274 Drs. Bedell and Crehore on the 



cosfl= . R ' . . . (4) 



\A' 2+ ((i- L '<») 2 



sin<?= Lc ° . . . (5) 



V R/2+ (cfe- L '")- 



Substituting in (1) and (2) these values, and similar values 

 for I 1? cos U sin 6 X ; and I 2? cos 2 , sin 6 2) &c. ; we have 



I,»cos0 W ^ E /fi 



= 2 7-= ^ = A. (6) 



E 



R,2+ (ci- L/w ) 2 R2+ ((i,- Lw J 



1 -T.- 1- LW 



T m sin 9 _ (J'© _ ^ Oca 



E "» , +(^- L '-y~ R2+ (i- L<B ) 2 



= 2 C 2 RV + (l-CL & ,y <B = B(0 - • <- 7) 



The letters A and B are introduced to simplify the results. 

 Dividing (7) by (6), 



tan0=^. ...... (8) 



Comparing (4) and (6), we obtain 



A cos 2 cos 2 



A= ~BT' ° r R "A~ (J) 



Comparing (5) and (7), we obtain 



-r sin2 # l t/ s iu 2 /1/v , 



For cos 2 # and sin 2 6 we may substitute the values 

 1 1 A 2 



cos 



2 (9= 



1+ tan 2 BV ~ A 2 + B 2 



+ A 2 



. 2 . 1 1 B 2 



sir 



l+cot 2 A 2 ~A 3 + BV 



BW 



