MATHEMATICAL SCIENCES SEVENTEENTH CENT. 155 



or in any one plane. Again, the facts which are embodied in Kepler's 

 laws (p. 91) remain inconsistent with the motions of vortexes. Much 

 ingenuity has been expended in the endeavour to make the Cartesian 

 theory agree with or explain these and other facts. The original idea 

 was so modified, so many secondary hypotheses had to be superim- 

 posed upon it, that all the simplicity which commended the theory to 

 the popular mind was really lost. The hold which the Cartesian theory 

 had taken upon men's minds is apparent from the fact that the vor- 

 texes found defenders even after Newton had brought forward his grand 

 conception of universal gravitation. An eminent French savant, the 

 author of a history of the Academic des Sciences, published so late as 

 1753 an elaborate defence of Descartes' theory. 



The scientific writings of Descartes comprise treatises on music, on 

 anatomy, on meteors, on mechanics, and on optics. In the last-named 

 treatise he gives a very clear expression of the law according to which 

 light is refracted in passing from one transparent medium to another. 

 The first discoverer of the law of refraction was not Descartes, but a 

 Dutchman named WILLEBRORD SNELL. Descartes makes no mention 

 of Snell or any previous investigator of this subject, but it is probable 

 that he may have made the discovery independently. He certainly 

 expresses the law in a more direct manner than Snell ; and as this law 

 is the foundation of a very extensive branch of optical science, we will 

 state it as laid down by Des- 

 cartes. The shaded part of 

 Fig. 58 represents water, the 

 surface of which is supposed to 

 be at right angles to the plane 

 of the paper. Let the line a c 

 be a beam of light falling upon 

 the water at c. This beam, in- 

 stead of continuing its course 

 in a straight line, is abruptly 

 bent on entering the water, 

 within which it pursues the 

 path c b. Suppose that a line 

 ^perpendicular to the surface 

 of the water is drawn through c, 

 and that c is made the centre 



of a circle, which cuts off from the incident and refracted rays the equal 

 portions c a and c b. From a draw a d, and from b draw b e, both perpen- 

 dicular to de. The law of refraction asserts that, whatever may be the 

 inclination of a cto the surface, the length of a # will have one fixed pro- 

 portion to the length of e b. If the experiment be tried with a ray pass- 

 ing from air into water, it will be found that the length of eb is always 

 three-fourths of the length of a d; or we may adopt a more concise ex- 

 pression. Premising that the angle a cd, which may now be called the 



FIG. 58. 



