70 
MINUTES OF PROCEEDINGS OF 
The first condition— i.e., the muzzle velocity—depends mainly on the 
relative charge of powder to the weight of the projectile— i.e., the 
greater the charge, the higher the muzzle velocity. 
The second— i.e., the rate of diminution of the velocity of the pro¬ 
jectile caused by the resistance of the air—is proportional to the square 
of the diameter of the projectile divided by its weight; thus depending 
mainly on the relative size of the bore to the weight of the projectile. 
Let us now consider the case of a shell projected vertically upwards 
at a low velocity. For all practical purposes it may be treated as under 
the influence of gravity alone, where the force of gravity is equal to 
32*2 lbs. acting vertically downwards. The tendency of this force is 
continually to diminish the upward velocity of the shell, till at the end 
of a certain time it reaches its highest point, remains motionless, and 
then commences to descend. The force of gravity now increases the 
velocity of the shell, so that it reaches the ground again with exactly 
the same velocity with which it was projected. The times of ascent 
and descent are also equal. For instance, suppose a shell projected 
vertically upwards with a velocity of 32*2 f.s.; it would ascend for 
1 second to a height of 16*1 ft., then it would commence falling, and 
ultimately arrive at the point of projection with the same velocity it 
started with, in another interval of 1 second—the total time of ascent 
and descent being 2 seconds. 
This, in other words, is called the “ time of flight,” and is directly 
proportional to the upward velocity of projection— i.e., the time of 
flight is longer, the greater the upward velocity of projection. 
When a shell is projected out of a gun at an angle of elevation, its 
motion may be considered as compounded of two motions—one in a 
vertical direction, the other in a horizontal direction. The motion in a 
vertical direction determines the time of flight; the motion in a hori¬ 
zontal direction, the range or distance travelled over during that time. 
Now, suppose a shell is fired out of a gun at a low elevation, so as 
to have a velocity of 32*2 f.s. in a vertical direction, and a velocity 
of 1300 f.s. in a horizontal direction; it will have a time of flight of 
2 seconds, exactly as in the former case, and it will arrive at the highest 
point of the trajectory (viz., 16*1 ft.) in 1 second. Now, this “time of 
flight” is the time the projectile has to get over the ground, and 
since it is travelling at the rate of 1300 ft. per second, it would range, 
if there were no resistance from the air, 2 x 1300 = 2600 ft., or 866 yds. 
But practically every projectile experiences more or less the resistance 
of the air, which tends continually to reduce its velocity; and it is just 
the question of the amount of this resistance which affects the “ flatness 
of trajectory.” 
Suppose now that, owing to the resistance of the air, the muzzle 
velocity of 1300 f.s. were reduced to 1100 f.s. at the end of 2 seconds; 
then the range would be only 791 yds., and the highest point of the 
trajectory would be, as in the former instance, 16*1 ft. Again, suppose 
the muzzle velocity of 1300 f.s. were reduced to 1000 f.s. at the end of 
2 seconds; the range would be still less—viz., 745 yds.—and the highest 
point of the trajectory would be, as in the previous cases, 16*1 ft. 
Now, what I want to show is this—viz., that for a given time of flight. 
