120 
MINUTES OF PROCEEDINGS OF 
it only remains so to alter the coefficient *0005137, that the error 
arising from neglecting this variation may be as small as possible. 
12 . According to Regnault, the weight of a cubic foot of dry air at a 
temperature of 32° Fahrenheit, and under a barometric pressure of 30 
inches, is = 566*56 grains ; and according to the same author the 
coefficient of the expansion of the air for an increase in temperature 
of 1 ° is = *002036. Hence if S be the weight in grains of a cubic foot 
of dry air at any temperature t , and pressure n, 
^ _ n 566*56 
S “ 30 ’ 1 + *002036 (t° — 32°) 
but (see Miller’s Hydrostatics, p. 28)— 
weight of moist air at any temperature and pressure T 
weight of dry air at same temperature and pressure — * ^ ^ IT 
where T = tension of the aqueous vapour. Hence the density of the 
air under any circumstances will be found from the following equation : 
(l _ °-37S^) 568-56 
B0 ’ 1 + -002036 (<° - 32°).. 
and if we assume as the English standard of comparison the weight of 
a cubic foot of air at a temperature of 60°, under a barometric pressure 
of 30 inches, and if we further assume the humidity = 0*5, from (3) 
we find S = 534*3 grains, and equation (2) becomes— 
p = -0005213 n E 2 v 1 (l + 53 J 3 .(4) 
8 
and under ordinary circumstances the fraction gg ' .pg may be taken as 
equal to unity. 
13. The above formula (4) applies to spherical projectiles ; in the case 
of the Armstrong projectiles, the resistance of the air is represented by 
= *0003475 R 2 v 2 
f ^ _ v \ 8 
l 1 + 1426-4/ 534-3. 
The velocity v at a point midway between the screens having been 
determined by observation, the initial velocity Y is deduced from it by 
the equation— 
where r = 1426*4, x == distance, on the axis of the gun produced, of 
w 
the point corresponding to v, c = ^ — , w being the weight of the 
projectile in lbs., g the acceleration of gravity, and ??, in the case of 
spherical projectiles, — *0005213 it R 2 , in the case of Armstrong pro¬ 
jectiles — *0003475 % R 2 . 
14. Discussion of the Results. The experiments numbered I. to 
XXIII. relate solely to the determination of the initial velocity of service 
projectiles fired from service guns with service charges. The detailed 
results of the practice furnished in extenso give every particular with 
regard to it, and the following table gives an abstract of the general 
results. 
