166 Professor Powell on certain points 



r+ sin 6 5; [/3j9' sin2^]"| 

 1 -cos6X[/3p' 2sin2^] Vsm^nt-kx) 

 ^f _ ,„ J - 2 [«? 2sin2^]J 



— cos 6 2 [|8p' sin 2^] >cos {nt—kx). 

 L- sin 6 2 [/3/ 2sin2^]J 



On comparing these expressions with those for the same 

 finictions (H.) (15.), which must be identical, and equating 

 the respective coefficients of sin [nt—k x) and of cos (nt — kx), 

 since they must hold good for all values of those terms, we 

 have the following equations: 



{+ sin 6 2 [^g sin 2 6] 

 - cos 6 2 [13 q 2sin2^] (21.) 



— 2 [«;^ 2sin-^] 



{— 2 [up sin 2^] 



- cos 6 2 [/3 ^ sin 2 6] (22.) 



— sin 6 2 [/3 q 2 sin^ ^] 



{+ sin Z» 2 [/3/ sin 2^] 

 — cos 6 2 [/3 y 2 sin-^] (23.) 



— 2 [a g- 2 sin- 6] 



{— 2 [a ? sin 2 6] 



- cos 6 2 [13 p' sin 2 6] (24..) 



- sin 6 2 [/3p' 2 sin^^] 

 From the two last forms (23.) (24.), by multiplication and ad- 

 dition, we obtain 



f- 2[/3/2sin2^] 



-«2 2 /3 = ;«<^ - cos 6 2 [« y 2 sin^^] (25.) 



[_ — sin 6 2 [ix. q sin- 0] 



In the case of elliptic polarization from the conditions be- 

 fore stated (7, 8, 9), we can obtain from the forms (21.) and 

 (25.), 



^^ 2 [;/ 2 sin^ 6] 



h (a^ + /32) < -\- oL^ 2 [2^ 2 sin^^] (26.) 



L +2 cos 6 a/3 2 [? 2sin2^] 



Also the form (24.) gives, on transposing, 



_ m [g 2 {q sin 2 ^) + /3 cos h 2 (^ sin 2 ^)] 



«"- A ^-m /3 2 (y 2 sin^ 6'] (27.) 



Upon the whole, then, we see that the formula (9.) for el- 



liptically polarized light, involving the above value of ?<, is the 



solution of the differential equations (10.) (11.) for the motion 



of a system of molecules constituted as at first supposed. 



