348 Rotation of the Plane of Polarization of Light. 



Appendix, by Alfeed Lodge, M.A., Coopers Hilly Staines. 

 The value of 



r" An 



\ sin^ddt, where ^=Ae-'"'sin nt, and C= . =, 

 Jo v/m^ + n^ 



For 



I sm2 6'^^=it (l-cos26')^f 



The general term of this series is 



— I e-^'^P* dw^P nt dt, 



\^ Jo 



and can be integrated by successive reduction. 

 Let U2p denote 



j: 



e-'^mpt ^'m'^p nt dt \ 

 then, integrating by parts, 

 U2p = — o • sin^^ wH +1 ~ . 2wp sin^P- ' nt . cos ri/J dt 



= + — » e-'^"'P* sin^P-' w« . cos nt dt ; 

 »Uo 



and again integrating by parts, 



^ g — 2mpt 



.sin^P"' nt . cos 71^ 



Jo 



m 2mp 



+ -C ^~ ""^ ((22? - 1) sin^^- 2 w^ cos^ w^ - sin^^ nt').n. dt 



m }^ 2mp ■' 



n^ f " 

 '^^ 2^ I ^"""^'((2jo-l)sin2p-2w«-2p.sin2/'n^)c/« 



_n^ 2p — 1 n^ 



TO^ 2j9 - m^ ^ 



