IN CRYSTALLIZED MEDIA. 335 



for by the symmetry of the medium 



„ Sx'Si/ . kSx' 

 2 — r-^ sin . -— — , 



and similar expressions for Sx', Sy' and Sx must all equal zero; 



.-. a = h - 3(?»'cos'0 + ii^^^ + ;/ cot^ xi/ cos' 0), 



sin -^ ^ 



I, = h - S (mcos^(j> + ti . + p'cot' ^ cos'^), 



c = h — 3 (»«'cos"v^ + y sin'^ \//), 

 adopting a notation similar to that in (1). 



Also X = 62.|(^a;'cos^ + ^y'4^|— _ ^x' cot v// cos 0) 



sm' —^ I 

 X (5a;' cos v//' 4- ^s'sinx/,) ^j' 



. , k^p 

 sin . — - 



= 62(5;r'"-cos0cosx/. - ^s'^cos^cosv/,) ^ 



= 3 {ni — J)') cos (f) cos \|/, 

 V = 3 {ni - J)') cos Q cos x//, 



Z = S {ni ^-„ — - + »' cot^ 4,\ cos Q cos d). 



sin'.x/^ / r/ r 



7. These values of u, h, &c. will be much simplified in an un- 

 crystallized medium, for in that case it is evident that 



. 2 hip . kip 



sin^ • —^ sm^ -— £- 



^hf r-=- = 26^2'^ r-2-; and .-. w' = ;/. 



This reduces the above equations to the following, in which I have 

 suppressed the accents for tiie sake of brevity. 



