486 HISTORY OF OPTICS. 



of these suppositions, he not only was enabled to 

 account for the simple phenomena of single plates 

 of quartz; but for many most complex and intricate 

 appearances 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 sym- 

 metry; 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 accounting for the continued dilata- 

 tion of circles, and the general representation of 

 the form 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 experiments, will be surprized at their perfect 

 agreement." 



4. Differential Equations of Elliptical Polariza- 

 tion. Although circular and elliptical polarization 

 can be clearly conceived, and their existence, it 

 would seem, irresistibly established by the pheno- 

 mena, it is extremely difficult to conceive any 

 arrangement of the particles of bodies by which 

 such motions can mechanically be produced; and 

 this difficulty is the greater, because some fluids 

 and some gases impress a circular polarization upon 



11 Camb. Trans, iv. p. 122. 



