Reflexion and Refraction. 89 



direction of the transversals ; but this inference was to be re- 

 ceived with caution, as being contrary to the hypothesis of 

 Fresnel ; and besides, I had in the meantime contrived a way 

 of adapting my analogy, in some degree, to that hypothesis, by 

 supposing areas to be compounded instead of vibrations ; so that 

 I hesitated which of the two opinions to prefer. Taking, how- 

 ever, the opinion of M. Cauchy as that which fell in more na- 

 turally with the aforesaid analogy, I was led to the conclusion, 

 that the vibration in the refracted ray is probably the resultant 

 of the incident and reflected vibrations ; and I saw that if this 

 principle were true for singly-refracting media, it should also, 

 from its very nature, be true, when properly generalized, for 

 doubly -refracting crystals ; so that in such crystals the resultant 

 of the two refracted vibrations would be the same, both in length 

 and direction, as the resultant of the incident and reflected 

 vibrations. 



This was the principle of equivalent vibrations. But I had 

 no sooner begun to regard it as probable, than an objection 

 started up against it. In the case of a ray ordinarily refracted 

 out of a rarer into a denser medium, the magnitude of the 

 refracted vibration, as deduced from this principle, was greater 

 than that which came out from the theory of Fresnel, in the 

 proportion of the sine of the angle of incidence to the sine of 

 the angle of refraction. Consequently, assuming with Fresnel 

 that the ether is more dense in the denser medium, the law of 

 the preservation of vis viva was violated. 



There was another embarrassment which I felt in my early 

 efforts to find out the laws of crystalline reflexion. Taking 

 for granted the hypothesis of Fresnel, that the density of the 

 ether in an ordinary medium is inversely as the square of its 

 refractive index, I was at a loss what hypothesis to make, in 

 this respect, for doubly-refracting crystals, wherein the refrac- 

 tive index changes with the direction of the ray. For the 

 density, being independent of direction, could not be con- 

 ceived to vary with the refractive index. About two years 

 ago I got over this difficulty, by supposing the density of the 



