IN CRYSTALLIZED MEDIA. 349 



and the sum of the squares of the velocities is 



(a' + ¥) cos= x/r + («= + e) cos- 6 sin^ ^ + {¥ + c') sin^ e sin'' ^}, 

 = a^ (cos' ^// + COS- e sin' v//) + b' (cos' x/. + sin^ e sin^ >//) 



+ (f sin' \// 

 = a' (cos' e + sin' e cos' >//) + i' (sin' € + cos' e cos' ^j,) 



+ c' sin' ^ 



which is the same expression as we deduced for the sum of the squares 

 of the velocities in (20). 



25. Having then results coinciding with those of M. Fresnel, I 

 shall pursue the subject no further. The formula which I have given 

 for the value of the difference of the squares of the velocities of the 

 two vibrations, is a very elegant and useful one. Whether it had 

 ever before been deduced froni theory, or not, I cannot tell. Mr 

 Herschel states that it has long been estabhshed by experiment. The 

 only analogous one which I can find, is that of M. Fresnel, viz., 

 "that the difference of the squares of the reciprocals of the velocities 

 of the two rays is proportional to the product of the sines of the 

 angles which their common direction makes with the optic axes of 

 the crystal." M. Fresnel also defines "optic axes" as those in which 

 the rays travel when their velocity is the same for both. I have 

 preferred to retain the name of optic axes to those directions which 

 are normals to the directions of waves which move with a common 

 velocity perpendicular to their own front; and it is very evident that 

 these are the optic axes of experiment. 



I wish to add that, as far as I am aware, M. Fresnel's law, 

 beautiful as it undoubtedly is, appears to me utterly incapable of 

 being tested by experiment; so far as I can see, it requires a con- 

 nexion with the index of refraction in order to apply experiment at 

 all, and the index of refraction depends only on the wave. It must 

 however be observed, that the older experimenters always use the 

 word ray, but the sliglitest examination is sufficient to convince us 

 that they mean, what we now caU wave. 



y Y 2 



