IN CRYSTALLIZED MEDIA. 125 



We will in the first place suppose that is symmetrical with regard 

 to three planes at right angles to each other, which we shall take as the 

 co-ordinate planes. The condition of symmetry with respect to the plane 

 (;/x), will require <f> to remain unchanged, when we change 



,> into \ , 



But thus a\ J 5 , c 1 and a evidently remain unaltered; moreover, 



,\ become I , 

 7 j I-7. 



Hence we get 



<{>=f(a\ b\ C\ a', (Z'\ 7 '«). 



Applying like reasoning to the other co-ordinate planes, we see that the 

 ultimate result will be 



<p=/(a\ b\ c\ «", /r, y s ). (2.) 



The foregoing values are perfectly general, whatever the disturbance may 

 be; but if we consider this disturbance as very small, we may make 



X = X + u, 



y' - y + % 



z' = K + w, 



u, v and w being very small functions of x, y, % and t of the first order. 

 Then by substitution we get 



• q^il (—Y ( dv X f_ V, 1 



— dx \dx) \dx) \dx) " ' 



., , rf« (du\ 2 (dv\* idwV , 



bt = l + *Ty + \dy) + Kdy) + (d*) " * + * SU PP OSe - 



(3.) 



