250 THEORETISCHE OPTIK. 



undertaken from any narrow point of view. Any faults of detail will 

 be readily forgiven, if the author shall give the theory of optics 

 the TTOU (rru) which it has sought so long in vain. We may add that 

 if this effort shall not be judged successful by the scientific world, 

 the author will at least have the satisfaction of being associated in his 

 failure with many of the most distinguished names in mathematical 

 physics. 



We have sought to test the proposed theory with respect to that 

 law of optics which seems most conspicuous in its definite mathe- 

 matical form, and in the rigor of the experimental verifications to 

 which it has been subjected, as well as in the magnificent develop- 

 ments to which it has given rise : the law of double refraction due to 

 Huyghens and Fresnel, and geometrically illustrated by the wave- 

 surface of the latter. We cannot find that the law of Fresnel is 

 proved at all in this treatise. We find on the contrary, that a law is 

 deduced which is different from Fresnel's, and inconsistent with it. 

 We do not refer to anything relating to the direction of vibration of 

 the rays in a crystal, which is a point not touched by the experi- 

 mental verifications to which we have alluded. We shall confine 

 our comparison to those equations from which the direction of 

 vibration has been eliminated, and which therefore represent relations 

 subject to experimental control. For this purpose equation (13) on 

 page 299 is suitable. It reads 



u 2 v 2 w 2 _ 



n x , n yy n z being the principal indices of refraction. This the author 

 calls the equation of the wave-surface or surface of ray-velocities. 

 It has the form of the equation of Fresnel's wave-surface, expressed 

 in terms of the direction-cosines and reciprocal of the radius vector, 

 and if u, v, w are the direction-cosines of the ray, and n the velocity 

 of light in vacuo divided by the so-called ray-velocity in the crystal 

 the equation will express Fresnel's law. But it is impossible to give 

 these meanings to u, v, w and n. They are introduced into the 

 discussion in the expression for the vibrations (p. 295), viz., 



t 



The form of this equation shows that u, v, w are proportional to the 

 direction-cosines of the wave-normal, and as the relation u 2 -\-v 2 +w 2 = 1 

 is afterwards used, they must be the direction-cosines of the wave- 

 normal. They cannot possibly denote the direction-cosines of the ray, 

 except in the particular case in which the ray and wave-normal 

 coincide. Again, from the form of this equation, \/n must be the 

 wave-length in the crystal, and if X here as elsewhere in the book 



