210 
MINUTES OP PROCEEDINGS OE 
or, putting, aN = x, NS — y, aM = X, MU — Y and retaining the same 
notation as before in other respects, 
X(W + Q + q) = aW+ acosa.Q, \ ^ 
Y(W+ Q + q) = rq +yW+ RQ. J 
Determining the values of X and J", and substituting the previously 
ascertained values of x and y of Equations II., we have 
l = a cos a ^ 1 — 
r= R + (R - r) 
/ + q 
W+ Q + qJ 
(P' — P) cot (j ). cot a — (p + q) 
TV+Q + q 
.IV. 
These last formulae will then answer for the determination of the centre of 
gravity of a gun and carriage limbered up. To determine that of a gun 
unlimbered, which is of importance in questions of the effect of firing on 
gun carriages. In such case r = 0, and q = 0, and the whole reasoning 
is equally applicable. Eor a gun unlimbered then 
X = a cos a 
JY+ Qj’ 
r=p + p 
(P'— P) cot (f) . cot a — P 
tr+Q 
v. 
To try these formulae practically I had a platform erected at an inclined 
plane, the vertical height ML being 51"'25 and the horizontal extent NL 
being 123"*5, or at an angle with the horizon of 22°. 32'. 14 /7 *7 or 0. In the 
first experiment I ran a Bengal 9-pr. gun of 10 cwt. on its carriage* and 
unlimbered, trail end upwards, up the inclined plane, so that both trail and 
wheels rested on the platform; the wheels being duly chocked with wedges. 
I had the beam of a large balance rigged up with one end immediately over 
the trail and connected the end of the beam to the trail handles by the 
scale chains; and ran the scale-board itself between the chains, so as not to 
alter the equipoise. When all was ready, I gradually added weights until 
the trail just lifted off the platform and no higher. I then took a note of 
the weight. The gun was next run down on to level ground, and the end 
of the trail placed in the centre of one scale-board, and weights gradually 
added until there was equilibrium. To ensure accuracy I had square holes 
dug under the scale-boards so that the upper surface of the scale-board was 
on the same level as the ground on which the wheels stood. I then again 
noted the weights in the scale. I proceeded in the like manner with the 
24-pr. howitzer 10 cwt.* 
* The 9-pr. and 24-pr. elevating screws were run down as far as they would go, giving re¬ 
spectively angles of 12°. 9' and 13°. 33 7 . 
