Willebrord Snell Biography

McBride 1

Megan McBride

Honors Astronomy

Percival 3

15 Oct 2010

Willebrord Snell Biography

            Willebrord Snell was born to an affluent family in Leiden, Netherlands in 1580. He studied law at the University of Leiden although he had a great passion for math. He traveled widely in Europe, visiting Paris, Würzburg, and Prague, and among the celebrated scientists he met were Johannes Kepler and Tycho Brahe. In 1613 he succeeded his father, Rudolph Snel van Royen (1546-1613), as professor of mathematics at the University of Leiden. Although he lived a relatively short life span, the accomplishments of Snell and his contributions to science are priceless.

It was 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 length of a degree of the meridian. His results were published in Eratosthenes batavus (1617). 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. His method of using triangulation in his work in this field set the foundation of geodesy. In another great contribution, Snell improved the classical method of calculating approximate values of π by polygons. Using his method 96 sided polygons give π correct to 7 places while the classical method yields only 2 places.

Willebrord's biggest contribution to science, however, is the law of refraction, even though it wasn't published until almost 70 years after he died. He found that a beam of light would bend as it enters a block of glass, and that the angle of bending would depend on the angle of the light beam. Light traveling perpendicular to the glass will not bend, however, if the light travels at an angle into the glass it will bend to a degree proportional to the angle of inclination. In 1621, Snell found a characteristic ratio between the angle of incidence and the angle of refraction. His law demonstrates that all substances have a specific bending ratio or "refractive index". The greater the angle of refraction, the higher the refractive index for a substance. This law can be described by the following formula: n₁ sin < = n₂ sin < Scientists from Ptolemy (fl. second century A.D.) to Johannes Kepler (1572-1630) had searched in vain for a law to explain this phenomenon.

Though Snell never published his own findings, the manuscript containing the discovery was examined by Isaacus Vossius (1618-1669) and Christian 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 did however publish Cyclometria sive de circuli dimensione (1621), and Tiphys Batavus (1624).

Snell's additional 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 at the relatively young age of 46 on October 30, 1626 in Leiden. He would never realize how the importance of his discovery of the basic laws of refraction would prominently position his name in textbooks on physics and optics!