418 
PROFESSOR F. BASHFORTH ON THE RESISTANCE OF THE 
same with that I have assigned in the former paper. Second , That, if the velocity be 
greater than that of 1100 or 1200 feet in a second, then the absolute quantity of that 
resistance in these greater velocities will be near three times as great as it should be by 
a comparison with the smaller velocities”*. Hutton remarks in a note on these con- 
clusions: — “ These suppositions are not nearly correct. In fact, by more accurate expe- 
riments with cannon-balls, it appears that the law of the resistance begins to increase 
above the ratio of the square of the velocity, from the very slowest motions, and thence 
goes on increasing gradually more and more above what is assigned by that ratio, till 
we arrive at the velocity of 1600 or 1700 feet per second, where it is at the greatest, 
amounting in that maximum state to only 2yg- times the quantity resulting from the 
ratio of the square of the velocity. And at the velocity of 1100 feet, instead of answer- 
ing to that law, it amounts to 1*86 times the same.” Euler, in the remarks which 
accompany his translation of Robins’ ‘ Gunnery,’ states that, the greater the velocity of 
the shot, so much the more does theory deviate from the truthf. Hutton’s formula of 
resistance consisted of two terms, one varying as the velocity, and the other as the square 
of the velocity. 
In the year 1836 M. Piobert reexamined Hutton’s experiments, and found that the 
resistance of the air for various velocities was sufficiently well represented by a formula 
of two terms, one of which varied as the square, and the other as the cube of the velo- 
city. In 1839 and 1840 numerous experiments were made at Metz, under the 
direction of a commission, by means of an improved ballistic pendulum. The projectiles 
used were spherical solid shot of 24, 12, and 8, or 26’47 lbs., 13*38 lbs., and 8*86 lbs. in 
weight, and 5*85 inches, 4*66 inches, and 4*06 inches in diameter, and a shell 50*71 lbs. 
in weight and 8*67 inches in diameter. The distances from the gun at which the pen- 
dulum was placed were 49 feet, 82 feet, 164 feet, 246 feet, and 328 feet. The resist- 
ance of the air to these projectiles was found to be represented by the formula 
ttRV x 0*027(1 + 0*0023*;) $ ; 
and the new calculation of Hutton’s experiments gave 
tf-RVx 0*02786(1 + 0*0023*;)+ 
When spherical balls and smooth-bored guns were used, it was only possible to strike 
the receiver properly when at a moderate distance from the gun ; and thus the variation 
of velocity to be measured was confined within very narrow limits. There was also the 
disadvantage that, as the velocity of the ball had to be reduced to that of the receiver in 
order to determine the striking velocity of the ball, only one velocity could be mea- 
sured for each round fired. It would therefore be quite impossible to employ Robins’ 
ballistic pendulum to find the velocities of the heavy elongated projectiles in use at the 
present day. 
* Robins’ Tracts on Gunnery, by Hutton, 1805, p. 181. 
f Neue Grundsatze der Artillerie, 1745, p. 508. 
X Didion, Traite de Balistique, 1860, pp. 61 & 64. 
