Willebrord Snell is best known for his discovery regarding the refraction of light rays. This discovery, known as Snell's law, demonstrates that when a ray of light passes from a thinner element such as air, into a denser element, such as water or glass, the angle of the ray bends to the vertical. Snell's law--a key revelation in the science of optics--was formulated after much experimentation in 1621. This is expressed as sin i =sin r (i=angle of incidence, r=angle of refraction and = a constant). However, he did not publish his findings, and the law did not appear in print until René Descartes discussed it (without giving Snell credit) in his Dioptrique in 1637. Snell also determined a formula to measure distances using trigonometric triangulation. His method, developed in 1615, used his home and the spires of Leiden churches as reference points. (In 1960, a plaque recognizing his work was placed on his home.) In an age of world exploration, this was very important work, because it contributed to improved accuracy in the art of mapmaking. Using the triangulation method, Snell measured the Earth's meridian for the first time, and also attempted to measure the size of the Earth using this method. He set down the principles of spherical trigonometry that determine the length of a meridian arc when measuring any base line. Snell's writings on his triangulation method were presented in Eratosthenes batavus (1617). His observations of comets sighted in 1585 and 1618 are described in his Cyclometricus de circuli dimensione (1621). His last works, Canon triangulorum (1626) and Doctrina triangulorum, published after his death in 1627, also addressed the measuring of distances through plane and spherical trigonometry.
Snell was born in Leiden, Holland, in 1591. He was the son of Rudolph Snellius (Snel van Royen), a professor of mathematics at the University of Leiden, and Machteld Cornelisdochter. He became interested in mathematics at an early age, but initially entered the University of Leiden to study law. Snell married Maria De Lange, daughter of a Schoonhoven burgher master, in 1608. They had eighteen children; only three survived. In 1613, after his father's death, he became mathematics professor at the University. He also taught astronomy and optics.
Snell occupied himself in his early career with travel throughout Europe and the translation of numerous mathematical treatises. In his travels, he consulted with such eminent scientists as Tycho Brahe, Johannes Kepler, and Michael Maestlin, Kepler's astronomy teacher. Snell's Latin translation of the German Wisconstighe Ghedachtenissen was published as Hypomnemata mathematica in 1608; books of Apollonius based on plane loci were also translated during this time. Other translations of books on mathematics published by Snell were Ramus' Arithmetica(1613), and Geometria (1622).
The book translations were done at a time when Snell was very involved in applying mathematics to determine the shape and size of the Earth and the exact position of points on its surface. This work was to occupy him from 1615 onward. The mathematics he used is called plane trigonometry, which deals with calculations in two dimensions for measuring distances that cannot be measured directly, such as across lakes or vast expanses of land. Plane trigonometry began to be used in the mid-15th century--not surprising that a method so useful in geography, surveying, and mapmaking would be needed at a time when Europeans were undertaking their systematic maritime journeys of discovery. Snell's method, triangulation, had been used by Tycho Brahe and also by Gemma Frisius in 1533, but Snell advanced it to such a higher level he became known as the father of triangulation. Using his house and the spires of churches as starting points, he determined angles with a quadrant more than 7 feet long (213 cm). Building on a network of triangles, he calculated the distance between two towns--Alkmaar and Bergen-op-Zoom--located on the same meridian approximately 80 miles (130 km) from each other. Taking this calculation further, he was able to determine the radius of the Earth. The calculations for this difficult work were tedious, given that he computed his measurements without the help of logarithms. In spite of that, they remain surprisingly accurate. In 1624, he published Tiphys batavus, a work on navigation which parallels his work on determining land measurements. In it, his geometric theories hint of the differential triangle developed by later mathematicians, especially Blaise Pascal.
Snell's work in astronomy resulted in two books: Cyclometricus de circuli dimensione, and Concerning the Comet, the latter published in 1618. His observations demonstrate his shorter method for determining comet distance and movements. Coinciding with this work was his study of light refraction. In his experimentation, he referred to Kepler's writings, as well as those of Risner. The phenomenon of refraction was known as far back as Claudius Ptolemy, but Snell's explanation--which states that the ratio of the sines of the angles of the incident and refracted rays to the normal is a constant--became known as Snell's law of optical refraction. The constant determines how much a ray of light will be bent as it travels through one medium to another. Some controversy surrounds the fact that, although Snell never published his findings, they appear uncredited in René DescartesDioptrique in 1637, more than ten years after Snell's death. Some have accused Descartes of plagiarism, but it is unknown whether Descartes knew of Snell's discovery and passed it off as his own, or if his knowledge was gained independent of Snell's work.
Snell died in Leiden on October 30, 1626, and he was buried in the Pieterskerk. A monument was erected there in his honor.
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