CONFIRMATION OF THE UNDULATORY THEORY. 485 



kind of double refraction gave a hypothetical ex- 

 planation of the laws which M. Biot had obtained 

 for the phenomena of this class ; for example 9 , the 

 rule, that the deviation of the plane of polarization 

 of the emergent ray is inversely as the square of 

 the length of an undulation for each kind of rays. 

 And thus the phenomena produced by light passing 

 along the axis of quartz were reduced into complete 

 conformity with the theory. 



3. Elliptical Polarization in Quartz. We now 

 come to one of the few additions to Fresnel's 

 theory which have been shown to be necessary. 

 He had accounted fully for the colours produced 

 by the rays which travel along the aocis of quartz 

 crystals ; and thus, for the colours and changes of 

 the central spot which is produced when polarized 

 light passes through a transverse plate of such 

 crystals. But this central spot is surrounded by 

 rings of colours. How is the theory to be extended 

 to these ? 



This extension has been successfully made by 

 Professor Airy 10 . His hypothesis is, that as rays 

 passing along the axis of a quartz crystal are circu- 

 larly polarized, rays which are oblique to the axis 

 are elliptically polarized, the amount of ellipticity 

 depending, in some unknown manner, upon the 

 obliquity; and that each ray is separated by double 

 refraction into two rays polarized elliptically; the 

 one right-handed, the other left-handed. By means 

 9 Bull, des Sc. 1822, p. 197- :o Camb. Trans, iv. p. 83, &c. 



