168 F. F. Wright — Transmission of Light through 



2M=SA'A 



2 A k »» k = 2 A \m\ 



2 A k ? H = 2 A X„ 



(18a) 



2 A kPk = 2 A 'kp'k 

 i i 



In case the crystal plate is surrounded by an isotropic 

 medium, these general equations become simpler; the index 

 ellipsoid for the isotropic medium is a sphere and its coeffi- 

 cients are a' u = a' aa = a' 3S = q* and a' aa = a' 3 =a\ 3 = 0. For the 

 passage of light from the isotropic medium to the crystal plate, 

 there are, in general, one incident wave (I), one reflected wave 

 (R) and two refracted waves, W„ W 2 (fig. 2) ; the boundary 

 equations are, then, 



Fig. 2. 



D, cos d i cos r, + D 2 cos <5 2 cos r 9 = (E cos c— R cos p) cos i 



D 1 sin d i +D 2 sin <5 2 = E sin e + R sin p 



D, cos d i sin ?*, + D 2 cos d 2 sin r 2 = (E cos e + R cos p) sin i 



sin 7* 

 D, — ^r-'fsin ($, (a„ cos r i — a l3 sin r,) + a 12 cos 5 ] + 



f / a 



D. 



2 [ sin ',(«„ cos *, — <*» sin ♦",)+«„ cos d ,] = 



(19) 



(E sin e — R sin p) sin i cos i 



wherein, for the incident wave (I), the reflected wave (R), the 

 faster refracted wave W, and the slower refracted wave W 2 , 

 respectively, E, R, D„ D 2 , are the amplitudes ; e, p, 8„ S„ the 

 polarization azimuths ; q , q , d t , d^ the normal velocities of 

 the wave ; i, ir—i, r 1} r„ the angles of the wave normals with 



