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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 .1 

 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 V, which is a function of the second degree, is supposed 

 to contain only the squares and products of the derivatives 

 X, Y, Z, X-i, Yz, Z z , Xt, &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, YI, Z^ X 3 , Y 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 



