DISCOVERY OF THE LAW OF REFRACTION. 57 



Huyghens' assertion, that Sncll did not attend to the proportion of 

 the sines, is very captious ; and becomes absurdly so, when it is made 

 to mean that Snell did not know the law of the sines. It is not denied 

 that Snell knew the true law, or that the true law is the law of the 

 sines. Snell does not use the trigonometrical term sine, but he ex- 

 presses the law in a geometrical form more simply. Even if he had 

 attended to the law of the sines, he might reasonably have preferred 

 his own way of stating it. 



James Gregory also independently discovered the true law of refrac- 

 tion ; and, in publishing it, states that he had learnt that it had already 

 been published by Descartes]. 



But though Descartes does not, in this instance, produce any good 

 claims to the character of an inductive philosopher, he showed consi- 

 derable skill in tracing the consequences of the principle when once 

 adopted. In particular we must consider him as the genuine author 

 of the explanation of the rainbow. It is true that Fleischer 4 and Kep- 

 ler had previously ascribed this phenomenon to the rays of sunlight 

 which, falling on drops of rain, are refracted into each drop, reflected 

 at its inner surface, and refracted out again : Antonio cle Dominis had 

 found that a glass globe of water, when placed in a particular position 

 with respect to the eye, exhibited bright colors ; and had hence 

 explained the circular form of the bow, which, indeed, Aristotle had 

 done before. 5 But none of these writers had shown why there was a 

 narrow bright circle of a definite diameter ; for the drops which send 

 rays to the eye after two refractions and a reflection, occupy a much 

 wider space in the heavens. Descartes assigned the reason for this in 

 the most satisfactory manner, 6 by showing that the rays which, after 

 two refractions and a reflection, come to the eye at an angle of about 

 forty-one degrees with their original direction, are far more dense than 

 those in any other position. He showed, in the same manner, that the 

 existence and position of the secondary boio resulted from the same 

 laws. This is the complete and adequate account of the state of 

 things, so far as the brightness of the bows only is concerned ; the 

 explanation of the colors belongs to the next article of our survey. 



The explanation of the rainbow and of its magnitude, afforded by 

 Snell's law of sines, was perhaps one of the leading points in the verifi- 

 cation of the law. The principle, being once established, was applied, 

 by the aid of mathematical reasoning, to atmospheric refractions, opti- 



4 Mont. i. 701. * Jfeteorol. iii. 3. ' Jleieorum, cap. viii. p. 193 



