[delta] represents the angle of the rifling; this factor may be ignored in
the subsequent calculations as small, less than 1%.

The mean effective pressure (M.E.P.) in tons per sq. in. is represented in
fig. 3 by the height AH, such that the rectangle AHKB is equal to the area
APDB; and the M.E.P. multiplied by 1/4[pi]d^2, the cross-section of the
bore in square inches, gives in tons the mean effective thrust of the
powder on the base of the shot; and multiplied again by l, the length in
inches of the travel AB of the shot up the bore, gives the work realized in
inch-tons; which work is thus equal to the M.E.P. multiplied by 1/4[pi]d^2l
= B - C, the volume in cubic inches of the rifled part AB of the bore, the
difference between B the total volume of the bore and C the volume of the
powder-chamber.

[Illustration: FIG. 5. Velocity Curves, from Chronoscope experiments in 6
inch gun of 100 calibres, with Cordite.]

Equating the muzzle-energy and the work in foot-tons

(2) E = w/2240 V^2/2g = {B - C} / 12 x M.E.P.

(3) M.E.P. = w/2240 V^2/2g 12/{B - C}

Working this out for the 6-in. gun of the range table, taking L = 216 in.,
we find B - C = 6100 cub. in., and the M.E.P. is about 6.4 tons per sq. in.

But the maximum pressure may exceed the mean in the ratio of 2 or 3 to 1,
as shown in fig. 4, representing graphically the result of Sir Andrew
Noble's experiments with a 6-in. gun, capable of being lengthened to 100
calibres or 50 ft. (_Proc. R.S._, June 1894).

On the assumption of uniform pressure up the bore, practically realizable
in a Zalinski pneumatic dynamite gun, the pressure-curve would be the
straight line HK of fig. 3 parallel to AM; the energy-curve AQE would be
another straight line through A; the velocity-curve AvV, of which the
ordinate v is as the square root of the energy, would be a parabola; and
the acceleration of the shot being constant, the time-curve AtT will also
be a similar parabola.

If the pressure falls off uniformly, so that the pressure-curve is a
straight line PDF sloping downwards and cutting AM in F, then the
energy-curve will be a parabola curving downwards, and the velocity-curve
can be represented by an ellipse, or circle with centre F and radius FA;
while the time-curve will be a sinusoid.

But if the pressure-curve is a straight line F'CP sloping upwards, cutting
AM behind A in F', the energy-curve will be a parabola curving upwards, and
the velocity-curve a hype