Refraction at the Surface of Crystals. 

 respectively, these conditions give 



TH + TH" TH' 



241 



or 



sin 2i + sin 2r 

 TH 



sin 2i — sin 2r 

 TH' 



2 sin 2i 



+ TH" 



sin (i + r) cos (i — r) sin 2i cos (e + r)sin (i — r) 



which give the ratios of the intensities in this case. 



Lastly, take the case of two crystalline media. Denote in 

 this case the angles of incidence, refraction, and reflexion by 



*, fu */, -*/'. -*."■ 



[The angles of reflexion are called ~^i", — fa' 1 because 

 the corresponding fronts are on the side of the face opposite 

 to that on which are the other fronts.] 



In fig. 7 let OP be the incident ray, OS the perpendicular 

 from on the front, OT the perpendicular on the trace, K the 



Fig. 7. 



point of intersection of TS and the parallel through P to the 

 trace, % the angle POS between the ray and the wave normal, 

 \iz — 6 the angle between H and the trace, and a the length 

 of OT. Since H is perpendicular to p, and therefore to PS, 

 the angle PSK = ^7r — 0. The lengths, in terms of a and the 

 an o-les, of the various lines, are sufficiently obvious from the 

 figure. 



Putting H for +TH, the components of H parallel to the 



Phil. Mao. S. 5. Vol. 49. No. 297. Feb. 1900. R 



