188 
MINUTES OF PROCEEDINGS OF 
would be more sensible from the diminished mass of the body it acted upon. 
For a slight increase of length in the cylindrical part of a shot there is but 
a very slight increase ot the resistance of the air. 
Having determined the law of variation of the velocity of a cannon ball 
moving through the air, there remains the scarcely less important problem 
to find according to what law the velocity is communicated to the shot inside 
the bore of the gun by the action of the gas of the exploding powder. The 
solution of this problem will shew how the work is distributed inside the gun, 
and consequently the amount of stress upon the gun corresponding to any 
position of the shot, for a given quality and 'weight of powder. If one 
powder exploded more suddenly and completely than another, and if the weight 
of the charges were so adjusted as to give the same velocity when the shot 
leaves the gun; although the total work done would be the same, the law of 
distribution of the work would be very different in the two cases. The 
rapidly exploding powder would give a high initial pressure upon the ball, 
which would decrease rapidly as the ball moved, and become less towards the 
muzzle than that arising from the explosion of a slowly burning powder. The 
former would therefore be a more severe trial of the gun than the latter, 
although the same velocity of the ball would be obtained in the two cases. 
If powder could be manufactured and fired so as to keep up a constant 
pressure upon the ball from one end of the bore to the other, in such a case 
a given velocity would be obtained with the least possible strain upon the 
gun. The introduction of rifled ordnance has rendered the degree of 
rapidity of the explosion of powder a question of greater importance than 
it was when smooth bores only were used; for the effect of rifling must be 
to hinder the forward motion of the ball at the first, and consequently to 
increase the initial strain on the gun. The increasing spiral groove is therefore 
a great improvement on the uniform spiral; its form ought to be such as to 
give equal additions to the angular velocity of the shot in equal times, not 
in equal spaces. Consequently, as the velocity of translation of a shot 
depends upon the nature of the powder, the weight of the charge, and the 
weight of the ball, a change in any one of these would, in strictness, call 
for a different kind of rifling. But probably great nicety is not required, 
provided the twist is small at the bottom of the bore, and that it increases 
gradually up to such an angle at the muzzle as is required to give steadiness 
to the shot. The angular velocity necessary to give the requisite steadiness 
to shot of various lengths and calibres requires careful experimental treat¬ 
ment, because we do not know theoretically the exact forces which act upon 
the projectile. 
The common formula for initial velocity is built upon the assumptions-— 
(1) That all the powder is converted into gas before the ball moves 
sensibly. 
(2) That the pressure of the gas afterwards always varies as its density. 
If these assumptions were true, it would not matter what air space was 
left between the powder and ball, or what was the number of shot put into 
the gun. For a given space occupied by the gas there could only be one 
