9 8 On tJie Laws of Crystalline 



directions which give only a single refracted ray. These, as well 

 as the corresponding ones in the reflected wave plane, may be 

 called uniradial transversals. They are the intersections of the 

 two refracted polar planes with the incident and reflected wave 

 planes. 



"When the incident transversal does not coincide with either 

 of the uniradial directions, it is to be resolved parallel to them, 

 and then each component transversal will supply a refracted 

 ray, according to the foregoing rules. The reflected transver- 

 sals, arising from the component incident ones, are to be found 

 separately by the same rules, and then to be compounded. 



In ordinary reflexion, if the incident transversal be in the 

 plane of incidence, or perpendicular to it, the reflected trans- 

 versal will be so likewise. But this does not hold in crystalline 

 reflexion. The general method just given will, however, enable 

 us to determine the positions and magnitudes of the reflected 

 transversals in these two remarkable cases ; and then, if we 

 choose, we can reduce any other case to these two, by resolving 

 the incident transversal in directions parallel and perpendicular 

 to the plane of incidence. 



If we conceive a pair of incident transversals, at right angles 

 to each other, to revolve about the origin, it is evident that there 

 will be a position in which the reflected transversals correspond- 

 ing to them will also be at right angles to each other. There 

 is no difficulty in finding this position, and there will be an 

 advantage in using it when common unpolarized light is in- 

 cident on the crystal. For, the incident transversals being 

 rectangular, we may suppose the light to be equally divided 

 between them, and then the intensities of the corresponding 

 reflected portions can be found by the preceding rules. As 

 the reflected transversals are also rectangular, the sum of these 

 intensities will be the whole intensity of the reflected light, and 

 their difference will be the intensity of the polarized part of 

 it. This part will be polarized in a plane passing through the 

 greater of the two reflected transversals. 



Common light will be completely polarized by reflexion when 



