THE ROYAL ARTILLERY INSTITUTION. 
77 
the greatest absolute height of trajectory is the same, whatever the 
range may be; so that if the time of flight is correctly observed, the 
absolute height of trajectory is also known, whatever the range may be. 
Thus, multiply the square of the time of flight in seconds by 4; it will 
give the greatest height of trajectory. For example, suppose the times of 
flight of shells fired out of different guns were observed to be 3*0 seconds 
and 3*3 seconds respectively— 
4 x (3 f 0) 3 = 4 x 9 = 36 ft. would be height of the one trajectory, 
4 x (3*3) 3 = 4 x 10*9 = 43*6 ft. » n the other. 
Elevating a gun means giving the shell time to range in. By 
increasing the elevation of a gun, the time of flight—or the time for 
the shell to range in—is increased. 
From what has been advanced, it will be seen that if two guns are 
fired at the same elevation (say 2°), and have the same muzzle velocity , 
the time of flight of their shells will be the same, and the greatest 
absolute height of their respective trajectories will be the same. Also, 
if the shells have the same weight, and the same form and sectional 
area, their trajectories themselves will be the same, because they will 
each lose velocity at the same rate; but if one of the shells differ, either 
in weight, or form, or sectional area, the height of the trajectory will 
still be the same, yet the trajectories themselves will not be the same, 
because one shell will lose velocity faster than the other, and will con¬ 
sequently range shorter. And here I must give a technical definition 
of “flatness of trajectory.” 
Fig. 2. 
/ 
D D 
Let us consider the trajectories ADB and AD'B' representing the 
case of two shells fired out of different guns with the same elevation 
and the same muzzle velocity, but subject to a different retardation from 
the resistance of the air—so that, having the same time to travel in, one 
arrives at B } and the other at B '. Now, suppose that each of the shells 
has an upward vertical velocity of 32*2 f.s.; then CD — C'B' = 16*1 ft. 
— i.e., the height of the two trajectories ADB, AD' B' is the same. The 
relative flatness of the trajectory ADB is estimated by the ratio of the 
greatest height of the trajectory (CD) to the range AB, which varies as 
