Reflexion and Refraction. 93 



were true, yet the presumption in their favour was very strong, 

 insomuch that, upon remarking, as I did soon after, that the 

 law of vis viva harmonized with my other hypotheses, I did not 

 think it worth while* to try what would be the consequence of 

 using this law, instead of the relation which I had put in its 

 place. In this state of my theory, I gave an account of it at 

 the meeting of the British Associationf in Dublin, in August, 

 1835 ; and the leading steps and results were afterwards pub- 

 lished in a letter to Sir David Brewster.J 



Now we are to observe, that when common light is polarized 

 by reflexion at the surface of a doubly-refracting crystal, the 

 polarization does not, in general, coincide with the plane of 

 reflexion, as in the case of ordinary media, but is inclined 

 to it at a certain angle, which may be called the deviation; and 

 it was by equating two values of the deviation that I obtained 

 the formula above mentioned for the polarizing angle. This 

 formula, as we have seen, was correct ; but it happened, singu- 

 larly enough, that the expressions for the deviation, which were 



* I had, besides, an objection to the law of vis viva, on the ground that it would 

 give an equation of the second degree ; and I wished to have all my equations 

 linear, lest, in the seemingly complicated question of crystalline reflexion, they 

 should give two answers when the nature of the question required but one. This 

 has actually happened, since the present Paper was read, in applying my hypothe- 

 ses to the case of internal reflexion at the second surface of a uniaxal crystal. 

 Supposing an ordinary ray to emerge after double reflexion, and putting for the 

 angle which the emergent transversal makes with the plane of incidence, I found, 

 for determining 0, an equation of the form 



A + B tan + G tan 2 = 0, 



wherein A is very small, but does not vanish ; so that the equation gives two roots, 

 one very small, the other about the proper value. It is clear, therefore, that there 

 is a want of adjustment somewhere : but I am now inclined to think that the fault 

 is not in the principle of vis viva. Possibly our laws of the propagation of light in 

 doubly refracting media are not quite accurate. "Whatever supplementary law 

 shall be found to remedy this untoward result will probably, at the same time, 

 account for the extraordinary phenomena observed by Brewster, in reflexion at 

 the first surface when the crystal is in contact with a medium of nearly equal 

 refractive power. 



t London and Edinburgh Philosophical Magazine, Vol. vn. p. 295. 

 Ibid., Vol. vni. p. 103; February, 1836. (Supra, p. 75.) 



