370 
MINUTES OF PROCEEDINGS OF 
with great exactness to facilitate the calculation of resistances of 
the air to other shot besides those specified in the tables. For a 
velocity of 1200 f.s. the resistance of the air to a round shot one 
inch in diameter = 8*2335 lbs., and therefore the resistance to a 
round shot 8 inches in diameter = 8*2335 x 8 2 = 526*944 lbs. = 527 
lbs. nearly, as before and as in Table 3. This method can be 
usefully employed for diameters not given in the table (as for a 
round shot 7*5 inches in diameter), moving with a velocity of 1450 
f.s. specified in the tables. The required resistance = 13*0393 x (7*5) 2 
= 733*455 lbs. Suppose, in the next place, that we have the given 
diameter specified in the table, but not the velocity, we may then 
proceed by proportional parts. Thus, suppose the projectile of the 
ogival form 9 inches in diameter, moving with a velocity 1320 f.s. 
The resistance to an elongated shot 9 inches in diameter, for a 
velocity 1300 f.s. is 596 lbs., and for a velocity of 1350 f.s. it is 659 
lbs., showing an increment of 63 lbs. in the resistance, correspond¬ 
ing to an increment of 50 f.s. in the velocity, or there would be an 
increment of 25*2 lbs. in the resistance, corresponding to an incre¬ 
ment of 20 f.s. in the velocity. Hence the resistance to the ogival¬ 
headed 9-inch shot moving with a velocity 1320 f.s., would be 
= 596 + 25*2 lbs. = 621*2 lbs. Lastly, if neither the diameter nor 
the velocity be specified in the table, find first by proportional parts 
the resistance of the air to the motion of a similarly-formed shot 
one inch in diameter moving with the given velocity, and then 
multiply this by the square of the diameter given, and the result 
will be the required resistance. 
Calculation of Remaining Velocities .—The simple formulae of the 
cubic law of resistance, previously referred to, are the following. Let 
v and v denote the velocities of a shot at two points of its course s 
feet apart, and t the time in which this space is described under the 
action of a retarding force 25' x (vel 3 ) acting in a direction opposed to 
the motion of the shot, then 
1000 
V 
1000 H 
V 
2000 b's 
• 
* 
• 
(1-) 
and 
1000 t= 
1000s 
V 
1000 b's 2 
• 
• 
« 
(2-) 
When the above formulae were used to calculate the following tables 
for intervals of 100 feet, s was replaced by n x 100 feet, so that 
1000 _ 1000 200,000 b'n (3), where n was made equal to 1, 2, 3, 
&c., in succession, and thus the values of v were found for intervals 
of 100 feet. The value of V requires to be varied to suit approxi¬ 
mately the value of v. The values of V used for elongated shot were 
those given in Table 1 for velocities 1700, 1650, 1600, 1550, 1500 
f.s., &c., and they were changed when v was nearly equal to 1675,1625, 
1575, 1525 f.s. &c. Thus making v = 1700 f.s., w= 700 lbs., and cl— 
11*52 inches; for v=1700 f.s. we find by Table 1, 20005' = *0000839 
x d 2 -+-w = *00001591, and for 1650 we also find 20005'= *0000854 
