Mr. MacCulIagh on the Laisos of Crystalline Rijlcjcion. 43 



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 aether in 

 tlifferent media, and the direction of the vibrations in polarized 

 light. In fact, a particular supposition respecting each of the 

 latter (juestions is included in my theory, the several prin- 

 ciples of which, making the single alteration that has been 

 mentioned, I shall here enumerate : 



1 . The density of the aether 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 ^t which 

 the plane of polarization of the reflected ray becomes inde- 

 pendent 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 existed some relation among the pressures. This 

 notion I had taken up from reading a little paper, by M. 

 Cauchy, in the Bulletin des Sciences Mathematiques for July 

 1830; and by combining such a relation with the three con- 

 ditions afforded by my own law of equivalent vibrations^ I 

 had actually obtained, for the polarizing angles in different 

 azimuths, a foruiula (that marked (5.) in my former paper,) 

 which I found to agree very well with Sir David Brewster's 

 experiments, and which M. Seebeck has found to agree still 

 better with his own. 



The formula for the polarizing angle is obtained by equa- 

 ting two values of the deviation ; and it is remarkable that the 

 very same formula comes out in my present theory, although 

 the values of the deviation are entirely different. Referring, 

 for brevity, to the notation* of my former paper, I find, for 

 the case of a uniaxal crystal, 



tan /3 = cos (2*4- 4>) tan 6, (at.) 



* Erratum in former paper, vol. viii. p. 106, line 2 from bottom, for 



-^ -|- read ~ B. 



G2 



