Notes on some Points in the Theory of Light. 197 



advert to some former researches of my own, which have a 

 direct bearing on the question. 



The same day on which M. Cauchy's letter was read to 

 the French Academy, I had the honour of reading to the 

 Eoyal Irish Academy a Paper " On the Laws of Double 

 Eefraction in Quartz"* wherein I showed that everything 

 which we know respecting the action of that crystal upon 

 light is comprised mathematically in the following equations: 



(1) 



dt* " dz 



which differ from the common equations of vibratory motion 

 by the two additional terms containing third differential co- 

 efficients multiplied by the same constant (7, this constant 

 having opposite signs in the two equations. The quantities 

 % and r] are, at any time , the displacements parallel to the 

 axes of x and y, which are supposed to be the principal di- 

 rections in the plane of the wave, one of them being there- 

 fore perpendicular to the axis of the crystal. The constants 

 A and B are given by the expressions 



where a and b are the principal velocities of propagation, 

 ordinary and extraordinary, and i/< is the angle made by the 

 wave-normal (or the direction of z) with the axis of the crys- 

 tal. The only new constant introduced is (7, which, though 

 the peculiar phenomena of quartz depend entirely on its ex- 

 istence, is almost inconceivably small : its value is determined 

 in the Paper just referred to. The equations are there proved 

 to afford a strict geometrical representation of the facts; not 

 only connecting together all the laws discovered by the dis- 

 tinguished observers to whom M. Cauchy refers, and includ- 



* See Transactions, R. I. A., VOL. xvn. p. 461 (supra, p. 63). 



