368 
MINUTES OP PROCEEDINGS OF 
from experiments made with a 40-pr. gun, that the coefficient did 
not sensibly differ for a hemispheroidal-head (prolate) and for 
ogival-heads struck with radii of one and of two diameters. 1 
When the resistance of the air is expressed by the help of a 
variable coefficient of some power of the velocity, it is a mere ques¬ 
tion of convenience what power shall be used. In the reports on 
experiments made with my chronograph the retarding effect of the 
air was expressed by 2 b'v 3 , where v is the velocity of the shot, and b' 
a varying coefficient. The cubic law has been preferred, because of 
the simplicity of the formulae to which that law gives rise, for cal¬ 
culating the velocity and time of flight. The tables of the values 
of the coefficient b' were arranged to give 2000 b'w~d 2 , because 
that quantity is independent of w 9 the weight in lbs. of the projectile, 
and of d its diameter in inches. The values of this quantity have 
been found for all velocities ranging from 900 to 1700 f.s., for 
elongated shot, and from 850 to 2150 f.s. for spherical shot. The 
following tables of remaining velocities, &c., have in each case been 
carried to the limits for which the values of V have been experi¬ 
mentally determined. It is not likely that the extremely high ex¬ 
perimental velocities, which were obtained by using high charges 
and hollow shot, will be employed in practice, while velocities below 
900 f.s. are not of great importance. 
Tables of Initial Velocity .—The experiments made with the 3, 5, 7, 
and 9-inch guns were carried out with a view to determine the 
resistance of the air, and for this purpose great care was taken to 
secure accuracy in weight and in diameter of projectile. As there 
was considerable variation in the weights of charges and of shot 
employed, the opportunity was taken to deduce systematic tables of 
initial velocities of the shot used, for all practical charges within 
the limits of our experiments. But inasmuch as the lengths of the 
experimental guns followed no particular law depending upon their 
calibres, and it is probable that the amount of windage varied ac¬ 
cording to the age and wear of the several guns used, the results 
cannot be expected to agree when different guns are compared. 
The initial velocities of the 3-inch gun appear to fall much below 
the average. The tables of initial velocities here reprinted may be 
looked upon as examples of the purely practical manner in which 
the subject of initial velocities should be treated when the service 
guns, and the kind of powder to be used, have been finally decided 
upon. It has been the custom to carry out costly experiments 
merely to determine isolated initial velocities, but here we have 
determined the law of initial velocity for each particular gun with 
great accuracy, and at the same time have secured other most im¬ 
portant results from our experiments. The following will suffice as 
examples of the practical use of these tables. Suppose that it was 
required to find the charge which must be used to give an initial 
velocity 1300 f.s., to a 5-inch elongated shot weighing 47*68 lbs. 
1 Reports. &c. pp. 10-17 ; and Phil. Trans. 1868, p. 417. 
