84 On the Laws of Crystalline Reflexion. 



person, although the want of a solution has long been felt. The 

 difficulties which we have to deal with, in entering upon this 

 problem, are not mere mathematical difficulties, but difficulties 

 arising from the want of first principles; and, in physical 

 questions of this kind, where we must, at the outset, have re- 

 course to conjecture, in order to supply the very principles of 

 our reasoning, it can hardly be expected that the whole truth 

 should be divined at once. I think, however, that I have now 

 obtained a true mechanical theory; and if so, it will help to 

 decide, not only the question immediately before us, but also 

 the other much-disputed, though more elementary, questions 

 concerning the density of the ether in different media, and 

 the direction of the vibrations in polarized light. In fact, a 

 particular supposition respecting each of the latter questions 

 is included in my theory, the several principles of which, 

 making the single alteration that has been mentioned, I shall 

 here enumerate : 



1. The density of the ether is the same in all media. 



2. The vibrations of plane-polarized light are parallel to the 

 plane of polarization. 



3. The vis viva is preserved. 



4. The vibrations are equivalent at the common surface of 

 two media. 



To these may be added the definition of the polarizing 

 angle of a crystal ; namely, the angle of incidence at which 

 the plane of polarization of the reflected ray becomes indepen- 

 dent of the plane of polarization of the incident ray. At the 

 polarizing angle, the former plane does not, in general, coincide 

 with the plane of reflexion, but makes with it a small angle 

 which may be called the deviation. 



It is curious that, about a year and a half ago, I employed 

 these four principles, precisely as I have now enumerated them, 

 in deducing Fresnel's well-known laws of reflexion for ordinary 

 media ; but I did not then apply the law of vis viva to crystals, 

 because my mind was preoccupied by the notion that there ex- 

 isted some relation among the pressures. This notion I had 



