114 
DR. G. R. GOLDSBROUGH OX THE INFLUENCE OF 
Terms involving argument 0 2 2)) : 
K r (i cos 2t 
« 2 , 2 » = 
05, 0 — A 
2 ’ 
^2, 2)! 
«-n 2 sin 2r 
3 ( ^ ^'1.005. u) 
A?. •>.„ — 
(0 5 , o -9n 2 ) X 0 sin (3n0-r ) 
9n*—a lt0 Q 6t0 
v 3*-nX 0 cos (3 rub — r) , (0= 0 + n 2 ) «-^X 0 sin 2 t sin (nd> — r) 
x - = 8(9 )4 *-«,.„e s , u ) + - ' 2 (e,„-„>)(, l <-a I .Aj 
Terms involving argument 0 4 r , where r is not n nor 2n: 
C 4 , r = 0, a 4 ,r = 0, 
A„w 2 /c (n — r) sin {(n —r) 0 — rj 
A 4 , 
X 4 „. = 
A 
. 0 7/ 2 /C 1 
[w + f) 
1 sin {( 
(n + r) 0 t} 
r i 
(2n + r) 
1 {« 
1,00.5,0 
-n 2 ( 
n + r) 2 } 
+ ■ 
A„n 2 {I 
[w + r] 
> 2 
—aj.ol cos {(n + r)0 —r} 
2/0 
(2n + r) 
» {«i, 005,0— n 2{ 
[n + r] 
> 2 } 
2 r (2n—r) {a^Q-.^-ri 2 {n-rf} 
Terms involving argument 0 4 „ : 
c 4 ,« = 0, a 4i „ = 0, 
3 («i, 0 
A n (An 2 
05,0 — 
0+ o) 
4n 4 ) 
1 cos 
? 
( 271 (f) — t) 
6 1 
(«1,O0 
5, 0 1 
^} 
) 
A n COS T 
20 , 
5, 0 
Terms involving argument 0 4 2 „: 
nr cos 2 t 
a 
C, a„ = 
4,2rt , . 2 5 ^4,2)1 
05,0-W 
nA sin 2 t 
(«l,O0.5,O-« 4 )’ 
A 4 ,o 
2r 
3rnA 0 sm (3 n <p — t) 
8 («i, o 0o,o-9« 4 ) 
v _ (9n 2 — a h0 ) A 0 cos (3n0 —t) , A n cos 2t cos (n0 —t) 
X j, v,/ — :" . /’ .. 7\ 
16Ko0 5 ,o- 9<) ' 2(0 5 , o -n 2 ) 
( r 0.o + ^ 2 ) sin 2 tA„ sin (n<f> — t) 
4 («i, o 05,o-^ 4 ) 
+ 
Terms involving argument 0 SiW when r is not n nor 2n: 
C-o,r = 0, + v , = 0, 
^ _ X„nA (n + r ) sin {(n + r) 0 — t \ _ X 0 nA (n—r) sin {{n—r) 0 —t} 
r (2 n + r) {«i tO 0. %o — w 2 (n + r) 2 } r (2n—r) {«i, o 0 5 ,o—^ 2 (n—r) 2 }’ 
X 0 n 2 {i 
(n + ry 
®l,o) 
• cos { 
(n + r) d> — r | 
2/- (2n + r 
) {«i,o< 
A,o — n 2 1 
(n + 'r) 
» 2 } 
X 0 n 2 {. 
(n—r) : 
0+0J 
■ cos {( 
1 
■o 
10- 
-t} 
2r (2n—r 
) {«l.u< 
A,o— w 
2 I 
(n—r) 
> 2 ] 
> 
