226 A. E. H. LOVE AND F. B. PIDDUCK ON LAGRANGE’S BALLISTIC PROBLEM. 
since P(1 — C/4M) is the mean pressure in the first gun. Hence we find that the relation 
of the ballistic constants in the two guns is 
w 
W 
c 
12M’ 
C_ 
6 M' 
The first two equations give the projectile and the size of cordite to be used in the ideal 
calculation, the third equation the ratio in which the calculated maximum pressure is 
to be increased. The theory would be seriously invalidated if the ratio of the pressures 
recorded by crusher gauges in the breech and in the base of the projectile is not approxi¬ 
mately 1+C/2M, and does not apply to extraordinary experiments with very quick 
combustion (for which the pressure ratio is, of course, nearly 1). 
From a few calculations I have made with full charges in guns, it appears that the 
empirical rule of adding one-half of the mass of the propellant to the mass of the projec¬ 
tile, without other change of ballistic constant, gives approximately correct pressures, 
while muzzle velocities are about Id per cent. low. The fraction one-third gives approxi¬ 
mately correct muzzle velocities, but maximum pressures about 4 per cent. low. 
An important factor in the future progress of internal ballistics would seem to be 
the determination of the rate of regression of colloidal propellants as a function of both 
temperature and pressure. Hitherto only the latter has been taken into account, 
although some experiments of Wolff* show a falling off of the rate for small charges 
in a very small closed vessel, which appears to be due to loss of temperature. The effect 
would be enhanced in a gun, where the whole mass of gas is cooled by expansion, instead 
of being cooled relatively strongly near the surface. One consequence of diminished 
burning would be the occurrence of unconsumed cordite at velocities higher than those 
which Sebert and Hugoniot’s formula would give 'with a burning constant derived 
from experiments in closed vessels. 
* W. Wolff, ‘ Kriegstechnisdie Zeitsckr.,’ vol. 6, p. 1, 1903. 
B R! TIS H 
MUSEUM 
25 MAR 22 
NATURAL 
HISTORY. 
