Lenses and Waves

THE 'PROJET' OF 1672 135
room for doubt concerning the physical causes he assumed”, Newton wrote
30 years later. 98 In view of Galileo’s science of motion it is doubtful whether
the motion of a ball struck through a frail canvas is subject to the
assumptions Descartes made. His explanation of refraction into a denser
medium – towards the normal – was regarded most problematic. In order to
account for the necessary increase of motion, he introduced the rather ad
hoc assumption that the ball was struck again at the refracting surface.
Besides rejecting Descartes’ theory of light on the conviction that the speed
of light is finite, in the ‘Projet’ Huygens explicitly mentioned this extra
assumption as one of the difficulties in Descartes’ derivation. 99
Newton and Huygens wrote at a time when the law of sines as such had
been generally accepted. This had taken some twenty years, during which it
only slowly became widely known. Cavalieri in 1647 did not employ the law
of sines and Gregory seems to have been ignorant of it as late as 1663. As we
have seen in the previous chapters, Huygens was one of the very few to
pursue the study of dioptrics in this period. Compared to the preceding
decades, the 1660s witnessed a true upsurge of the study of light. The
investigations of Grimaldi, Boyle, Hooke, Newton, Bartholinus, brought to
light a collection of new properties shaking the foundations of optics.
Remarkably, the final acceptance of the law of sines coincided with
accusations of plagiarism directed at Descartes. In De natura lucis et proprietate
(1662) Isaac Vossius said that Descartes had seen Snel’s papers and
concocted his own proof. We now know this charge to be undeserved but it
has been adopted by many since. Descartes may have heard of Snel’s
achievement through his contacts with the circle that included Golius (Snel’s
successor) and Constantijn Huygens sr. around 1632, but he had found the
law much earlier. Christiaan Huygens started to display doubts regarding
Descartes’ originality since the early 1660s. Probably spurred by Vossius’
claims, he traced and examined Snel’s papers. As late as 1693 he voiced his
opinion as follows: “It is true that from all appearances these laws of
refraction aren’t the invention of Mr. des Cartes, because it is certain that he
has seen the manuscript book of Snel, which I also have seen.” 100 Most
remarkable about this is that Huygens could have known, through his father,
much earlier about Snel’s achievement. Constantijn sr. had heard of it
through a letter from Golius of 1 November 1632. Apparently the topic had
never entered their conversation.
The slow adoption of the sine law may have been brought about by the
bad odor of Descartes’ philosophy, or simply the slow diffusion of his
works. Fermat was convinced of the sine law’s validity only after he found
98 Newton, Optical lectures, 170-171 & 310-313.
99 A similar conclusion can be drawn with respect to Descartes’ theory of hydrostatics on which his
concept of ‘conatus’ was based. Shapiro, “Light, pressure”, 260-266.
100 “Il est vray que ces loix de la refraction ne sont pas l’invention de Mr. des Cartes selon toutes les
apparences, car il est certain qu’il a vu le livre manuscrit de Snellius, que j’ay vu aussi; ...” OC10, 405-6. See
also OC13, 9 note 1.