only
for provisional extrapolation at high or low velocity, pending further
experiment.

The foundation of our knowledge of the resistance of the air, as employed
in the construction of ballistic tables, is the series of experiments
carried out between 1864 and 1880 by the Rev. F. Bashforth, B.D. (_Report
on the Experiments made with the Bashforth Chronograph_, &c., 1865-1870;
_Final Report_, &c., 1878-1880; _The Bashforth Chronograph_, Cambridge,
1890). According to these experiments, the resistance of the air can be
represented by no simple algebraical law over a large range of velocity.
Abandoning therefore all a priori theoretical assumption, Bashforth set to
work to measure experimentally the velocity of shot and the resistance of
the air by means of equidistant electric screens furnished with vertical
threads or wire, and by a chronograph which measured the instants of time
at which the screens were cut by a shot flying nearly horizontally.
Formulae of the calculus of finite differences enable us from the
chronograph records to infer the velocity and retardation of the shot, and
thence the resistance of the air.

As a first result of experiment it was found that the resistance of similar
shot was proportional, at the same velocity, to the surface or cross
section, or square of the diameter. The resistance R can thus be divided
into two factors, one of which is d^2, where d denotes the diameter of the
shot in inches, and the other factor is denoted by p, where p is the
resistance in pounds at the same velocity to a similar 1-in. projectile;
thus R = d^2p, and the value of p, for velocity ranging from 1600 to 2150
ft. per second (f/s) is given in the second column of the extract from the
abridged ballistic table below.

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 62deg 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 60deg 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 tha