PRINCIPLES OF GUNNERY. 
43 
where C is a coefficient varying in different guns, which may be deter¬ 
mined by experiment. 
But this formula is not strictly correct, for three reasons 
(1) On account of the difference between the sectional areas of 
the projectile and of the bore of the gun when there is windage . 
(2) On account of the uncertainty of the amount of momentum 
communicated to the gun by the motion of the centre of gravity of the 
powder charge. 
(3) On account of the small additional momentum communicated to 
the gun after the projectile has left the muzzle. 
Since the sectional areas of the bore and projectile are as the squares 
of their diameters, if d be the diameter of the projectile and I) that 
D 2 
of the bore, the momentum communicated to the gun will be wvy 
and if the small additional momentum communicated to the gun and 
carriage after the projectile has left the muzzle be expressed by W"V, 
and if Cw'v be the amount of momentum communicated to the gun 
and carriage by the motion of the centre of gravity of the powder 
charge, then 
W"V" = Dh + Oto'v + W"V .(2) 
It is the uncertainty of these terms that makes the measurement of ^un pen- 
muzzle velocities by means of the gun pendulum so inaccurate; but 
the instrument is well adapted to measure the velocity of recoil. 
The gun pendulum consists of a frame in which a light gun is 
suspended by means of a rod. The pendulum, of which the gun forms 
the bob is capable of moving freely when the gun is fired. An arc 
graduated in degrees and minutes is attached to the frame, by means 
of which the angle of recoil is registered. 
Great care is necessary, in adjusting the weights, to get the centre of 
percussion very nearly in the axis of the bore.* 
Some experiments with a gun pendulum were made at the Royal Experi- 
Laboratory, Woolwich, in 1874, to determine the recoil of the Martini- Scoii„° n 
Henry and Snider rifles. The rifles were alternately fixed in the 
pendulum with their barrels horizontal and weighted up to the same 
weight, and so adjusted that the centre of percussion was very nearly 
in the axis of their barrels. They were fired by means of a hair 
trigger, so as to avoid communicating any sensible motion to the pen¬ 
dulum in firing. The angle of recoil was then read off, and the mean 
angle of five rounds recorded, and the work done on the pendulum by 
the discharge of the rifle computed, and thence the work done in 
recoil. (See the following table.) 
* See Boxer’s “ Treatise on Artillery,” p. 36, 
