126 On the Laws of Crystalline 



and thence 



fl , _ sin (p + ti) sin (p + <,) cos a/ 



tan u 3 - - , . > p 77- - -. , ; 



sin tan o> cos (j - i 1 ) sm <? cos ( jt) - t 2 ) 



and finally, 



tan 0' 3 = sin (p + tO cotan y ; (71) 



a result which shows that the plane of polarization of the re- 

 flected ray is perpendicular to a plane drawn through the ray 

 itself and the axis of the crystal. 



Moreover, we find, from the first of formulae (39), by 

 proceeding as above, 



tan B\ = - sin (p - ti) cotan q = - cotan 6 ; (72) 



and from (38) it is evident that 0i = 6. Therefore all that re- 

 lates to the case under our consideration may be summed up in 

 the following statement : 



When N= B, and the incident light is polarized in a plane 

 passing through the axis, the course of the light is unaltered, 

 and there is neither reflexion nor refraction. When it is pola- 

 rized in the perpendicular plane, all the light which enters the 

 crystal undergoes extraordinary refraction. Whatever light is 

 reflected is always polarized in a plane at right angles to that 

 which passes through the reflected ray and the axis of the 

 crystal; and this is true, whether the incident light is pola- 

 rized or not. 



Here, for the present, we must terminate our deductions 

 from the general theory propounded in this Paper. Several 

 other questions remain to be discussed, such as the reflexion of 

 common light* at the first surface, and the internal f reflexion 



* The mode of treating the case in which common light is incident has been 

 pointed out at the bottom of p. 100. 



1 1 have since found that the problem of reflexion at the second surface may be 

 reduced to that of reflexion at the first surface by means of a very simple rule. 

 Let us suppose the two surfaces of the crystal to be parallel; and let a ray 1, 

 uniradially polarized, and incident on the first surface, give the ray 7?s by reflexion, 

 and the single ray RZ by refraction. Let RZ be the ray which suffers internal reflex- 

 ion at the second surface, thereby giving the two reflected rays J?,,, J2' <( , and the 



