Notes on some Points in the Theory of Light. 



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: 



^?_ % A _ c^ 



df ~ dz* ~ dz 3 ' 



which differ from the common equations of vibratory motion 

 by the two additional terms containing third differential co- 

 efficients multiplied by the same constant C, this constant 

 having opposite signs in the two equations. The quantities 

 and >j are, at any time tf, 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 



A = a\ B = cf- (a 2 - 2 ) sin 2 !//, 



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 C, 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. xvu. p. 461 (supra, p. 63). 



