THE ROYAL ARTILLERY INSTITUTION. 
369 
Referring to Table 2, it appears that a charge of 7 lbs. gives an initial 
velocity of 1306 f.s., and a charge of 6*75 lbs. gives 1292 f.s. ; or 
4 oz. of powder additional gives an increment of 14 f.s. in velocity. 
By proportional parts, it follows that 2\ oz. of powder gives an in¬ 
crement of 8 f.s. in velocity, and therefore the charge of 6 lbs. 
12 oz.+ 2^ oz. — 6 lbs. 14£ oz. of powder gives an initial velocity of 
1292-+8 f.s. = 1300 f.s. Again, suppose it required to find what 
charge must be used to give an initial velocity of 1260 f.s. to a 250-lb. 
shot fired from a 9-inch gun. It appears that 36 lbs. of powder 
gives an initial velocity of 1257 f.s., and that an addition of 1 lb. to 
the charge gives an increment of 9 f.s. in the initial velocity, and 
therefore an addition of ^ of a lb. would give an increment of 3 f.s. 
in initial velocity. Hence, 36J lbs. of powder would give the re¬ 
quired initial velocity of 1257 + 3 = 1260 f.s. 
Further, when tables are prepared for three different weights of 
shot, as for the 3-inch gun, it is possible to calculate with great 
exactness the initial velocity which would be given to any interme¬ 
diate weight of shot by any given charge. Thus, a charge of 1 lb. 
8 oz. gives initial velocities of 1050, 1176, and 1394 f.s. to shot of 
12, 9, and 6 lbs. respectively. Here the differences are too large to 
allow proportional parts to be used. But by interpolation we find 
that the charge of 1 lb. 8 oz. would give initial velocities of 1050, 
1102, 1176, 1273, and 1394, to shot of 12, 10|, 9, 71, and 6 lbs. 
respectively. By a new interpolation we might find what velocities 
would be given to other intermediate weights of shot. For the 
larger guns it would be desirable to make experiments with four 
different weights of shot of the kind indicated. Thus, by a purely 
practical process, the law of initial velocity can be found, which 
may lead to some useful formulae. 
Calculation of Resistances. —The coefficients given in Table 1 may 
be used to calculate the resistance cf the air to spherical and 
elongated shot. If the Newtonian law be used, the resistance 
= 2c'v 2 w-+-g lbs.; or if the cubic law be used, the resistance = 2b'vhv-+-g 
lbs. In all cases 'w denotes the weight of the shot in lbs.; v the 
velocity of the shot in f.s.; d the diameter of the shot in inches; and 
g the ftnce of gravity =32T91. Suppose that the shot is spherical, 
and that d — 8 inches. In Table 1 we find opposite 1200 f.s. the 
value of 20Q0b / w-~-d 2 = +001534 ; and 2000c'w~~d 2 = T841. By the 
w _ *0001534 x 8 2 x (1200) 3 
cubic law, the resistance of the air = 26V 
9 
1000 x 32-191 
= 527 lbs. and by the Newtonian law the resistance 
2cV- = + 4 1 * 82 + 12 M 2 =527 lbs. 
9 
1000x 32*191 
And in precisely the same way, using the proper coefficients, we 
may calculate the resistance of the air to ogival-headed projectiles. 
In this manner Tables 3 and 4 have been calculated. As the re¬ 
sistance varies as the square of the diameter of the shot, the 
resistance of the air to a shot one inch in diameter has been given 
