Willebrord Snell

1580-1626

Dutch Physicist and Mathematician

Willebrord Snell is remembered for discovering the law of refraction that bears his name. He has also been called the father of modern geodesy for perfecting the method of determining distances by trigonometric triangulation.

Snell was born in 1580 in Leiden, Netherlands. He was the son of Rudolph Snell van Royen (Latinized as Snellius), professor of mathematics at the University of Leiden. Willebrord studied law and taught mathematics at Leiden. After touring Europe (1600-04) he returned home, where he prepared a Latin translation of Simon Stevin's (c. 1548-1620) Wisconstighe Ghedachtenissen and worked on restoring the two existing books of Apollonius's (c. 262-c. 290 b.c.) work on plane loci. In 1608 he received his M.A. and married. After the death of Rudolph in 1613, Willebrord assumed his father's teaching duties, officially succeeding him in 1615.

It was also during 1615 that Snell set himself the task of determining the length of a degree of the meridian. For this purpose he chose the method of triangulation originally suggested by Gemma Frisius (1533). Starting with his house and taking the spires of nearby churches as reference points, he measured a net of triangles from Alkmaar to Bergen-op-Zoom using a huge 130-inch (210-centimeter) quadrant. This allowed him to accurately compute the distance between these towns and also calculate the length of a degree of the meridian. His results were published in Eratosthenes batavus (1617). Seeking to improve his work he extended the net of triangles from Bergen-op-Zoom to Mechelen. Reduction of this data occupied him throughout the rest of his life, and his findings were published posthumously by one of his students. His corrected value of 69 miles (111 kilometers) for the length of a degree of the meridian is within a few hundred meters of the presently accepted value.

In 1621, or shortly thereafter, Snell discovered the law of refraction that today bears his name. When light rays pass obliquely from a rarer to denser medium (e.g. air to water) they are bent toward the vertical. Scientists from Ptolemy (fl. second century a.d.) to Johannes Kepler (1572-1630) had searched in vain for a law to explain this phenomenon. Ptolemy thought the angles of the incident and refracted light rays maintained a constant relationship, while Kepler had produced nothing more than approximate empirical relations. Snell's years of research revealed that it was the ratio of the sines of the angles of the incident and refracted rays to the normal that remains constant.

Though Snell never published his findings, the manuscript containing the discovery was examined by Isaacus Vossius (1618-1669) and Christiaan Huygens (1629-1695), who commented upon it in their own works. However, priority of publication goes to René Descartes (1596-1650), who presented the law without proof in his Dioptrique (1637). Huygens and others accused Descartes of plagiarism. Though Descartes's many visits to Leiden during Snell's life make the charge plausible, there seems to be no evidence to support it.

Snell's astronomical work includes observations of the comet of 1618. His parallax measurements clearly indicated the comet was above the sphere of the Moon. Nevertheless, his support for the Ptolemaic system remained unshaken. In Cyclometricus (1621) he used Van Ceulen's methods to determine the value of π to 34 decimal places. His work on navigational methods focused on the study and tabulation of Pedro Nuñez's rhumb lines (1537), which Snell referred to as loxodromes. This material appeared in Tiphys batavus (1624). Canon triangulorum (1626) and Doctrina triangulorum (1627) contain the fruits of his research on plane and spherical trigonometry. The latter unfinished work was completed and published posthumously by his student Martinus Hortensius. Snell died in Leiden on October 30, 1626.

STEPHEN D. NORTON