122 
DR. G. R. GOLDSBROUGH ON THE INFLUENCE OF 
Ha = 2 
"V ^^/x 
cos ( 
[p — A) 
1 Tr/il 
1 8 sill 2 1 
[p— a) 
i —j u 
T = J cos ( 
M ' A M l 8 sin 2 
- r - 7 - r sin \jj. — A 6i t u ' 5 
/n v1 ' J 
f COS (/x—A) irjn • i ,. \ 0 / 1 
-—r-7--r—-sin U —A) 2 t r/n f > 
U sill 2 (/x-A) it In v 7 7 J 
j, - ' .... V J_ '■ 
M [4 sin" (/x —a) 7 rjn 
■P' _ y 
A , M 
f 3 cos (/x —A) tt/w \ 
1.8 sin 2 (/x—A) 7 r/nl 
= i ~ 4 ~r ' ~r +2sin (^~ x ) 2 ™a4’ 
M [ 8 sin \/ul — A) -/a } 
r'os l ii — A1 27 tI n, i • 
N . ( cos (/x — 
a) 2 ~/n 
;Y sill" (/U —A) 27 rjn 
7 M 1 8 sin 3 (m 
1 
•S’ 
i 
sin 5 (ju — \)-jr/n 
g; 
H' a 
j;,a 
These equations may be written, with a slq 
0 from those formerly obtaining, in the form, 
J 
f COS (fjL 
-A) 
i 2 
’7 t/ti db sm" (/x — A 
) 2 t r/ll 
M [8 sin 3 ( 
— 
A) 
l tt/u sin 5 ( 
M a) 
irfn 
..1 
(3 
■ of the quantit 
p"\ — 2/fCr' A + {0 lir COS V(f>} + 
r 
r <p} 
ft i o > 
(T aT 6Kp 
r 2 G M \pn + <r A 2 { 0 2 , T sin r< 
lx r 
+ hTJ Fi a o> = 20 3 , r cos r<p, 
M r 
2 K p\ + p K 3Z { 0 4 , r sin r<{>} +r2G' N ^ + cr A 2 { 0 5>r cos r<j>} 
r fx r 
+ /c 2 2 = 20 e , r sin 
/x r 
8 
We shall determine the particular integral arising from one term of the right-hand 
member of the first equation, writing it typically |- 0 3 , m e tm< h 
Assume that 
px = Ke lm \ 
and 
o-a — N A e 
for all values of A. 
Equations (33) then become 
— m~Ax + 2miA A + A a *t2/c (i?tiX a 4-XT)T' A a 2 |0], r cos 
+ /c 2 2 A m Ct m , a + X A 2 {0 2 r sin r^>| + /c"2X M J^, A = ^0 3 , m , 
—m 2 X A + 2imX\ + X" A + 2/r (mA A + A' a ) + A a 2 {0 4 , r sin r<J>} 
T /c 2 2A^Gy, A -j- X A 2 {0 5 r cos T<p } + v2 X M J 7 m A = 0. 
(34) 
There are n pairs of equations in this form corresponding to the n values of A. 
