XX. ON THE LAW OF DOUBLE REFRACTION. 



[From the Philosophical Magazine, VOL. xxi., 1842]. 



HAVING mentioned, in an article * which I sent a few days ago 

 for insertion in the Philosophical Magazine, that I had been led, 

 in following out an hypothesis, to a law of double refraction 

 more general than that of Fresnel, I think it may be well to 

 state very briefly the nature of that law, and to point out the 

 difference between it and the law of Fresnel, especially as I 

 have since observed that the difference is one of a very extra- 

 ordinary kind, and one which, if it has a real existence (a 

 question which experiment only can decide), may serve to 

 account for phenomena that have seemed hitherto inexpli- 

 cable. 



I have said, in the article referred to, that when the poten- 

 tial Y, which is a function of the second degree, is supposed 

 to contain only the squares and products of the derivatives 

 X, Y 9 Z, X. z , Y 2 , Z^ 3T 4 , &c., we get the law of Fresnel, as well 

 as the law of crystalline dispersion ; but if we make the more 

 general, and apparently the more natural supposition, that it 

 contains also the squares and products of the alternate deriv- 

 atives Xi, Fi, Zi, X 9 , F 3 , Z 3 , &c., then we get, of course, a dif- 

 ferent law. Now I find that there will still be two optic axes 

 for each colour, and that the two directions of vibration in a 

 given wave-plane will have the same relation to them as be- 



* " On the Dispersion of the Optic Axes, and of the Axes of Elasticity, in Biaxal 

 Crystals" (supra, p. 221). 



Q2 



