IN CRYSTALLIZED MEDIA. 129 



Neglecting the double integrals which relate to the extreme boun- 

 daries only of the medium, and which we will suppose situated at an 

 infinite distance, we get for the general equations of motion, 



^df= {G + ^dP +{N + ^ay +{M+C) d¥ 



(5.) 

 d 2 v , xr .. d*v . r , „, d 2 v . _ _ d 2 v 



? M*- = {N+ A ^dW + {H + B ^df + {L + C) d* 



dxdy ' dy d% ' 



d 2 w .,, j,d 2 w , /T n.d^w , T s^d 2 w 



p-d¥-= {M+A) ^ + {L+B) W + {I + C) d^ 



If now in our indefinitely extended medium we wish to determine 

 the laws of the propagation of plane waves, we must take, to satisfy 

 the last equations, 



u = of (ax + by + ex + et), 



v = fif(ax + by + cz + et), 



w = ^/(ttx + by + c% + et) ; 



a, b and c being the cosines of the angles which a normal to the wave's 

 front makes with the co-ordinate axes, a, /3, 7 constant coefficients, and 

 e the velocity of transmission of a wave perpendicular to its own front, 

 and taken with a contrary sign. 



Substituting these values in the equations (5), and making to 

 abridge 



A'=(G + A)a 2 +(N + B)b*+(M + C)c\ 



B=(N + A)a 2 + (H+ B)b* + (L + Qc 2 , 



C - (Jf + A) a 2 +(L + B)¥ + (I + C) c*; 

 Vol. VII. Part II. R 



