528 Mr. R. T. Glazebrook on the Application of the 



cone given by (29), and this with equation (24) determines 

 its position completely. 



Again, let x, y, z be the coordinates of the point in which 

 the wave-front touches the wave-surface. Then we have*, if 



x 2 +y 2 + z 2 =r 2 , 



Ix + my + nz = Y ", 

 x=lY 



y=mV 



z = nY y2 _^. 

 Also from (9) or (27) , we find 



aH ~ ~i : 



r 2 - 



-a 2 



v«. 



-a 2 ' 



r 2_ 



-b* 



V 2 - 



-b*> 



r 2_ 



-c 2 



(30) 



(31) 



-s— = /e say. 



(32) 



V 2 -a 2 V 2 -6 2 V 2 ^ 



Thus 

 Hence 



X - K \w^?~ 1 } 



(r *-V*) X=K {y*^Jll-l(r*-Y')} 



= K\xY-lr*\ 



(33) 



Thus 



X# + /i# + kz=0 (34) 



Now #, y, z give the direction of the ray corresponding to 

 the wave-normal /, m, n, and the direction of vibration X, /j,, v. 

 Thus the direction of vibration is normal to the ray. 

 Again, multiply (11) by X/a 2 &c. and add. Then 



SS-'hSff-O+Sff^) 



A— B.,^ , N //X fflu wv\ 



A(A-B) 



- B2 y 2 (tK + mfi + nv)*. . . . 

 * Aldis, ' Tract on Double Befraction/ page 12. 



(35) 



