s report reconnoitering party to find land far was the first English account of the New enough north to be safe from the Span- World.3,4 iards. In 1585, he mounted a full-scale ex- In the typically verbose fashion of the pedition with 10 ships under the com- time, the title page reads: mand of Sir Richard Grenville. They sailed along the Atlantic coast, found a channel A briefe and true report of the new found land through the barrier island, and landed at of Virginia, of the commodities and of the na- ture and manners of the naturall inhabitants. the island of Roanoke near 2 Indian vil- Discovered by the English Colony there seated lages (Figure 1). by Sir Richard Grenville Knight. In the Year 1585...byThomas Hariot [sic] servant to... From the Welch Institute of History of Medicine, Johns Hopkins University, Sir Walter, a member of the Colony, and there Baltimore, Md. imployed in discovering.4

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©2000 American Medical Association. All rights reserved. Downloaded From: https://jamanetwork.com/ on 09/24/2021 This is said of a party of unruly men whose leader later described them as “wild men of mine own na- tion.”1(p11) This scruffy lot of ex- soldiers had been away from their homes for many months. They were certainly in the advanced stages of that condition to which the long voy- age around Cape Horn (with its ex- tended period of enforced sexual ab- stinence) was later to give its name. “...[N]either did we care for any of theirs.”? This is such a bare-faced unlikelihood, and since we know that Harriot was not an obtuse man, we assume that he was being deliberately misleading. He was putting the best face on what was essentially an ad- vertisingorpropagandabrochure.Far from being a true report, the whole Figure 1. The island of Roanoke and its approaches in the 1585 expedition to Virginia, reproduced in “A book is guarded, selective, remark- Briefe and True Report of the New Found Land of Virginia,” 4 the first English account of the New World, able for what it does not say. There written by Thomas Harriot. is no hint that the colony became a The dedication, written by De its, religion, and social organiza- shambles. The gentlemen-adventur- Bry, the publisher in 1590, in- tion, writing what would now be ers had come for gold, not farming. cludes 2 pages of fulsome praise for called ethnology or cultural anthro- The party became dependent on the Ralegh with only a slight mention of pology. Harriot actually learns some- Indians for food, and eventually made Harriot and no mention of John thing of the Algonkin Indian lan- enemiesofthem.After10months,the White at all. Ralegh himself never guage and evidently converses with English feared for their lives. Ralegh’s crossed the Atlantic at this time. His them after a fashion. He shows them resupply ships were late. When Sir big sacrifice was financial; he was a Bible and tries to explain it, but he FrancisDrakeunexpectedlyappeared saved from bankruptcy by Gren- is chagrined that it is the physical na- on his way home from a privateering ville’s capture of a Spanish treasure ture of the book itself that im- expedition, the party leaped at the ship on the way home. Privateering presses them. chance to leave. at this time was much more profit- Worst of all, the lesson was not And although I told them the book ma- learned. Ralegh sent another party of able than colonizing. terially and of itself was not of any such Despite Harriot’s servant sta- virtue, as I thought they did conceive, colonists to the New World in 1587. tus, the book shows a modern mind but only the doctrine therein con- Although this group was recruited at work—curious, inquiring, and ob- tained; yet would many be glad to touch from farmers and artisans with skills servant. Harriot inventories the it, to embrace it, to kiss it, to hold it to more useful for sustaining them- land’s resources, and the whole ac- their breast and head, and stroke over selves, this group was also undersup- count is characterized by the same all their body with it, to show their hun- plied and unwisely, even treacher- effort shown by the other leaders of gry desire of that knowledge which was ously, landed at the same Roanoke 3(p761) the expedition: the urge to show how spoken of. site. These were the unlucky souls the land could be commercially ex- Here Harriot is deceiving him- who inherited the ill will fostered by ploited, the more quickly the bet- self. The reaction of the Indians is Harriot’s party. They became known 1,2 ter. Harriot takes note of minerals the same as that of the isolated as the lost colony of Roanoke. As such as iron ore, but we can as- mountain-dwelling natives of New for the Indians, they eventually felt sume what a disappointment the Guinea during World War II, who the full civilizing effects of smallpox meager amount of precious metal ascribed supernatural qualities to the and other contagion already seeded is—some copper plates, some sil- strange contents of crashed cargo by the Englishmen. But the adven- ver earrings in an Indian chief’s ears planes. Any advanced technology ture was a good career move for Har- and, worst of all, no gold. True, the seems like magic to the more primi- riot. When he returned to England, climate is good, and the soil is fer- tive one. Harriot also writes: Ralegh introduced him to the Earl of tile. There are many game animals Northumberland, and both men sup- and many valuable trees that could Some people could not tell whether to ported Harriot’s career as the first En- make masts for ships. The natives are think us gods or men...there was no glish scientist. man of ours known to die, or that was spe- already farmers of peas, barley, oats, cially sick. [Actually 4 of the 108 English- and corn (good for making beer). men left at Roanoke for 10 months did HARRIOT’S LATER CAREER Best of all to the modern sen- die of illness.]... They noted also that sibility, Harriot shows himself to be we had no women among us, neither that Harriot never left England again. He a serious student of the Indians’ hab- we did care for any of theirs.3(p762) remained Ralegh’s friend even after

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©2000 American Medical Association. All rights reserved. Downloaded From: https://jamanetwork.com/ on 09/24/2021 Ralegh became a victim of the para- and True Report of the New Found F noid politics of the time and was for Land of Virginia,” were unpub- D some years imprisoned in the Tower lished at the time of his death in of . Harriot contributed to 1621. Just a few days before his Ralegh’s defense in what was a trav- death, probably in agony, he made i esty of a trial and visited Ralegh of- his will, named his literary execu- ten, bringing books and gossip. He tors, and asked them to publish his helped Ralegh to get his affairs in or- papers. The executors did a poor job der prior to his execution for trea- of it. Except for one published book C A B son in 1615.5-7 of mathematics, the papers were Harriot made many contribu- soon lost. When the Royal Society tions to mathematics, particularly al- in London was founded in 1660, its gebra. His notations for greater than, early meetings were full of discus- less than, and root of became part of sion as to where Harriot’s papers r algebraic notation, and there is a might be. Harriot had made the se- Harriot’s Law on the number of roots rious error of perishing before pub- E G in an equation. He also made im- lishing. His ideas played only a small Figure 2. The sine law of refraction. The ratio of portant contributions to the geom- part in the growth of British sci- the sine of the angle of incidence (FCD) to the etry of map making, navigation, and ence. In effect, he had disappeared, sine of the angle of refraction (ECG) is a practical seamanship (one of the rea- and he remained a largely un- constant for media of specific optical densities, sons Ralegh sent him out to sea in known scientific genius until rela- which interface at AB. the first place), and he wrote on bal- tively recently.7,12 friends: and Sir Tho- listics and practical gunnery.8-10 mas Aylesbury. No description of Most important for this story, THE SINE LAW these experiments has ever been Harriot became interested in as- found in Harriot’s own papers, but tronomy. He made the first tele- If Harriot’s papers had been pub- Warner, before he died in 1640, de- scopic map of the ’s surface, lished, there would have been one scribed the experimental setup and and Harriot’s crater is located on the particular gem in them, the most geometrical reasoning to Dr John reverse side of the moon, the side not crucial of all optical principles: the Pell, who took meticulous notes that seen until satellites investigated it, sine law of refraction. This relates the did survive. Pell13-15 wrote: the features of which were named af- angle of incidence (between the in- ter prominent scientists. Harriot also cident ray and a line perpendicular Mr Warner says he had of Mr Hariot [sic] made many sightings of the major to the interface between optical me- this proportion. As the sine of one angle of Jupiter, probably before dia of differing densities) to the angle of incidence to the sine of its refracted Galileo. He studied sunspots enough of refraction (the angle between the angle, found by experience... Hetold to calculate the period of the ’s refracted ray and its perpendicular). me that their manner of trial was thus: axial rotation for the first time. Since The ratio between the sines of the 2 Upon a table about 2 yards long at Sir Thomas Aylesbury’s house, they drew he preferred to view the sun di- angles is a constant, related to the the line FO parallel to the side of the rectly, usually from behind a thin differing speeds of light in the dif- table, and FP at the end perpendicular mist of cloud, he complained once ferent optical media. This is the to it. To this they drew a parallel QR that “my sight was after dim for an physical law basic to all lens sys- through the middle of FO... houre.”7(p206) Another early astrono- tems (Figure 2). mer, John Greaves of Oxford, En- Harriot began experimenting Pell goes on in labored Eliza- gland, after measuring the sun’s di- with refraction in the 1590s. He an- bethan prose to describe the setup ameter complained that “for some notated a copy of an old book on op- as if one were looking down on the days after, to that eye, with which I tics with a table of new refraction val- table from above (Figure 3). Mul- observed, there appeared, as it were, ues, dated 1597, and these values tiple observers and multiple read- a company of crows flying together strongly suggest that he had calcu- ings were taken, an eminently sci- in the air at a good distance.”11(p40) lated them by the sine relationship. entific technique (pioneered by the Astronomers eventually learned to He probably discovered the sine law astronomer Tycho Brahe) to de- view the sun indirectly, but their before 1602, but neither stated it nor crease observational error. Prisms of early days recall the blase´ attitude of described his technique and reason- differing glass densities were stud- early radiologists using x-rays. ing in any extant document. He cor- ied and their indices of refraction responded with compared. THE PERIL OF PERISHING about from 1606 to 1609, but The man who is usually cred- BEFORE PUBLISHING only in a curiously guarded way, ited with the sine law is Willebrord without mentioning the sine law. Snell, who worked in Holland.16 Although he had ample warning that This is a great pity since there was Snell circulated his manuscript with he should get his affairs in or- no one at that time who would have the sine law among his friends in der—it took the cancer in his nose been more likely to honor the ac- 1621, the year of Harriot’s death, so more than 8 years to kill him— complishment for what it was. But Harriot has the priority for discov- Harriot’s papers, other than “A Briefe Harriot had worked with 2 younger ering Snell’s Law. Snell also never

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©2000 American Medical Association. All rights reserved. Downloaded From: https://jamanetwork.com/ on 09/24/2021 M the law especially impressive by ex- nism, pure and simple. The retinal plaining it as a logical consequence image (first conceived by Johannes PAF of conceiving light as acting in a cer- Kepler in 1604) was only a repre-

H tain way in optical media of differ- sentation, a 2-dimensional model of ent densities. This fit well with his a 3-dimensional world, subject to C philosophical aim of obtaining the optical illusions and other limita- B 20 Q TRobjective truth by deducing from ba- tions. We are left with the enigma S sic principles. Unfortunately, his ac- of how the mind and external real- count28 is not to be trusted.27 It was ity are truly related, an epistemo- G conspicuously inconsistent with his logical angst that has continued for I own declared idea of the instanta- 4 centuries through the present. neous transmission of light—of light According to Smith,26(p80) this OY that did not travel in time and space was a Faustian bargain, and there is an elegiac tone to his admission: Figure 3. A posthumous reconstruction of at all. It also rested on other physi- Thomas Harriot’s experimental determination of cal assumptions that were by no the angle of refraction, according to John Pell13 means obvious, such as the alto- For good or ill, then, the most funda- in 1640. The preferred visible object (A) was a gether erroneous assumption that mental and lasting legacy of Cartesian lamp behind the edge of a board, which made optics was the wholesale and largely un- the object into a luminous line. The object (A) the speed of light increases in the methodical destruction of the medieval was viewed through a glass prism (CST) by an denser medium. This was evident to world-view for the sake of a simpler, observer (O). The line MBG is perpendicular to contemporary thinkers, such as the air-glass interface (CT) at point B. In modern more mathematically precise account of terms, the angle of incidence is ABH and the Pierre de Fermat, and modern his- light and refraction. The resulting angle of refraction is OBG (different from the torians of science, such as Richard mechanistic world-view is no real world- terms used by Pell). Westfall, who called the argument view at all. For, by closing the gap be- “preposterous... arbitrary and con- tween virtual and real mechanism in the published the sine law during his tradictory.”29 physics of light, Descartes’ successors lifetime. The person who gave Snell G. Schuster and A. Mark created an unbridgeable chasm be- real notice was Christiaan Huy- Smith,22,26 who have been most as- tween us and the external reality we so desperately strive to understand. What- gens, the noted theorist who dis- tute in trying to recapture Des- ever comfort the Scholastics could take cussed light as a wave form. Huy- cartes’ actual path to discovering the from their assurance in a fundamental gens gave Snell credit in Dioptrica, sine law, feel that Descartes’ real ap- correspondence between the two is ir- published in 1703, 8 years after Huy- proach was through concepts that retrievably lost to us now. But, unlike gens had died. had long been known by medieval them, we have the sine-law. optical thinkers, the Perspectivists. THE CURIOUS CASE This was a debt he did not wish to THE LARGER SIGNIFICANCE OF DESCARTES AND THE admit since he did not want to ap- OF THE SINE LAW SINE LAW pear as though he were arguing from the authority of others. In using their Three men living within a few hun- The person who first actually pub- assumptions, Descartes’ argument dred miles of each other, never com- lished the sine law was Rene´ Des- carried a basic logic after all, and municating, independently discov- cartes in “Dioptrique” published in Harriot and Snell most likely fol- ered the sine law. It was not just a 1637, 1 of 3 essays meant to dem- lowed a similar route. For instance, coincidence. The new interest in as- onstrate his “method for rightly di- the Perspectivists held a crucial con- tronomy and the telescope made recting one’s reason and searching cept that refraction occurred only at lenses interesting to many people at for truth in the sciences.” Since Des- the interface of 2 media and did not the time, particularly in the effort to cartes is such a central personality continue to change during the pas- grind the lenses in such a way— in the history of science, many writ- sage of light through a uniform me- with an anaclasic surface—as to ers throughout the years have dium. Perspectivists and scholastic minimize the spherical and chro- probed his contribution to op- philosophers believed that there was matic aberrations so prominent with tics.17-27 a direct relation between the object the commonly used biconvex lenses. Unlike Harriot and Snell, whose itself and the subjective idea re- This technical challenge was prob- methods of achieving the sine law are ceived from it via the passage of light. ably uppermost in their priorities, poorly documented and obscure, Although they drew light-ray dia- making the sine law only a means to Descartes went to some length to ex- grams, they were vague about what an end. For the most part, these plain his reasoning, never claiming exactly this direct interaction be- people were few and isolated, work- for a moment that it was the result tween the object and eye consisted ing alone or with a small group of of empirical experiment. It is worth- of and noncommittal regarding any friends. They were true eccentrics. while to consider Descartes’ ac- mathematical relationships in the There were no learned societies yet, count since it may cast light on how process of vision. no periodical journals. Publishing Harriot and Snell arrived at the sine What Descartes did was to was expensive and often required a law themselves. stipulate the mathematics in- wealthy patron. Even modern re- Descartes achieved the sine law volved. This served to emphasize the searchers are tempted by procrasti- by geometrical reasoning but made idea of the eye as an optical mecha- nation, postponing the hard labor of

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©2000 American Medical Association. All rights reserved. Downloaded From: https://jamanetwork.com/ on 09/24/2021 organizing data into a coherent re- is possible to guess from one part York, NY: Oxford University Press; 1983:474. port. So 2 discoverers of the sine law what the rest is going to do?... I 8. Lohne JA. Thomas Harriot: Dictionary of Scien- tific Biography. Gillispie CC, ed. New York, NY: died without publishing it. think it is because Nature has a sim- Charles Scribner & Sons; 1972:124-129. What is clear about the story of plicity and, therefore, a great 9. Rosen E. Harriot’s science, the intellectual back- the sine law is that it was not sim- beauty.” ground. In: Shirley JW, ed. Thomas Harriot, Re- ply an empirical induction from ex- naissance Scientist. Oxford, England: Clarendon periment, neither by Harriot, nor HARRIOT’S GRAVE Press; 1974:1-15. 30 10. Lohne JA. Essays on Thomas Harriot: a survey of Snell, nor Descartes. Their mea- Harriot’s scientific writings. Arch Hist Exact Sci. surements could not be exact It is not possible today to find Har- 1979;20:265-312. enough, particularly at the higher riot’s grave. Although he was bur- 11. King HC. The History of the Telescope. Mineola, angles of refraction. What all of them ied near the altar of St Christopher NY: Dover Publications Inc; 1979:40. did do is to approach it as a prob- le Stocks in London, the church was 12. Tanner RCH. The study of Thomas Harriot’s manu- scripts: Harriot’s will. Hist Sci. 1967;6:1-16. lem in geometry. Their data fit the destroyed in the great fire of 1666. 13. Pell J. manuscript, Birch MSS sine relation well, and so they be- There is a plaque in the entrance hall 4407, folio 183a. Cited by: Shirley JW. An early lieved that the sine law must be the of the , which is experimental determination of Snell’s Law. Am J answer. This was a kind of faith,a close to the site of Harriot’s grave. Phys. 1951;19:507-508. faith about an underlying order in It reproduces the original Latin 14. Lohne JA. Thomas Harriot, 1560-1621: the Tycho 7(p474) Brahe of optics. Centaurus. 1959;6:113-121. nature. This order could be de- wording of his epitaph. An En- 15. Shirley JW. An early experimental determination scribed and analyzed adequately only glish would read: of Snell’s Law. Am J Phys. 1951;19:507-508. by mathematics. 16. Volgraff JA. Snellius’ notes on the reflection and Stay, traveler, lightly tread; refraction of rays. Osiris. 1936;1:718-725. If one finds it strange to speak Near this spot lies all that was mor- of faith in a field built on a rigid skel- 17. ScottJF.TheScientificWorkofRene´ Descartes,1596- tal 1650. London, England: Taylor & Francis; 1952. eton of logic, one can sometimes Of that most celebrated man Tho- 18. BlakeRM.TheroleofexperienceinDescartes’theory hear mathematicians describe their mas Harriot. of method. In: Blake RM, Ducasse CJ, Madden EH, field in peculiarly transcendental He was that most learned Har- eds.TheoriesofScientificMethod:TheRenaissance ways. The late Hungarian mathema- riot... Through the Nineteenth Century. Seattle: Univer- tician Paul Erdos used to speak of Who cultivated all the sciences and sity of Washington Press; 1960:75-103. excelled in all... 19. Buchdahl G. Descartes’ Anticipation of a “Logic the “transfinite Book... [kept by of Scientific Discovery” in Scientific Change. Crom- the Supreme Being]... that con- A most studious searcher after bie AC, ed. London, England: William Heine- tains the best proofs of all math- truth... mann Ltd; 1963:399-417. ematical theorems, proofs that are el- 20. Crombie AC. 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