122 HISTORY OF OPTICS. 



four internal reflections instead of t\vo ; two of the four taking place 

 when the surface of the glass was dry, and two when it was wet. The 

 rhomb was made ; and when all the points of reflection were dry, the 

 light was not circularly polarized ; when two points were wet, the 

 light was circularly polarized ; and when all four were wet, it was not 

 circularly polarized.] 



3. Elliptical Polarization in Quartz. "We now come to one of the 

 few additions to Fresnel's theory which have been shown to be neces- 

 sary. He had accounted fully for the colors produced by the rays 

 which travel along the axis of quartz crystals ; and thus, for the co- 

 lors and changes of the central spot which, is produced when polar- 

 ized light passes through a transverse plate of such crystals. But this 

 central spot is surrounded by rings of colors. 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 crys- 

 tal are circularly 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 of these suppositions, 

 he not only was enabled to account for the simple phenomena of sin- 

 gle plates of quartz ; but for many most complex and intricate appear- 

 ances which arise from the superposition of two plates, and which at 

 first sight might appear to defy all attempts to reduce them to law 

 and symmetry ; such as spirals, curves approaching to a square form, 

 curves broken in four places. " I can hardly imagine," he says, 11 very 

 naturally, " that any other supposition would represent the phenomena 

 to such extreme accuracy. I am not so much struck with the ac- 

 counting for the continued dilatation of circles, and the general repre- 

 sentation of the forms of spirals, as with the explanations of the minute 

 deviations from symmetry ; as when circles become almost square, 

 and crosses are inclined to the plane of polarization. And I believe 

 that any one who shall follow my investigation, and imitate my expe- 

 riments, will be surprised at their perfect agreement." 



4. Differential Equations of Elliptical Polarization. Although 

 circular and elliptical polarization can be clearly conceived, and their 

 existence, it would seem, irresistibly established by the phenomena, it 



Cainb. Trans, iv. p. 83, &c. " Camb. Trans, iv. p. 122. 



