188 
therefore 
therefore 
MR. W. M. HICKS OK THE STEADY MOTION AND 
^-B 2 — V ‘ 3*2 (16a? 1) k 
=^( 2 a:+l)F 
k~‘ 
9 Z-—i 
)^|_ t 
7—l^o 16- L—2 
2L-1 
Q f ‘iXr, 1 
L —2 
+i(2x 0 +l) V& 
= K+f+iir L _ 2 
i_ 121^-15, 
^— i6 x, —2 ^ 
Hence, substituting their values for a, (3, y 
U= 
, k 1 1 L + 5 7 , k 2 
^L—2 I L—2^ * L—2 M C0S 
+ {( 2te 0 -i|^2 ¥ cos2v )l? 
2 ^0 
a 2 
+ 
24r n _ 12L-15. 
‘TT> Xj_2 k cos'^v 
MU, 
k \L —2 
— 2 cos 2u 
The condition that the coefficient of cos 2a vanishes gives 
or since 
M 
therefore 
or 
Also, since fi=0, 
Therefore 
2Uo _i Ho l,i 12L—15 2* 0 
k 4 a 2 & 2 ( L-2)J“ t ' 16 ' L —2 a 2 
k - 1 2 a|t 0 
U ° 4 L—-2 a 2 
, Mr 2 , 12L-15 
4 L —2 ^ L —2 * 
M=-i(12L-15)F 
6 x 0 =0 
U = 
i- L — 2 8 L—2^ j 
=;£Ui-i(L+5)F} 
4:7rak 
Hence, 
(1.) The velocity of translation remains unaltered to this order. 
(2.) The form of the hollow is given by 
k=&{1— 1(12L-15)Fcos 2u} 
(3.) The surface velocity is 
4:7rak 
{l_i(L+5)P} 
