29 



lem is, thei'efore, completely solved in this case ; and it is 

 obvious, that a construction precisely similar vrill apply to the 

 other case, in which ot' is the only refracted ray. The plane 

 B, which, in this second case, answers to the plane a in the 

 first case, is perpendicular to the plane ot'm, and parallel 

 to the right line t'm. 



If the incident ray be polarized in a direction interme- 

 diate between the two transversal directions which give only 

 a single refracted ray, the incident vibration may be resolved 

 into two vibrations parallel to those two transversals. The 

 reflected vibrations arising from each of the component 

 incident vibrations are to be found by the foregoing rules, 

 and then to be compounded. 



When the intersection of the planes a and b is perpendi- 

 cular to the direction of the reflected ray, this ray is polar- 

 ized parallel to that intersection, whatever be the plane of 

 polarization of the incident ray. The angle of incidence at 

 which this takes place is the polarizing angle. 



When the refracted ray ot or ox' is a normal to the wave- 

 surface, the plane a or b is the plane of polarization of the 

 ray. For example, if ot be the ordinary ray in a uniaxal 

 crystal, the plane a contains the ray ot and the axis of the 

 crystal. 



The hypotheses from which Mr. Mac Cullaghhas obtained 

 the foregoing laws, are these : — 



1. The density of the aether is the same in all media. 



2. The vibrations are parallel to the plane of polarization. 



3. The vis viva is preserved. 



4. The vibrations are preserved : that is, the resultant of 

 the incident and reflected vibrations is the same as the resul- 

 tant of the refracted vibrations. 



The author finds that his theory represents very accu- 

 rately the experiments of Sir David Brewster and M. Seebeck, 

 on the fight reflected in air from a surface of Iceland spar. 



