SPECIAL ARTICLE
Perish, Then Publish
Thomas Harriot and the Sine Law of Refraction
Ronald S. Fishman, MD
A
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 Virginia,” distinguished
by its serious effort to describe and understand the American Indian. Harriot went on
to make innovations in mathematics and was one of the first astronomers to use the
telescope. His largely unappreciated contribution to the history of ophthalmology was the first formulation of the sine law of refraction of light, found in his unpublished papers long after his death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 formally publishing it. René 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 1584, Sir Walter Ralegh (or Raleigh) received a monopoly charter from Queen
Elizabeth I “to discover, search, find out,
and view such remote heathen and barbarous lands, countries, and territories, not
actually possessed by any Christian prince,
nor inhabited by Christian people.”1,2(p5)
Elizabeth did not commit government
funds herself since she was well aware that
Crown funds were usually abused by these
adventurers. She also wanted to avoid an
official confrontation with Spain, but her
name was enough to get Ralegh some private backing.
With the Spanish in Florida and
Georgia and the French in Canada, there
was still unclaimed coastline between
them. In 1584, Ralegh sent a small 2-ship
reconnoitering party to find land far
enough north to be safe from the Spaniards. In 1585, he mounted a full-scale expedition with 10 ships under the command of Sir Richard Grenville. They sailed
along the Atlantic coast, found a channel
through the barrier island, and landed at
the island of Roanoke near 2 Indian villages (Figure 1).
From the Welch Institute of History of Medicine, Johns Hopkins University,
Baltimore, Md.
ARCH OPHTHALMOL / VOL 118, MAR 2000
405
In that party were 2 unusual men.
One was John White, an artist whose watercolor paintings of the Indians and the
land with its flora and fauna are still precious historical documents themselves.
White’s maps remained the best available
of the area for most of the 17th century.
The other unusual man in the party
was 25 years old and a recent graduate of
Oxford University, Oxford, England: Thomas Harriot. No portrait of him has been
found. Harriot was a naturalist (the word
scientist did not yet exist). He made notes
of his observations on Roanoke and in
1588—the year of the Armada—
published them in Latin in a small edition of which only 6 copies remain. In
1590, an English version was published,
which included engravings made from
John White’s paintings. Harriot’s report
was the first English account of the New
World.3,4
In the typically verbose fashion of the
time, the title page reads:
A briefe and true report of the new found land
of Virginia, of the commodities and of the nature and manners of the naturall inhabitants.
Discovered by the English Colony there seated
by Sir Richard Grenville Knight. In the Year
1585 . . . by Thomas Hariot [sic] servant to . . .
Sir Walter, a member of the Colony, and there
imployed in discovering.4
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Figure 1. The island of Roanoke and its approaches in the 1585 expedition to Virginia, reproduced in “A
Briefe and True Report of the New Found Land of Virginia,” 4 the first English account of the New World,
written by Thomas Harriot.
The dedication, written by De
Bry, the publisher in 1590, includes 2 pages of fulsome praise for
Ralegh with only a slight mention of
Harriot and no mention of John
White at all. Ralegh himself never
crossed the Atlantic at this time. His
big sacrifice was financial; he was
saved from bankruptcy by Grenville’s capture of a Spanish treasure
ship on the way home. Privateering
at this time was much more profitable than colonizing.
Despite Harriot’s servant status, the book shows a modern mind
at work—curious, inquiring, and observant. Harriot inventories the
land’s resources, and the whole account is characterized by the same
effort shown by the other leaders of
the expedition: the urge to show how
the land could be commercially exploited, the more quickly the better. Harriot takes note of minerals
such as iron ore, but we can assume what a disappointment the
meager amount of precious metal
is—some copper plates, some silver earrings in an Indian chief’s ears
and, worst of all, no gold. True, the
climate is good, and the soil is fertile. There are many game animals
and many valuable trees that could
make masts for ships. The natives are
already farmers of peas, barley, oats,
and corn (good for making beer).
Best of all to the modern sensibility, Harriot shows himself to be
a serious student of the Indians’ hab-
its, religion, and social organization, writing what would now be
called ethnology or cultural anthropology. Harriot actually learns something of the Algonkin Indian language and evidently converses with
them after a fashion. He shows them
a Bible and tries to explain it, but he
is chagrined that it is the physical nature of the book itself that impresses them.
And although I told them the book materially and of itself was not of any such
virtue, as I thought they did conceive,
but only the doctrine therein contained; yet would many be glad to touch
it, to embrace it, to kiss it, to hold it to
their breast and head, and stroke over
all their body with it, to show their hungry desire of that knowledge which was
spoken of.3(p761)
Here Harriot is deceiving himself. The reaction of the Indians is
the same as that of the isolated
mountain-dwelling natives of New
Guinea during World War II, who
ascribed supernatural qualities to the
strange contents of crashed cargo
planes. Any advanced technology
seems like magic to the more primitive one. Harriot also writes:
Some people could not tell whether to
think us gods or men . . . there was no
man of ours known to die, or that was specially sick. [Actually 4 of the 108 Englishmen left at Roanoke for 10 months did
die of illness.] . . . They noted also that
we had no women among us, neither that
we did care for any of theirs.3(p762)
ARCH OPHTHALMOL / VOL 118, MAR 2000
406
This is said of a party of unruly
men whose leader later described
them as “wild men of mine own nation.”1(p11) This scruffy lot of exsoldiers had been away from their
homes for many months. They were
certainly in the advanced stages of
that condition to which the long voyage around Cape Horn (with its extended period of enforced sexual abstinence) 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 advertising or propaganda brochure. Far
from being a true report, the whole
book is guarded, selective, remarkable for what it does not say. There
is no hint that the colony became a
shambles. The gentlemen-adventurers had come for gold, not farming.
The party became dependent on the
Indians for food, and eventually made
enemies of them. After 10 months, the
English feared for their lives. Ralegh’s
resupply ships were late. When Sir
Francis Drake unexpectedly appeared
on his way home from a privateering
expedition, the party leaped at the
chance to leave.
Worst of all, the lesson was not
learned. Ralegh sent another party of
colonists to the New World in 1587.
Although this group was recruited
from farmers and artisans with skills
more useful for sustaining themselves, this group was also undersupplied and unwisely, even treacherously, landed at the same Roanoke
site. These were the unlucky souls
who inherited the ill will fostered by
Harriot’s party. They became known
as the lost colony of Roanoke.1,2 As
for the Indians, they eventually felt
the full civilizing effects of smallpox
and other contagion already seeded
by the Englishmen. But the adventure was a good career move for Harriot. When he returned to England,
Ralegh introduced him to the Earl of
Northumberland, and both men supported Harriot’s career as the first English scientist.
HARRIOT’S LATER CAREER
Harriot never left England again. He
remained Ralegh’s friend even after
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Ralegh became a victim of the paranoid politics of the time and was for
some years imprisoned in the Tower
of London. Harriot contributed to
Ralegh’s defense in what was a travesty of a trial and visited Ralegh often, bringing books and gossip. He
helped Ralegh to get his affairs in order prior to his execution for treason in 1615.5-7
Harriot made many contributions to mathematics, particularly algebra. His notations for greater than,
less than, and root of became part of
algebraic notation, and there is a
Harriot’s Law on the number of roots
in an equation. He also made important contributions to the geometry of map making, navigation, and
practical seamanship (one of the reasons Ralegh sent him out to sea in
the first place), and he wrote on ballistics and practical gunnery.8-10
Most important for this story,
Harriot became interested in astronomy. He made the first telescopic map of the moon’s surface,
and Harriot’s crater is located on the
reverse side of the moon, the side not
seen until satellites investigated it,
the features of which were named after prominent scientists. Harriot also
made many sightings of the major
moons of Jupiter, probably before
Galileo. He studied sunspots enough
to calculate the period of the sun’s
axial rotation for the first time. Since
he preferred to view the sun directly, usually from behind a thin
mist of cloud, he complained once
that “my sight was after dim for an
houre.”7(p206) Another early astronomer, John Greaves of Oxford, England, after measuring the sun’s diameter complained that “for some
days after, to that eye, with which I
observed, there appeared, as it were,
a company of crows flying together
in the air at a good distance.”11(p40)
Astronomers eventually learned to
view the sun indirectly, but their
early days recall the blasé attitude of
early radiologists using x-rays.
THE PERIL OF PERISHING
BEFORE PUBLISHING
Although he had ample warning that
he should get his affairs in order—it took the cancer in his nose
more than 8 years to kill him—
Harriot’s papers, other than “A Briefe
and True Report of the New Found
Land of Virginia,” were unpublished at the time of his death in
1621. Just a few days before his
death, probably in agony, he made
his will, named his literary executors, and asked them to publish his
papers. The executors did a poor job
of it. Except for one published book
of mathematics, the papers were
soon lost. When the Royal Society
in London was founded in 1660, its
early meetings were full of discussion as to where Harriot’s papers
might be. Harriot had made the serious error of perishing before publishing. His ideas played only a small
part in the growth of British science. In effect, he had disappeared,
and he remained a largely unknown scientific genius until relatively recently.7,12
THE SINE LAW
If Harriot’s papers had been published, there would have been one
particular gem in them, the most
crucial of all optical principles: the
sine law of refraction. This relates the
angle of incidence (between the incident ray and a line perpendicular
to the interface between optical media of differing densities) to the angle
of refraction (the angle between the
refracted ray and its perpendicular).
The ratio between the sines of the 2
angles is a constant, related to the
differing speeds of light in the different optical media. This is the
physical law basic to all lens systems (Figure 2).
Harriot began experimenting
with refraction in the 1590s. He annotated a copy of an old book on optics with a table of new refraction values, dated 1597, and these values
strongly suggest that he had calculated them by the sine relationship.
He probably discovered the sine law
before 1602, but neither stated it nor
described his technique and reasoning in any extant document. He corresponded with Johannes Kepler
about optics from 1606 to 1609, but
only in a curiously guarded way,
without mentioning the sine law.
This is a great pity since there was
no one at that time who would have
been more likely to honor the accomplishment for what it was. But
Harriot had worked with 2 younger
ARCH OPHTHALMOL / VOL 118, MAR 2000
407
F
D
i
B
r
E
G
Figure 2. The sine law of refraction. The ratio of
the sine of the angle of incidence (FCD) to the
sine of the angle of refraction (ECG) is a
constant for media of specific optical densities,
which interface at AB.
friends: Walter Warner and Sir Thomas Aylesbury. No description of
these experiments has ever been
found in Harriot’s own papers, but
Warner, before he died in 1640, described the experimental setup and
geometrical reasoning to Dr John
Pell, who took meticulous notes that
did survive. Pell13-15 wrote:
Mr Warner says he had of Mr Hariot [sic]
this proportion. As the sine of one angle
of incidence to the sine of its refracted
angle, found by experience . . . He told
me that their manner of trial was thus:
Upon a table about 2 yards long at Sir
Thomas Aylesbury’s house, they drew
the line FO parallel to the side of the
table, and FP at the end perpendicular
to it. To this they drew a parallel QR
through the middle of FO . . .
Pell goes on in labored Elizabethan prose to describe the setup
as if one were looking down on the
table from above (Figure 3). Multiple observers and multiple readings were taken, an eminently scientific technique (pioneered by the
astronomer Tycho Brahe) to decrease observational error. Prisms of
differing glass densities were studied and their indices of refraction
compared.
The man who is usually credited with the sine law is Willebrord
Snell, who worked in Holland.16
Snell circulated his manuscript with
the sine law among his friends in
1621, the year of Harriot’s death, so
Harriot has the priority for discovering Snell’s Law. Snell also never
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C
A
M
P
A
F
H
C
B
Q
T
R
S
G
I
O
Y
Figure 3. A posthumous reconstruction of
Thomas Harriot’s experimental determination of
the angle of refraction, according to John Pell13
in 1640. The preferred visible object (A) was a
lamp behind the edge of a board, which made
the object into a luminous line. The object (A)
was viewed through a glass prism (CST) by an
observer (O). The line MBG is perpendicular to
the air-glass interface (CT) at point B. In modern
terms, the angle of incidence is ABH and the
angle of refraction is OBG (different from the
terms used by Pell).
published the sine law during his
lifetime. The person who gave Snell
real notice was Christiaan Huygens, the noted theorist who discussed light as a wave form. Huygens gave Snell credit in Dioptrica,
published in 1703, 8 years after Huygens had died.
THE CURIOUS CASE
OF DESCARTES AND THE
SINE LAW
The person who first actually published the sine law was René Descartes in “Dioptrique” published in
1637, 1 of 3 essays meant to demonstrate his “method for rightly directing one’s reason and searching
for truth in the sciences.” Since Descartes is such a central personality
in the history of science, many writers throughout the years have
probed his contribution to optics.17-27
Unlike Harriot and Snell, whose
methods of achieving the sine law are
poorly documented and obscure,
Descartes went to some length to explain his reasoning, never claiming
for a moment that it was the result
of empirical experiment. It is worthwhile to consider Descartes’ account since it may cast light on how
Harriot and Snell arrived at the sine
law themselves.
Descartes achieved the sine law
by geometrical reasoning but made
the law especially impressive by explaining it as a logical consequence
of conceiving light as acting in a certain way in optical media of different densities. This fit well with his
philosophical aim of obtaining the
objective truth by deducing from basic principles. Unfortunately, his account28 is not to be trusted.27 It was
conspicuously inconsistent with his
own declared idea of the instantaneous transmission of light—of light
that did not travel in time and space
at all. It also rested on other physical assumptions that were by no
means obvious, such as the altogether erroneous assumption that
the speed of light increases in the
denser medium. This was evident to
contemporary thinkers, such as
Pierre de Fermat, and modern historians of science, such as Richard
Westfall, who called the argument
“preposterous . . . arbitrary and contradictory.”29
G. Schuster and A. Mark
Smith,22,26 who have been most astute in trying to recapture Descartes’ actual path to discovering the
sine law, feel that Descartes’ real approach was through concepts that
had long been known by medieval
optical thinkers, the Perspectivists.
This was a debt he did not wish to
admit since he did not want to appear as though he were arguing from
the authority of others. In using their
assumptions, Descartes’ argument
carried a basic logic after all, and
Harriot and Snell most likely followed a similar route. For instance,
the Perspectivists held a crucial concept that refraction occurred only at
the interface of 2 media and did not
continue to change during the passage of light through a uniform medium. Perspectivists and scholastic
philosophers believed that there was
a direct relation between the object
itself and the subjective idea received from it via the passage of light.
Although they drew light-ray diagrams, they were vague about what
exactly this direct interaction between the object and eye consisted
of and noncommittal regarding any
mathematical relationships in the
process of vision.
What Descartes did was to
stipulate the mathematics involved. This served to emphasize the
idea of the eye as an optical mecha-
ARCH OPHTHALMOL / VOL 118, MAR 2000
408
nism, pure and simple. The retinal
image (first conceived by Johannes
Kepler in 1604) was only a representation, a 2-dimensional model of
a 3-dimensional world, subject to
optical illusions and other limitations.20 We are left with the enigma
of how the mind and external reality are truly related, an epistemological angst that has continued for
4 centuries through the present.
According to Smith,26(p80) this
was a Faustian bargain, and there is
an elegiac tone to his admission:
For good or ill, then, the most fundamental and lasting legacy of Cartesian
optics was the wholesale and largely unmethodical destruction of the medieval
world-view for the sake of a simpler,
more mathematically precise account of
light and refraction. The resulting
mechanistic world-view is no real worldview at all. For, by closing the gap between virtual and real mechanism in the
physics of light, Descartes’ successors
created an unbridgeable chasm between us and the external reality we so
desperately strive to understand. Whatever comfort the Scholastics could take
from their assurance in a fundamental
correspondence between the two is irretrievably lost to us now. But, unlike
them, we have the sine-law.
THE LARGER SIGNIFICANCE
OF THE SINE LAW
Three men living within a few hundred miles of each other, never communicating, independently discovered the sine law. It was not just a
coincidence. The new interest in astronomy and the telescope made
lenses interesting to many people at
the time, particularly in the effort to
grind the lenses in such a way—
with an anaclasic surface—as to
minimize the spherical and chromatic aberrations so prominent with
the commonly used biconvex lenses.
This technical challenge was probably uppermost in their priorities,
making the sine law only a means to
an end. For the most part, these
people were few and isolated, working alone or with a small group of
friends. They were true eccentrics.
There were no learned societies yet,
no periodical journals. Publishing
was expensive and often required a
wealthy patron. Even modern researchers are tempted by procrastination, postponing the hard labor of
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organizing data into a coherent report. So 2 discoverers of the sine law
died without publishing it.
What is clear about the story of
the sine law is that it was not simply an empirical induction from experiment, neither by Harriot, nor
Snell, nor Descartes.30 Their measurements could not be exact
enough, particularly at the higher
angles of refraction. What all of them
did do is to approach it as a problem in geometry. Their data fit the
sine relation well, and so they believed that the sine law must be the
answer. This was a kind of faith, a
faith about an underlying order in
nature. This order could be described and analyzed adequately only
by mathematics.
If one finds it strange to speak
of faith in a field built on a rigid skeleton of logic, one can sometimes
hear mathematicians describe their
field in peculiarly transcendental
ways. The late Hungarian mathematician Paul Erdos used to speak of
the “transfinite Book . . . [kept by
the Supreme Being] . . . that contains the best proofs of all mathematical theorems, proofs that are elegant and perfect.” An especially
good proof for Erdos was straight
from “the Book.”31 The Indian genius Srinivasa Ramanujan once said:
“An equation for me has no meaning unless it expresses a thought of
God.”31,32
All this makes the sine law of
refraction more than just the prime
law of optics. When it was formulated in the first decades of the 17th
century, it joined Kepler’s laws of
planetary motion as the harbinger of
a new way of looking at Nature—a
way that became known as physical
law. Mathematics and physics became inseparable. In a few decades,
Isaac Newton was to invent differential calculus to calculate gravity,
and the road was open to E = mc2.
If this worldview has its disadvantages, it is also a boon. Two modern physicists have eloquent commentsaboutthis.EugeneWigner32(p14)
said: “The miracle of the appropriateness of the language of mathematics for the formulation of the laws
of physics is a wonderful gift which
we neither understand nor deserve.” Richard Feynman33(p167) said:
“What is it about Nature . . . that it
is possible to guess from one part
what the rest is going to do? . . . I
think it is because Nature has a simplicity and, therefore, a great
beauty.”
HARRIOT’S GRAVE
It is not possible today to find Harriot’s grave. Although he was buried near the altar of St Christopher
le Stocks in London, the church was
destroyed in the great fire of 1666.
There is a plaque in the entrance hall
of the Bank of England, which is
close to the site of Harriot’s grave.
It reproduces the original Latin
wording of his epitaph.7(p474) An English translation would read:
Stay, traveler, lightly tread;
Near this spot lies all that was mortal
Of that most celebrated man Thomas Harriot.
He was that most learned Harriot . . .
Who cultivated all the sciences and
excelled in all . . .
A most studious searcher after
truth . . .
Accepted for publication July 19, 1999.
Presented in part at the 12th
Meeting of the Cogan Society for the
History of Ophthalmology, Montreal, Quebec, June 19, 1999.
Corresponding author: Ronald S.
Fishman, 42120 St Andrews Church
Rd, Leonardtown, MD 20650.
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