238 
PRINCIPLES OP GUNNERY. 
Hutton’s 
experi¬ 
ments. 
Hutton’s 
law. 
Didion’s 
law. 
Welter’s 
law; 
Helie’slaw, 
three times as great as it should be by a comparison with the lower 
velocities.* 
Hutton afterwards (1790) made experiments with guns firing large 
spherical iron projectiles, and an improved ballistic pendulum, and 
came to the conclusion—(1), that the law of the resistance of the air 
was in a higher ratio than the square of the velocity , even at very low 
velocities; (2), that this ratio gradually increased with velocities up to 
1600 f.s., where it is at the greatest, amounting in that maximum state 
to 2xo times (instead of 3 times, as Robins asserted,) the quantity 
resulting from the ratio of the square of the velocity; (3) that for 
velocities greater than 1600 f.s. this ratio gradually decreased . 
Hutton's law of the resistance of the air, deduced from his experi¬ 
ments, consisted of two terms—one varying as the velocity, the other 
as the square of the velocity; i.e., if R denote the resistance of the air, 
and v the velocity of the projectile, 
R cx av + bv^; 
where a and b are constants determined experimentally. 
General Didion, of the French army, proposed another law of 
resistance, which, from experiments carried on at Metz in 1840, he 
considered to be nearer the truth. Didion's law of resistance also 
consisted of two terms—one varying as the square, the other as the 
cube of the velocity, or 
R oc-027 G 2 + -0023^).f 
This formula not having proved entirely satisfactory, experiments 
were again carried on at Metz, in 1857, by Captain Welter, Professor 
at the School of Practical Artillery and Engineering, but this time 
With improved ballistic instruments. The old ballistic pendulum was 
discarded, and the velocities of spherical projectiles were taken by 
means of an electro-ballistic pendulum. J Captain Welter came to the 
conclusion that the resistance of the air to spherical projectiles moving 
at high velocities was simply proportional to the cube of the velocity; 
or R oc v 3 . 
Further experiments were carried on in 1860-1 at Gavre with 
ogival-headed elongated projectiles, under the direction of M. Helie 
(Professor in the French School of Naval Gunnery), from which he 
came to the conclusion, in his work “Traite de Balistique Experi- 
mentale," published in 1865, that the results of these experiments 
“ authorised him to consider that the resistance of the air was propor¬ 
tional to the cube of the velocity, at least as long as the axis of the 
projectile did not deviate much from the tangent to the trajectory 
* Vide Robins’ “ Tracts on Gunnery,” by Hutton, p. 181. 
f Vide “ Traite de Balistique Experimentale,” par Helie, p. 168. 
+ An electro-ballistic pendulum is an instrument by which the exact instant of the passage of a 
projectile through a screen is registered by electricity , and the time of passing from one screen to 
another by means of a pendulum falling freely. These instruments have since been superseded by 
the more accurate instruments of Le Boulenge, Bashforth, and Watkin. 
