264 PROFESSOR POWELL'S REMARKS ON THE DISPERSION OF LIGHT. 



account, does not here depend on the arrangement of the molecules of ether in the 

 medium, but on the retardation of one of the vibrations behind the other, or the ab- 

 sence of it, originally impressed on the ray in the respective cases. 



These inferences appear of importance in connexion with the consideration of the 

 causes on which polarization depends, and the laws of elasticity of the ether in crys- 

 tallized bodies, as also the state of the ether at the bounding surfaces of media of 

 different density, and the changes which may be effected in the state of polarization 

 of a ray: and in what has here been laid down, I trust that the whole subject 

 (without entering into specific controversy) will be found relieved from some degree 

 of difficulty and objection. 



Note to Art. 6. 

 If in equation (5.) 6 = -g- (without supposing a = |8) the vibration resulting is still 



elliptical. In this case the expressions may be put into the form 



7} = ^ {cc sin (n t — kx)}'] 



^ ^^ } (52.) 



^ = 2 {|8 cos (w/- A: 07)} J ' ^ ^ 



This form is that adopted by Professor Maccullagh* to express the elliptical vi- 

 brations of the two rays in quartz, and by means of which he connects the laws of 

 M. Biot, and the theory of Mr. Airy, with certain differential equations of vibratory 

 motion, provided the quantities a, (5, w, and k, are so assumed as to fulfil these condi- 

 tions, viz. that if A and B be the squares of the velocities of the ordinary and extraordi- 

 nary rays in common double refraction, in quartz we replace them respectively by 



A-A;|-C andB-ArjC 



where C is a new constant determined from Bjot's observations. The differential 

 equations referred to are these : 



\ . (53.) 



dt^ — ^ dx''~' ^ da^. 



But on taking the partial differential coefficients of the expressions (52.) it is easily 

 seen (from the particular forms of those functions) that the equations (53.) are re- 

 ducible to, 



dt^ — l^ a; ^ L. J ^^2 



^^3 — [^ + ^ /3 ^ J dx^^ 



which are of the well-known form (§. 7.) for vibratory motion. 



* Memoirs of the Royal Irish Academy, 1836. 



