le* Professor Powell on certain points 



This constitutes elliptically polarized light: if a = /3, it is cir- 

 cularly polarized. 



The retardation b is constant for the whole ray ; and if we 

 suppose that for all the ellipses the values of « and of /3 re- 

 spectively are equal, these quantities will become constant co- 

 efficients in the summation, and we may write 



2 a = A « 2 /3 = A /3 (8.) 



And the formulas (6.) will become 



rj = a 2 (sin [n t—kx)) ,„ v 



^ = ^'%{sm{nt-kx-h)). ^^'^ 



(4.) In order to obtain the equations which express the 

 motions of a system of molecules, connected by their attractive 

 and repulsive forces so as to form an elastic medium, (which is 

 the idea originally pursued by M. Navier and since by M. 

 Cauchy and others,) I will suppose the same method followed 

 as in all these investigations, and which it will not be neces- 

 sary here to repeat; these equations in their general form will 

 be found in several papers in this Journal, as in my abstract 

 of M. Cauchy* (though in a different form) ; in Mr. Tovey's 

 paperf ; or again in my paper in the Phil, Trans, 1838, part ii. 

 eq. (13,), and in Mr. Kelland's memoir, Camb. Trans., vol. vi. 

 p. 158. 



When we adopt the supposition of the ray coinciding with 

 a,', as above, the equations in question are 



'^ =7;i2[<^(r)A>, + ^I/(7-)A2/(A^Ar, + A.. A^)] (10.) 



^ = mX [<^(r)A?+'vI/(r)A;s(A.^A? + Aj/A,)], (n.) 



where vi is the unit of force, r the distance from the molecule 

 first agitated, A j/ A s the differences of coordinates of the 

 molecules from the first, A tj A ^ the corresponding differ- 

 ences of the displacements. 



It is also material to observe, that these equations have been 

 obtained isoithout any iiarticular supposition being made as to 

 the arrangement of the molecules in space : they consequently 

 apply ifiQe imagine the molecules distributed in the most irre- 

 gular or nnsymmetrical manner. 



(5.) If we consider the two component displacements rj ^ 

 which enter the above equation as I'elated in the way ex- 

 pressed by the formula (6.), 



>) = S [a sin {7it — kx)'\ 



? = 2 [|3sin {nt-kx-b)'] 

 (in which, if « /3 and b are assumed as before explained, we 



* L. & E. Phil. Mag. and Journal of Science, vol. vi. No. 31, p. 25. 

 t Ibid, vol, viii. No. 43, 



