t if the standard density
changes from unity to any other relative density denoted by [tau], then R =
[tau]d^2p, and [tau] is called the _coefficient of tenuity_.

The factor [tau] becomes of importance in long range high angle fire, where
the shot reaches the higher attenuated strata of the atmosphere; on the
other hand, we must take [tau] about 800 in a calculation of shooting under
water.

The resistance of the air is reduced considerably in modern projectiles by
giving them a greater length and a sharper point, and by the omission of
projecting studs, a factor [kappa], called the _coefficient of shape_,
being introduced to allow for this change.

For a projectile in which the ogival head is struck with a radius of 2
diameters, Bashforth puts [kappa] = 0.975; on the other hand, for a
flat-headed projectile, as required at proof-butts, [kappa] = 1.8, say 2 on
the average.

For spherical shot [kappa] is not constant, and a separate ballistic table
must be constructed; but [kappa] may be taken as 1.7 on the average.

Lastly, to allow for the superior centering of the shot obtainable with the
breech-loading system, Bashforth introduces a factor [sigma], called the
_coefficient of steadiness_.

This steadiness may vary during the flight of the projectile, as the shot
may be unsteady for some distance after leaving the muzzle, afterwards
steadying down, like a spinning-top. Again, [sigma] may increase as the gun
wears out, after firing a number of rounds.

Collecting all the coefficients, [tau], [kappa], [sigma], into one, we put

(1) R = nd^2p = nd^2f(v), where
(2) n = [kappa] [sigma] [tau],

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 horizontall