646 
Proceedings of the Royal Society 
Angle of elevation, 
Initial velocity, 
Time of ascent, 
Rise, 
Time of descent, 
Horizontal range, 
Final velocity, 
Angle of incidence, 
20°"27 / . 
1745*5 feet per sec. 
12*5 sec. 
3208 feet. 
15*6 sec. 
23420 feet. 
622 feet per sec. 
39°-19'. 
If the same ball be shot from the same gun, but at another inclina- 
tion, the shape of the path is changed and the details thereof must 
be sought for in another table. We search among the various 
tables for that one in which the given initial velocity is found op- 
posite the proposed angle of elevation ; if the tables be constructed 
for values of V sufficiently close, we shall find this either directly 
or by an easy interpolation ; and then, proceeding as above, we can 
get all the desired information. 
Similarly, if the initial velocity and the horizontal range be given, 
we convert these into the corresponding tabular numbers, and search 
among the various tables for that one in which these two are found 
together; the angle of inclination, the time of flight, and all the 
other qusesita of the problem are then to hand. 
It has been stated that three data suffice to determine the path. 
When the terminal velocity is one of these, the solution is obtained 
by simple inspection ; but when that velocity is one of the qusesita, 
the operation becomes indirect. 
Suppose that the velocity communicated to a given shot by a 
specific charge of gunpowder has been ascertained, say, by help of the 
ballistic pendulum, we may discover the terminal velocity of that 
shot by observing the angle of elevation and the horizontal range. 
For this purpose we assume some terminal velocity, thence compute 
the corresponding tabular initial velocity, and thereby obtain the 
corresponding horizontal range. If this come out too much, we 
must reduce the assumed terminal velocity, and continue our trials 
until the computed agree with the measured distance. If the time 
of flight have also been carefully noted, we get a corroboration of 
the accuracy of the result. 
Hot only so, we may dispense altogether with the ballistic pen- 
