346 Mr KELLAND, on THE TRANSMISSION OF LIGHT 



.-. £ = 0, 



TT 



or e = -, 

 and the vibration is either in the plane of xx or of yz. 



And from equation (a), if 6 = 0, 



fl2 _ i^ + (b- - (f) sin= >// = 0, 





and, tan ^\, = sj — — ^^ ; 



ir — c 

 therefore a is intermediate to h and c. 



If e = ^ vve get {a' - 6^)cos'x// = {¥ - c')s\xv^; 



& — 0- 



tani 



" c' 



and b must be intermediate to a and c. Both these cannot be true 

 for the same medium : let the latter only be true, then the transmis- 

 sion is in the plane of xx, and there are two directions, one on each 

 side of the axis of 2, for which the velocities of transmission of both 

 vibrations are the same, which directions are the optic axes*. 



We will call m the angle made by this optic axis with the axis 

 of X, so that 



b'-d a' -b' 

 tan^,;, = ___=__^. 



22. The equation (a) gives 



_ (a' - b') (cos^£ - sin°6 cos^>//) + jb' - c') siif^ 



— cot 2 m — 7 z TT\ '• 7^ i "" 



(«- — b') sm2€ cosy 



_ cos^ 6 — sin- 6 cos^ x^/ + cot^ >« sin- >// 

 ~ sin 2 6 cos ^ 



* The optic axis here is not the same as that which Fresnel calls by the same name. 

 This is determined by the direction of the wave, his by that of the ray. As I shall 

 have to compare them, I will use the term radial axis instead of optic axis when speak- 

 ing of the latter. 



