(1) R = nd2p = nd2f(v), where
(2) n = κ σ τ,
and n is called the coefficient of reduction.
By means of a well-chosen value of n, determined by a few experiments, it is possible, pending further experiment, with the most recent design, to utilize Bashforth's experimental results carried out with old-fashioned projectiles fired from muzzle-loading guns. For instance, n = 0.8 or even less is considered a good average for the modern rifle bullet.
Starting with the experimental values of p, for a standard projectile, fired under standard conditions in air of standard density, we proceed to the construction of the ballistic table. We first determine the time t in seconds required for the velocity of a shot, d inches in diameter and weighing w lb, to fall from any initial velocity V(f/s) to any final velocity v(f/s). The shot is supposed to move horizontally, and the curving effect of gravity is ignored.
If Δt seconds is the time during which the resistance of the air, R lb, causes the velocity of the shot to fall Δv (f/s), so that the velocity drops from v+½Δv to v-½Δv in passing through the mean velocity v, then
(3) RΔt = loss of momentum in second-pounds,
= w(v+½Δv)/g - w(v-½Δv)/g = wΔv/g
so that with the value of R in (1),
(4) Δt = wΔv/nd2pg.