539 



Conversely, there are two directions, P 1 0, P 2 0, in which a ray may be 

 incident internally so as to furnish a ray refracted along OP, and in 

 each case no second refracted ray will be produced, provided the 

 incident ray be polarized in the same manner as the refracted ray 

 OP X or OP 2 . In the case of a crystal, then, equation (1) must be 

 replaced by 



(l-A)Rcos^=(l AJB^cosi^+Cl A 2 ) R a cos * a ty a . (2) 

 In the most general case it does not appear in what manner, if at 

 all, equation (2) would split into two equations, involving respectively 

 Rj and R 2 . For if an incident ray PO were so polarized as to furnish 

 only one refracted ray, say OP 1} a ray incident along P X O and polarized 

 in the same manner as OP : would furnish indeed only one refracted 

 ray, in the direction OP, but that would be polarized differently from 

 PO ; so that the two systems are mixed up together. 



But if the plane of incidence be a principal plane, and if we may 

 assume that such a plane is a plane of symmetry as regards the optical 

 properties of the medium *, the system of rays polarized in and the 

 system polarized perpendicularly to the plane of incidence will be 

 quite independent of each other, and the equality between the radiation 

 incident externally and that proceeding in the contrary direction, and 

 made up partly of a refracted and partly of an externally reflected radia- 

 tion, must hold good for each system separately. In this case, then, 

 (2) will split into two equations, each of the form (1), R now standing 

 for half the whole radiation, and R', A', &c. standing for R p A lt &c., 

 or R 2 , AJJ, &c., as the case may be. It need hardly be remarked that 

 the value of A is different in the two cases, and that R' has a value 

 which is no longer, as in the case of an isotropic medium, alike in all 



* According to Sir David Brewster (Report of the British Association for 1836, 

 part ii. p. 13, and for 1842, part ii. p. 13), when light is incident on a plane sur- 

 face of Iceland spar in a plane parallel to the axis, the plane of incidence, which 

 is a principal plane, is not in general a plane of optical, any more than of crystal- 

 line symmetry as regards the phenomena of reflexion, although, as is well known, 

 all planes passing through the axis are alike as regards internal propagation and 

 the polarization of the refracted rays. Hence, strictly speaking, the statement as 

 to the independence of the two systems of rays should be confined to the case in 

 which the principal plane is also a plane of crystalline symmetry. As, however, 

 the unsymmetrical phenomena were only brought out when the ordinary reflexion 

 was weakened, almost annihilated, by the use of oil of cassia, we may conclude 

 that under common circumstances they would be insensible. 



