70 
MINUTES OF PROCEEDINGS OF 
Then considering the motion to be horizontal, the range being x 3 and 
the time t, we shall have 
dv 
dt 
but v = ^; therefore ^ =-— f 1 + - ) , 
dt dx 2c V rj* 
or 
dx = — 2c 
Then integrating, we shall have 
x = 2c log 
This equation, the result of the Trench experiments at Metz, contains 
all the data necessary for computing the velocity of shot at different distances, 
the angle of elevation being small. 
r — a constant=1427 ft. 
V r = initial velocity, 
V = velocity at the range x 3 
c = a ballistic coefficient different for all natures of projectiles. This 
coefficient is given by tables computed for the purpose, and depends upon 
the diameter, form, and weight of the projectile. 
* This equation may he put under the following form:- 
V' 
(1 + Z) 
v r t r 
x is the distance, measured on the prolongation of the axis of the lore , hut with small angles of 
elevation this distance may practically be said to equal the range. 
The correction for this would bring the equation to this form, 
V' 
V= m 
^ j F'cosft j ffc V'c 
$ being the angle of projection above the horizontal plane, 
0 the inclination of the trajectory at the point x, where the velocity is V\ 
2C = —- , in which P = weight of shot, and g = gravity, the others as before. 
ATtK z g 
