These values of p refer to a standard density of the air, of 534.22 grains per cubic foot, which is the density of dry air at sea-level in the latitude of Greenwich, at a temperature of 62° F. and a barometric height of 30 in.
But in consequence of the humidity of the climate of England it is better to suppose the air to be (on the average) two-thirds saturated with aqueous vapour, and then the standard temperature will be reduced to 60° F., so as to secure the same standard density; the density of the air being reduced perceptibly by the presence of the aqueous vapour.
It is further assumed, as the result of experiment, that the resistance is proportional to the density of the air; so that if the standard density changes from unity to any other relative density denoted by τ, then R = τd2p, and τ is called the coefficient of tenuity.
The factor τ 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 τ 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 κ, 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 κ = 0.975; on the other hand, for a flat-headed projectile, as required at proof-butts, κ = 1.8, say 2 on the average.
For spherical shot κ is not constant, and a separate ballistic table must be constructed; but κ 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 σ, 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, σ may increase as the gun wears out, after firing a number of rounds.
Collecting all the coefficients, τ, κ, σ, into one, we put