PRINCIPLES OP GUNNERY. 
245 
By substituting the mean value of K in the above table corresponding 
to the mean velocity in equation (5), the remaining velocity, v, 
u 
may be approximated to; but in order to get accurate results it would 
be necessary to change the value of K continually, to correspond to the 
continual change of velocity owing to the resistance of the air, which 
would be a laborious calculation. 
In order to obviate this, Mr. Bashforth has tabulated the values of Table con. 
d* (\ 1\ (1000)% ... , SaSe 
— «? = ( — r T ^ — for all values of K corresponding to velocities and veio- 
W \V V / A city. 
from 1700 f.s. to 500 f.s. In the absence of exact experiments for 
velocities below 900 f.s., it has been assumed that the coefficient K 
remains constant and equal to its value at 900 f.s., and that the cubic 
law holds good below 900 f.s. (Vide Table I., Distance and Velocity, 
p. 250.) 
It has been stated that the rate at which a projectile loses velocity Thepow&? 
owing to the resistance of the air equals pSf&ctiie 
in motion 
has of 
maintain¬ 
ing its 
velocity; 
x d l ( v V. 
w \ 1000 / 5 
[vide equation (2)] ; but as K is a coefficient depending only on the 
form an*d velocity of the projectile, it follows for similarly shaped pro¬ 
jectiles fired from guns of different calibres and moving with the same 
alterations of velocity, that 
the rate of loss of velocity varies simply as 
w 
or, inverting and putting it into other words, 
tlie power which a projectile has of maintaining its velocity 
weight of projectile 
varies as ^ or - r -—, 
a A square ot its diameter 
or the power of a projectile to maintain its velocity varies directly as 
its weight, and inversely as the square of its diameter. 
With similarly shaped elongated projectiles the weight varies nearly 
as dH, where l is the length of the projectile; consequently 
power of the projectile oc a —^ a l; 
or the power of the projectile varies as its length. 
Thus the longer the projectile {cmteris Paribas') the harder will it hit 
at any given range, and the greater will be its absolute range for any 
given muzzle velocity ; but practical considerations limit the length of 
a projectile to about 3 calibres. 
If elongated projectiles of similar shape were made the same length 
in calibres , it follows from what has been stated above* that 
the power of the projectile varies as the calibre of the gun. 
31 
