THE ROYAL ARTILLERY INSTITUTION. 
367 
TABLES OF 
REMAINING VELOCITY, TIME OF FLIGHT, AND 
ENERGY OF VARIOUS PROJECTILES, 
CALCULATED FROM THE RESULTS OF EXPERIMENTS MADE WITH 
THE BASHFORTH CHRONOGRAPH, 1 1865-1870: 
BY 
The Rev. F. BASHFORTH, B.D. 
PROFESSOR OF APPLIED MATHEMATICS TO THE ADVANCED CLASS, ROYAL ARTILLERY. 
Although the amount of the resistance of the air to the motion 
of spherical and elongated projectiles has at length been satisfactorily 
determined for ballistic purposes for all practical velocities above 
800 or 900 f.s., it unfortunately happens that no simple law can be 
found to express the resistance of the air to the motion of a pro¬ 
jectile in terms of the velocity of that projectile. For ogival-headed 
elongated shot, the resistance of the air may be considered to vary 
roughly as the sixth power of the velocity for velocities 900-1100 f.s.; 
to vary as the third power for velocities 1100-1350 f.s.; and to vary 
as the second power for velocities above 1350 f.s.; which last is the 
Newtonian law of resistance, and is based on the supposition that 
the shot is at every moment penetrating an undisturbed medium ,, 
which supposition only holds for velocities higher than the velocity 
of sound. 
Under these circumstances the resistance of the air to the motion 
of projectiles has been expressed by the help of a variable coefficient, 
which depends (1) upon the form of the projectile and (2) upon the 
velocity with which it moves. Table 1 gives the values of the 
variable coefficients for velocities of 900 f.s. and upwards, for both 
spherical and ogival-headed elongated projectiles for both the cubic 
and Newtonian laws of resistance. 2 As the coefficients given for 
elongated shot were derived from experiments made with muzzle¬ 
loading guns, in calculating resistances, no further allowance will be 
necessary on account of the studs of shot. Also it appears that the 
coefficients derived from experiments with ogival-heads struck with 
radii of one and a half diameter, may be used without much error 
for all ogival-heads of practical utility, and for other approximate 
forms, differing only in a more or less pointed apex, for it was found 
1 For a description of the Basliforth Chronograph, see Vol. V. p. 161. 
2 Reports on Experiments made with the Bashforth Chronograph, pp. 114 and 152. 
49 
