CAPTAIN NOBLE AND MR. F. A. ABEL ON FIRED GUNPOWDER. 
113 
We have not space within the limits of our paper to enter upon a discussion of the 
methods of calculation and correction necessary to arrive at the results tabulated ; they 
are attended with very great labour, and a full consideration of the question would 
necessitate a separate paper. As we shall hereafter show, it is not difficult, if we were 
to suppose the powder entirely converted into gas on the instant of explosion, to lay 
down the law according to which the pressure would vary in the bore of the gun ; but 
the case under consideration is a much more complicated one. The charge of powder 
is not instantly exploded, but is generally ignited at a single point; the pressure (com- 
mencing at zero) goes on increasing at an extremely rapid rate until the maximum 
increment is reached. It still goes on increasing, but at a rate becoming gradually 
slower, until the maximum tension is reached, when the increase of density of the gas, 
aided by the combustion of the powder, is just counterbalanced by the decrease of 
density due to the motion of the projectile. After the maximum of tension is reached, 
the pressure decreases, at first rapidly, subsequently slower and slower. 
If these variations in pressure be represented by a curve, it would commence at the 
origin convex to the axis of x, would then become concave, then again convex, and 
would finally be asymptotic to the axis of x. 
In the same way, the curve representing the velocity would commence by being 
convex to the axis of abscissse ; it would then become concave, and, were the bore 
long enough, would be finally asymptotic to a line parallel to the axis of x. 
The results of Table X. are graphically represented in black lines in Plate 19, the 
space described by the shot being taken as the equicrescent or independent variable, 
and the two curves giving respectively the velocity and pressure at any point of the 
bore. 
From the Table (or curves) it will be seen that the maximum pressure attained by 
the powder is 18 tons per square inch (2745 atmospheres), and that this pressure is 
reached when the projectile has moved '5 feet (T53 metre) and at '00437 second from 
the commencement of motion. 
The results given in the Table have, as we have said, been arrived at by special 
methods of correction and interpolation ; and their general correctness can be tested by 
examining whether a material alteration of pressure or velocity at any point can be 
made without seriously disturbing the times actually observed. It will be found that 
they cannot. But another question here presents itself for consideration. We have, in 
the curves on Plate 19, taken s as the independent variable ; but if t were taken as the 
independent variable, and the relation between s and t were capable of being expressed 
by the explicit function the velocity corresponding to any value of t would be 
represented by the first derived function of f(t), and the pressure by the second derived 
function. This, then, if a simple relation between s and t could be established, would 
be an easy method of treating the problem ; but it has appeared to us practically im- 
possible to obtain a single expression which shall represent the relation between s and 
t for the whole time occupied by the shot in its passage through the bore. 
MDCCCLXXV. Q 
