THU ROYAL ARTILLERY INSTITUTION. 
159 
two targets, over which the shot must pass. The angle A! therefore denotes 
the time occupied by the falling of the weight, plus the time occupied by the 
projectile in passing from the first target to the second. Therefore the 
difference between these angles, or {A!—A), corresponds to the time 
occupied by the projectile, in passing through the space included between 
the two targets. 
This angle is converted into time, by employing a table, giving the times 
corresponding to the arcs passed through by the pendulum. 
Calculation of the Table of Times, 
16. This calculation is founded upon the duration of one very small 
oscillation of the pendulum. To obtain this datum, the whole oscillating 
system is suspended upon a support, Fig. 8. The pendulum is then made to 
Fig. 8. 
V i 
oscillate, and the time observed by a chronometer; this time divided by 
the number of oscillations, gives the time of one small oscillation of the 
pendulum. When this is known, it is easy to compute the time employed 
by the pendulum in describing any part of an oscillation. For (Fig. 9) 
calling l } the length of a pendulum beating the 
time t, of one very small oscillation; v the velocity 
of the centre of oscillation of the pendulum, or, 
the velocity of the point m 9 situated at a distance 
l , from the axis of suspension after a vertical 
descent h\ x, the angle, variable with the point 
m; T, the time that the point m would take to 
move through a circumference whose radius is l , 
with a uniform velocity v. 
Then v = f %gh, 
17. By the common equation of the pendulum, 
i-y, 
where t is the time of one small oscillation. But, 
v = s/ 2gh t 
[VOL. III.] 
Fig. 9. 
