182 
MR. W. M. HICKS OK THE STEADY MOTION - AHD 
a 2 U 
0 . =u-\-/3 cos v-\-y cos 2y+§ cos Sv 
zy 0 
*= -£(1 -B)x+±(l+ie)BJr*-^ B# 
y=h(\-W)x-± B 0 F-i B^+i Bjr* 
~B# 
477 1 
For the first approximation the lowest term in h in /3 must vanish. Hence 
x ~~i i=0 
Now 
P x „ A 1 P 1 
P — _ 1 A —I_3 
-° 0 — 2 -^ 0 ^ x 
and the lowest terms in B 2 are 
R 0 4 Bj 
P P 
P —3 A ±2_|_1A AO 
- D l““ 4-^-1 p W 2 A 0p 
K 1 -ty) 
Substituting the values of A 0 , &c., from (19) 
J_ p — .u-i_ A__3 ^ _ 1 UaL 
277^0“!^ 4L-1 * q LU 
Hence 
1 B 1 = A^(4*-l)f^ 
1 r* 
277 
'U- 
2 L&* 
161/ (iL-l)Zr* 
= {i(te-i)-ijA_}p 
03- 
4(L—2) 
■03 
_ 1 _ 1 
4 4 L—2 
= 0 
4 L—2 
03 = 
12L —1 
8 L—2 
(20) 
