176 F. E. Wright — Transmission of Light through 



cos 7\ cos if/ l sin r„ cos i/^ + cos r, cos «/»„ sin r } cos i/^ + 



sin r, sin li, r . , . , , , , , 



— Ji t sm *iK, cos r i- a ii sin r .) + «n cos^,]+ (33) 



sin /•„ sin iA r . , . , , T 



— ^ n [sin </r s (a u cos r 2 — a, 3 sin rj + a ia cos i/<J = 



an equation, which, like 18a, can be written in the abbreviated 

 form 



This equation is the general Potier relation 1 and is applicable 

 to any two of the four possible waves within the crystal. 



Uniradial azimuths. 



At the boundary surface of a crystal plate with an envelop- 

 ing isotropic medium, an incident plane polarized, monochro- 

 matic light wave furnishes, in general, one reflected wave in the 

 isotropic medium and two refracted waves, W„ W 2 , within the 

 crystal. The directions and azimuths of the two refracted 

 waves are definitely fixed by equations (16) and (17) and a 

 rotation of the plane of polarization of the incident wave can 

 produce a change in the amplitudes only of the two refracted 

 waves. For a certain value of the azimuth, the amplitude of 

 either W, or W 2 becomes zero, and but one refracted wave is 

 transmitted. Such azimuths, e„, of the plane of polarization 

 of the incident wave, for which only one refracted wave 

 results, are called uniradial azimuths, and were first inves- 

 tigated by MacCullagh 2 and Neumann. 3 For D 2 = in equa- 

 tion (19) we find 



(a) (E cos £j — R cos p) cosi = D 1 cos tJ x cos r 1 



(b) E sin Cj + Ii sin p = D x sin S i 



(c) (E cos e, + R cos p) sin i. = ~D l cos d l sin r 1 (34) 



(d) (E sin e 1 — R sin p) sin i cos i = 



— ^i ifsin 8 t (a„ cos r t -a u sin rj + a 12 cos dj 



The last equation of this set can be readily reduced by means 

 of (32) to the form 



(d 1 ) (E sin £, — R sin p) sin i cos i = 



D 1 sinVj(cot 7\ sin ^ i — tg sj 



By multiplying the first of these equations with sin i, the third 

 with cos * and adding ; also the second with cos i sin *, and 

 adding to the fourth, we obtain 



1 Potier, Jour, de Phys. (2). x, 352, 1891. 



2 Trans. Roy. Irish Acad., xviii, 31, 1837. Collected Works, p. 110, 1880. 



3 Berliner Akad. Abh., Math. Abt. 144, 1835 ; Pogg. Ann., xlii, 9, 1837. 



