THE EOYAL ARTILLERY INSTITUTION. 
163 
Before the discovery of electro-magnetism, the ballistic pendulum of 
Robins and Hutton afforded the only known practical means for determining 
the velocities of projectiles and the resistance to their motion exerted by the 
air. This instrument is so well known that there is no necessity for entering 
into a minute description of all its parts, and of the precautions to be taken 
in the use of it. The shot is fired into a body at rest much heavier than 
itself, to which it communicates motion, so that the two move on together * 
with a common velocity which is capable of being measured. Towards the 
end of the last century numerous experiments were made with the ballistic 
pendulum, by Hutton, 1 2 at Woolwich, with 1, 3, and 6 lbs. spherical balls. 
Their velocities were measured at distances varying from 30 to 430 feet from 
the gun. Experiments were also made at Metz with the ballistic pendulum 
in 1839, &c. with balls of about 8, 12, and 24 lbs. 3 It was found that 
at 15m. (49 ft.) from the muzzle, the blast from the gun was very sensible. 
The velocities of the shot were determined at 15, 40, 65, and 90 metres 
(49, 148, 197, 295 ft.) from the gun. Beyond 295 feet the gun was not 
sufficiently accurate. Thus the law of the resistance of the air, deduced 
from the later and more careful experiments, depends upon the loss of 
velocity of spherical balls moving, at most, through 246 feet. But it is 
possible to make only one observation on each round. Therefore if it be 
desired to find the velocity lost by a ball in moving from 15 to 90 metres from 
the gun, one shot must be fired at the pendulum at a distance of 15 metres, 
and another at a distance of 90 metres; and, besides the errors in the mea¬ 
surement of the velocities at the moment of impact, there will be a doubt 
whether the velocity of the second ball, at 15 metres from the gun, was the 
same as that of the first shot at the jame point. The initial velocity there¬ 
fore enters into the question, and the only thing that can be done in such a 
case is, to make numerous experiments and trust to the mean of the results. 
Hutton concluded from his experiments that the resistance of the air to a 
spherical ball 2i£ inches in diameter, was expressed by the formula, 3 
p — (-0000073 v — -0015) v (2 Rf. 
M. Piobert 4 re-calculated the experiments, and deduced'the law, 
p = 0-030586 (1 + *0025 v) in French measures. 
Afterwards M. Didion 5 examined them and obtained the law, 
p= 0-027 (1 + *00257 v)v^H z } 
and M. Didion 6 gives as his final result, deduced from the Metz experiments, 
p = 0-027 (1 + *0023 v) 
concluding his Lois de la Resistance ” w r ith the remark on this formula: 
“Elle peut done etre appliquee avec confiance au tir de tous les projectiles 
sjoheriques en usage.” It is quite plain that Hutton's experiments could 
not indicate any particular law with great precision since such varied 
formulse have been deduced from them. 
1 Hutton, Traets, 1812. 
2 Didion, Traite de Balistique, 1848; 2nd Edition, 1861. hois de la Resistance de PAir, 1857s 
3 Hutton, Tract 37, p. 229. 4 Didion, Traite, 1848, p. 44. 
5 Didion, Traite, 1861, p, 64. 3 Didion, Traite, 1848, ps 52; 1861, ps 66; LoiS, 1857, p. 79s 
