THE ROYAL ARTILLERY INSTITUTION. 
415 
And substituting these values of ( & c * in (8), we have for the direction 
cosines at the point P } 
k cos 
cos X = — 
COS [A = ■ 
cos V = —■ 
(• 
\kr n) 
V 4 *+ (“;)* 
Jc sin (— - 
\kr n) 
,(23) 
aA + ^T 
And putting the values of a, ft y, X, p, v in the equations of motion (2) 
and (3), we have 
i aA + ( s! %)j 
dt 2 ' 
(24) 
d 2 (f> _ Hr 
It 2 = Mp* 
f tm (p~0 ‘‘■■‘■g l . 
1aA + h)' vrp ‘ 
r 
— , sin — 
k 2 kr 
[a, cos k s 
kr 
n/1 + k 2 
in fe~3 
aA + ( sin 0 
1 jtp 
7 * 77 
# sm - 
IaA+H) 
2 
./*! 
} Vi + f 
(25) 
Hence 
A = - 
if.p 2 
& sin - 
1 _ __ 
IV^B/ ' /1+ "J 
