Crystalline Reflexion and Refraction. 33 



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 refractive index changes with the 

 direction of the ray. For the density, being independent of direction, could not 

 be conceived to vary with the refractive index. About two years ago, I got over 

 this difficulty by supposing the density of the ether to be the same in all media.* 

 At the same time I was compelled to employ the principle of equivalent vibra- 

 tions, in order to have a sufficient number of conditions, though for a while I 

 overlooked the perfect agreement which now subsisted between this principle 

 and the law of vis viva ; it happened, in fact, that the new hypothesis of a 

 constant density made the vis viva of the refracted ray exactly the same as in 

 the theory of Fresnel.f 



But to see why it was necessary to assume the principle of equivalent vibra- 

 tions, we must observe, that when a polarised ray is incident on a crystal, there 

 are four things to be determined, namely, the direction and magnitude of the 

 reflected vibration, and the magnitudes of the two refracted vibrations. Hence 

 we must have four conditions, or we must have relations affording so many 

 equations. But the hypotheses of Fresnel, by which he solved the problem of 



* This hypothesis is maintained by Mr. Challis ; and certainly it falls in extremely well with 

 the astronomical phenomenon of the aberration of light. — See, on this subject, Professor Lloyd's 

 Report on Physical Optics, Fourth Report of the British Association for the Advancement of 

 Science, pp. 311, 313. 



"t See hereafter, p. 42, note. 



VOL. XVIII. F 



