at a Twin Plane of a Crystal. 249 



medium, and to — B/+C# in the second, gives 



Bq-Cp + O' (Bq-Cp')=-e i (Bq + Cp l ). . . (35) 



The continuity of c leads, when regard is paid to (31), (32), 

 merely to the repetition of the condition (34). 

 If we eliminate 9 X between (34), (35), we find 



6 , {'2Bq-Cp f -Cp 1 } = C(p-p 1 )-2Bq = by (33). 



Hence 6 X vanishes. Neither in this case, nor when the vibra- 

 tions are perpendicular to the plane of incidence, is there any 

 reflexion of light incident in the plane of symmetry. And 

 this conclusion may of course be extended to natural light, 

 and to light plane or elliptically polarized in any way 

 whatever. 



Plane of Incidence perpendicular to that of Symmetry. 



V>e have now to consider the case when the plane of inci- 

 dence is the plane y = 0, perpendicular to that of symmetry. 

 Here/, g, h are all finite, but they (as well as P, Q, R ; &c.) 

 are independent of the coordinate y. The problem is more 

 complicated than when the plane of incidence coincides with 

 that of symmetry, because an incident wave is here attended 

 by two reflected waves, and two refracted waves. 



The equation of the incident wave in the upper medium 

 may be expressed 



f,ff,h={\,fi,v)<** x + r *+*> l 



or, since by (2) \p + vr = 0, 



f,ff,h=(r, M ,-p)J<P*+™+' l >. . . . (36) 



The differential equations to be satisfied in the upper medium 

 assume the form 



If we substitute for /, g, h from (36), the first and third 

 equations give 



s*=r(Ar + Bfi)+p*D, .... (37) 



and the second equation gives 



/ ^=( i , 2 + r' 2 )(Br + C/z) (38) 



