IN CRYSTALLIZED MEDIA. 131 



Let us therefore investigate the relation which must exist between 

 our coefficients, in order to satisfy this condition for two of our three 

 waves, the remaining one in consequence being necessarily propagated 

 by normal vibrations. 



For this we may remark, that the equation of a plane parallel to the 

 wave's front is 



= ax + by + c%. (a) 



If therefore we make 



x = x' + a\, 



y = y + b\, 



% = z + c\, 



and substitute these values in the equation (7) of the ellipsoid: re- 

 storing the values of 



A', B, C, D, E', F, 



the odd powers of \ ought to disappear in consequence of the equa- 

 tion (a), whatever may be the position of the wave's front. We thus 

 get 



G = U = / = n suppose, 



and P = n — 2L, 



Q = /n- 2M, 



R = fi - 2N. 



In fact, if we substitute these values in the function (4) there 

 will result 



- 20 = - 2^ -20 2 = 



2A-j- + 2B-j- + 2C-j- 

 ax ay dx 



+ A 



i(du\* (dv\ 2 (dw\ s \ 



\{dx) + \dx) + Kdlc) j 



R 2 



