MATHEMATICAL PHYSICS. 



9 



G sin ft G sill ff 



Evidently the quantities , also represent the distances of the reciprocal 



R tan q) R cot (p 



lines from the central axis. 



III. 



The extreme points of emergence for rays refracted through a prism in a principal 

 plane may be exhibited as in the accompanying figure, where BAD represents the prism, 

 B is the point of incidence, ABC the complement of the critical angle BAE = EAF, and 

 the circle is described around BAF. The angles marked at B and D being equal, BD is 

 the last ray which emerges. Thus as the angle of the prism is increased, one point of 

 emergence will always lie on the circle, whilst the other will be the intersection of 

 BC with the second side of the prism ; and when the angle of the prism becomes equal 

 to twice the critical angle C and D coincide at F. 



Sec. Ill, 1889. 



