THE ROYAL ARTILLERY INSTITUTION. 
Therefore the angles which the normal to the driving-surface makes 
with the axes are given by 
x2 
k . COS 
cos A. =: — 
COS 
cos v — 
6 H 
4<z 2 (sin 8) 2 + k 2 
*- sin (£~ 8 ) 
a/4 z 2 (sin 8) 2 -f- k 2 
2z . sin 8 
a/4 z 2 (sin S) 2 + k 2 _ 
-( 9 ) 
16. Substituting in (2) and (3) the values given for a , /3, y , A, ji } v 
in (6) and (9), the equations of motion become 
nr d 2 Z 
M -w 
I=g-r[ 
2z sin 8 
y 4 z 2 (sin 8) 2 + k 2 a/4^ 2 + k 2 
d 2 (f> _ R . r 
k . sin 8 
W 
M . -f __ 
dt 2 p 2 (. y 4 z 2 (sin 8) 2 + k 2 a/40 2 + k 2 
and from (11), 
R = 
M.p< 
{ 
k . sin 8 
2/^0 
y 4 0 2 (sin 8) 2 + k 2 y\z 2 + k 2 
17. To determine —- 
From (4), 
} 
i}.< io > 
}; .(ii) 
d k± .( 12 ) 
dfi 
krd> = z 2 , 
■ hr d -i-2z - 
‘ ' k dt ' dt’ 
{'•S + -}‘ ■■ 
dt 2 kr 
and substituting this value of in (12), 
R = - 
dt 2 
2Mp 2 
kr 2 \ _ h • sin = _V 
a/ 40 2 (sin 8) 2 + /c 2 a/40 2 
i2 1 
+ * 2 ) 
{-S+-} 
or, for brevity, 
j ys +v *}’ 
d 2 z 
or, substituting the value of derived from (10), 
J ( Gr . z Rz / 2 z . sin 8 «-* \ ** 
( 13 ) 
