d the chamber capacity C = 13.25 x 55.01 = 730 cub. in.,
equivalent to 25.8 in. or 2.15 ft. length of bore, now called the
equivalent length of the chamber (E.L.C.).

If the shot was not free to move, the closed chamber pressure due to the
explosion of the charge at this G.D. (= 0.5) would be nearly 49 tons per
sq. in., much too great to be safe.

But the shot advances during the combustion of the cordite, and the chief
problem in interior ballistics is to adjust the G.D. of the charge to the
weight of the shot so that the advance of the shot during the combustion of
the charge should prevent the maximum pressure from exceeding a safe limit,
as shown by the maximum ordinate of the pressure curve CPD in fig. 3.

Suppose this limit is fixed at 16 tons per sq. in., corresponding in Table
1. to a G.D., 0.2; the powder-gas will now occupy a volume b = 3/2 x C =
1825 cub. in., corresponding to an advance of the shot 3/2 x 2.15 = 3.225
ft.

Assuming an average pressure of 8 tons per sq. in., the shot will have
acquired energy 8 x 1/4[pi]d^2 x 3.225 = 730 foot-tons, and a velocity
about v = 1020 f/s, so that the time over the 3.225 ft. at an average
velocity 510 f/s is about 0.0063 sec.

Comparing this time with the experimental value of the time occupied by the
cordite in burning, a start is made for a fresh estimate and a closer
approximation.

Assuming, however, that the agreement is close enough for practical
requirement, the combustion of the cordite may be considered complete at
this stage P, and in the subsequent expansion it is assumed that the gas
obeys an adiabatic law in which the pressure varies inversely as some
m^{th} power of the volume.

The work done in expanding to infinity from p tons per sq. in. [v.03
p.0278] at volume b cub. in. is then pb/(m - 1) inch-tons, or to any volume
B cub. in. is

(9) pb/{m - 1}[1 - (b/B)^{m-1}]

It is found experimentally that m = 1.2 is a good average value to take for
cordite; so now supposing the combustion of the charge of the 6-in. is
complete in 0.0063 sec., when p = 16 tons per sq. in., b = 1825 cub. in.,
and that the gas expands adiabatically up to the muzzle, where

(10) B/b = (216 + 25.8)/(2.5 x 25.8) = 3.75

we find the work realized by expansion is 2826 foot-tons, sufficient to
increase the velocity from 1020 to 2250 f/s at the muzzle.

This muzzle velocity is about 5% greater than the 2150 f/s of the range
table, so on these considerations we