THE ROYAL ARTILLERY INSTITUTION. 
415 
The moment, therefore, about OF due to the friction at 1 
= (y — b) xAx. 
But 
7 . a — b 
h + ®. —— =y> 
y — b = x . 
a — b 
Therefore the moment of T about OF 
[iTF (a — b) 
x 2 Ax; 
and in the limit. 
lb n 
= 
Therefore the whole moment due to FE 
__ fxW {a — b) S' 2 f from x — o 
“ bln J x X * \ to x — n 
— [iW (a b) 
- m • 
Similarly, the whole moment due to FE 
and the whole moment about an axis intersecting, and at right angles to, the 
axis of the axletree-arm, is equal to the sum of these moments. Calling the 
whole moment %” we have 
Remembering that b = a — v - -, we eliminate £ in this equation; and 
L 
then substituting for n and {l — n) their respective values already found, 
« _ pWl (a — c\ 
~ 6 \a + c)' 
But if the angle of the hollow of the arm—its inclination to the hori¬ 
zontal plane—be called “ a” then {a — c) = l tan a; also, calling “ h ” the 
mean height of the wheel, {a + c) = h. 
The whole moment, therefore, about an axis intersecting, and at right 
angles to, the axis of the axletree-arm, is equal to 
/L lW l 3 tan a # 
IT ’ It ’ 
l being the breadth of the tire. 
