INTERFERENCE OF POLARIZED LIGHT. 219 



one another ; and finally, they vanish altogether when the 

 axes form a right angle. 



In this law we find the account of the fact which hitherto 

 perplexed us, namely, that no phenomena of interference or 

 colour are produced, under ordinary circumstances, by the 

 two rays which emerge from a crystalline plate, and which 

 are polarized in opposite planes ; and we learn that, to pro- 

 duce these phenomena, the planes of polarization of the two 

 rays must be brought to coincidence by the analyzer. 



The non-interference of rays, polarized in planes at right 

 angles to one another, is a necessary result of the mechanical 

 theory of transversal vibrations. In fact, it is a mathematical 

 consequence of that theory, that the intensity of the resultant 

 light in that case is constant, and equal to the sum, of the in- 

 tensities of the two component lights, whatever be the phases 

 of vibration in which they meet. 



Fresnel and Arago discovered, further, that two op- 

 positely-polarized rays will not interfere, even when their 

 planes of polarization are made to coincide, unless they belong 

 to a pencil, the whole of which was originally polarized in one 

 plane ; a ad that, in the interference of rays which had under- 

 gone double refraction, half an undulation must be supposed 

 to be lost or gained, in passing from the ordinary to the extra- 

 ordinary system, just as in the transition from the reflected 

 to the transmitted system, in the colours formed by thin 

 plates. 



The principle of the allowance of half an undulation is a 

 simple consequence of the theory of transversal vibrations. 

 In fact, the vibration of the wave incident on the crystal is 

 resolved into two within it, at right angles to one another, one 

 in the plane of the principal section, and the other in the per- 

 pendicular plane. Each of these must be again resolved, in 

 two fixed directions which are also perpendicular ; and it will 

 easily appear from the process of resolution, that of the four 



