AND ITS APPLICATION TO MR. B. TOWER’S EXPERIMENTS. 
199 
Multiplying equation (51) by sin 0 and integrating 
f 01 /sin Odd /sin 20, cos <£ n n . \ _ /sin 30, sin 2<£ n . „ . ^ , 
•J e Ko =B^- \ ---#! COS fa)~ B fa - ~s - - sm °1 sm 200 
[sin (271 + 1)0! sin 2 nfa sin (2 n— 1 )6 X sin 2 nfa 
~ 3 "[ 2 n +1 2ti — 1 
. -n [ sin (2% + 2)0 1 cos (2ti + 1)0 O sin 2n0 1 cos (2%— 1)0'. . 
+ Bo, i + 1 j 9 /m _L 9 9/m f • • • ( 64 ) 
2%-+ 2 
Integrating equation (51) 
— ( l yr^=2B o 0 1 —2B X sin sin 0 o -f- yy- 3 sin 20 : cos 2</> 0 
- ft. R r * 
2 B„ 
2n 
2B 
sin 2wd x cos 2 n<j> 0 
_ ir+i sin ( 2re + 1 )^ l s: » (-'•■+ l ) r k 
(65) 
Substituting from equations (61)—(65) in the equations of equilibrium (44), (45), 
(46), there results— 
From (44) 
0 = 2(K 1 cA 0 +K 3 B 0 ) sin 6 X — 2K 1 cA 0 d 1 cos 9 X 
+ (KjcAi-KgB!) sin fa— (KjcAjH-K gBj)^ sin fa 
+ &c. 
^— , /KjcAgB \ sin (271 — 1)0, cos 2 ?i0 o 
H"2,»=l 1 ( o.. H"-^-2 44 2« 
+ 
2n 
R-] cA 
2n 
^i®^2»+i 
271+1 " 
I\ rA 
271+1 
KoBo ?i 
271-1 
sin (271 + l)0j cos 2710 o 
2ti+ 1 
\ sin 2 ti0j sin (2 ti + 1)0 O 
l * h 
- K Am-1/ 2n 
I 
■K.,B. 
2 XJ 2>‘ +1 
sin (2 ti + l)0 a sin (2 ti + 1)0 O 
2?i + 2 
From (45) 
|=(K 1 cA 1 -K s B 1 )(^-0 1 ) cos 
+ Cr{(K l0 A.+KA.) 
+(K 1 cA 2 „ +1 K 2 B 2m+1 ) 
sin (2 ti + 1)0 1 sin (2?i — 1)^ 
2n-f 1 2ii — l 
sin(27i+2)0 1 sin 2 ti0 1 
271 + 2 2n 
sin 2 nfa 
cos (2 l)fa 
( 66 ) 
( 67 ) 
