36 Mr. Mac Cullagh on the Laws of 



formula was compared with the experiments of Sir David Brewster* on the 

 polarising angles of Iceland spar, the accordance was so satisfactory, as to leave 

 no doubt upon my mind that I had arrived at the true formula for these angles ; 

 and though the truth of the conclusion did not allow me to argue that the 

 premises 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 whilef 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 Association J in Dublin, in August, 1835; and the leading 

 steps and results were afterwards published in a letter to Sir David Brewster.§ 



Now we are to observe, that when common light is polarised by reflexion 

 at the surface of a doubly refracting crystal, the plane of polarisation 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 polarising angle. This formula, as we have seen, was correct ; 

 but it happened, singularly enough, that the expressions for the deviation, which 



* Phii. Trans. 1819, p. 150. 



t 1 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 hypotheses 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 S for the angle which the emergent 

 transversal makes with the plane of incidence, I found, for determining 9, an equation of the form 



A + Btan5 + Ctan'9=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 some- 

 where ; 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 Jirst 

 surface, when the crystal is in contact with a medium of nearly equal refractive power. 



X London and Edinburgh Philosophical Magazine, vol. vii. p. 295. 



§ Ibid. vol. viii. p. 103; February, 1836. 



