Snell

Full Name: Willebrord Snellius

Nickname/Alias: born Willebrord Snel van Roijen (also Royen)

Achievements: Discovered law of refraction

Born: 1580; Leyden, Netherlands 

Died: October 30, 1626; Leyden, Netherlands (Aged 46)

Field & Discipline: Mathematics; Science; Optics; Astronomy

Language: Dutch

Father: Rudolph Snellius

Mother: Machteld Cornelisdochter

Siblings: Unknown

Spouse: Maria de Lange

Children: 18 children, 3 survived infancy

Education: University of Leyden, Holland

Major Work:

"Eratosthenes batavus"

Life & Times:

Although Snell studied law at the University of Leyden, he had shown an early gift for mathematics, and in 1600, through the influence of mathematician [helped by] Stevin*,  was appointed lecturer in mathematics at the University.  

In 1601, at 21, he went to Prague, where he worked as a research assistant under famous Danish astronomer [assistant to] Brahe*.  During this period, he met German astronomer [met] Kepler*, and later, Kepler's teacher, [met] Maestlin*.  

In 1602, Snell went to Paris to resume his law studies for two years, after which he traveled to Switzerland with his father, who was then attached to the court of Prince Maurice of Hesse in Kassel. 

In late 1604, Snell returned to Leyden, where he met physicist [met] Beeckman* .   Between 1607 and 1608, Snell published a restoration of two books on plane loci by Greek mathematician Apollonius of Perga written in the 3rd century B.C.  Until Snell's restoration, the books had been preserved only in abstract,  by 4th century Greek mathematician Pappus.

In 1608, Snell received his M.A. and married Maria de Lange, daughter of a burgomaster of Schoonhoven.  After his father died in 1613, Snell succeeded him,  teaching at Leyden University, and two years later, at 35, was made professor of mathematics, astronomy and optics.  In 1613, he arranged for the publication of "Arithmetica" by the 16th-century French scholar Petrus Ramus and included a commentary. 

He also published a short work of his own, "De re numeraria", which dealt with money in ancient  Israel, Greece and Rome,  dedicating it to Dutch jurist and theologian [dedicated work to] Grotius*. 

In 1615, Snell set out to determine the length of the meridian (the imaginary north-south line that connects the Earth's two geographic poles and which is used to indicate longitude), and decided to try a method of triangulation proposed by Gemma Frisius in 1533 and used by Brahe, Snell’s former instructor, in the 1590s.  (The idea of triangulation is to establish a network of stations that form connecting triangles, with one side of the first triangle in the chain as the baseline, and all angles of the triangles accurately measured).

Starting with his house in Leyden (now marked with a memorial plaque), Snell used the spires of town churches as points of reference.  Through a chain of 33 triangles, he calculated the distance from Alkmaar to Bergen-op-Zoom (roughly 130 kilometers), the two towns lying on approximately the same meridian, using the distance from Leyden to Zoeterwoude (about 5 kilometers) as a baseline. 

Using instruments made by [used instruments by] Blaeuw*, including the huge centimeter quadrant which is now displayed in the hall of the Leyden astronomical observatory, Snell established the science of triangulation.

Snell's results, remarkably accurate (his estimate of the Earth's size is only 3.4 per cent too small), were published in "Eratosthenes batavus" in 1617.  Soon after, Snell began to make corrections to his work, and extended his measurements to include the distance from Bergen-op-Zoom to Mechelen.  His early death in 1626 prevented him from publishing definitive calculations. 

Also fascinated with astronomy, Snell published observations by [published work of] Burgi* and Brahe in 1618, and the following year his own observations of the comets of 1585 and 1618.  The work reveals him to be a follower of the Ptolemaic system (see Ptolemy*).  In 1621 came the discovery that was to make him internationally famous: the law of refraction of light rays, now known as “Snell's Law.”   This was the result of many years of experiment and of the study of such books as Kepler's "Ad Vitellionem paralipomenia" (1604) and Risner's "Optica" (1606).

Snell's wording of his law has been preserved in an index of the manuscript kept in Amsterdam: "If the eye "O" (in the air) receives a light ray coming from a point "R" in a medium (for example, water) and refracted at "S" on the surface "A" of the medium, then "O" observes the point "R" as if it were at "L" on the line RM | surface "A".  Then "SL:SR" is constant for all rays.  This agrees with the present formulation of the law, which states that sin"r":sin"i" is constant, where "i" and "r" are the angles that "OS" and "SR" make with the normal to "A" at "S"."   

However, Snell never published this law, and priority of publication remains with the French philosopher and mathematician [discovered refraction prior to] Descartes*, who stated it in his "Dioptrique" of 1637, although without experimental verification. (Descartes was accused of plagiarism, particularly by Dutch physicist [defended by] Christiaan Huyghens*, who expressed his suspicions in his "Dioptrica" of 1703 and of 1728.  It is known Descartes visited Leyden both during and after Snell's days, but the charges of plagiarism have never been proven.)

In 1622, Snell published "P. Rami Meetkonst", an annotated Dutch translation by Dirck Houtman of Ramus's "Geometria", and in 1624 he brought out "Tiphys batavus" on navigation, in which he studied and tabulated Pedro Nunez's so-called rhumb lines (1537), which Snell called "loxodromes".  Snell's consideration of a small spherical triangle bounded by a loxodrome, a parallel, and a meridian circle as a plane right triangle presages the differential triangle of French mathematician [anticipated] Blaise Pascal and others.

Snell's last published works were "Canon triangulorum" (1626) and "Doctrina triangulorum" (1627).  "Doctrina", which dealt with plane and spherical trigonometry, was completed by his pupil Hortensius.  A monument, to Snell and his wife, stands at Leyden.

Extra Connections: Influenced by [influenced by] Al Hazen*, [influenced by] Witelo*  and [influenced by] Ptolemy*

His work was used by [work used by] Picard*

He advanced the development of the [advanced development of] theodolite*

Assessment: Best known for his discovery of the law of refraction of light rays.

Oneliner: W. Snell, discoverer of refraction law

Bibliography:

• Dictionary of Scientific Biography.
• Encyclopedia Britannica.