THEORY OF INTERFERENCE. 215 



property of the rays has been once established, is it not 

 still more extraordinary that we can deprive them of it? 



plain the unequal refrangibility of light. To give some general notion 

 of the nature of the subject, we may here briefly observe, that in the 

 explanation of refraction before given, [Life of Malus, note,] it is 

 clear that as the inclination of the common tangent to the contempo 

 raneous circular waves determines the refraction, this depends on the 

 diminution of the wave length within the denser medium ; and if this 

 inclination be determined for a ray of any given wave length, then for 

 another whose wave length Avithin the medium is different, and in a 

 given ratio to the former, the radii of the contemporaneous waves will 

 be in the same ratio as the former, or their difference from the former 

 will be in the same ratio, consequently the common tangent of these 

 second circles will not be parallel to the first, but inclined at a differ 

 ent angle: or the angle of refraction will be different. Thus if for 

 any particular ^primary ray the wave length within the medium be 



h 

 &quot;ki= that of the incident ray being /I and fj. the index for that 



ray, A = b sin i. 



A 

 then ^ = b sin r ~ 



or in other words, the refraction will be different from each primary 

 ray. But fi, and A, do not follow any simple ratio. The more com 

 plex expression on which that relation depends, is the result of M. 

 Cauchy s theory, viz: 



1 11 



^ = p -^ Q + ;F R - &c - 



[See Professor Powell s Treatise on the Undulatory Theory, sect, 

 vi.] 



Experimentally, the transverse vibrations receive their main sup 

 port from the analysis of the coloured tints, developed in polarized 

 light by the interposition of plates of crystal (such as those of mica, 

 selenite, &c.), when examined by an analyzer. 



Young ascribed these colours generally to interference ; but both 

 Fresnel and Arago pointed out that this explanation was incomplete. 

 Why did it only take place in polarized light, and even then not until 

 the analyzer had been applied ? These questions could not be an 

 swered till another law had been discovered; as it soon after was, by 

 the joint labours of those two philosophers. 



It was clear that in polarization all the vibrations were performed 

 in one and the same plane, in whatever direction they might be exe- 



