History. 
ced by Dr 
Hutton, 
568 
3. It appears that the velocity continually increases 
as the gun is longer, though the increase in velocity is 
but’ very small in respect of the increase in length, the 
velocities being in a ratio somewhat less than that of 
the square roots of the length of the bore; but somewhat 
than that of the cube roots of the length, and 
is indeed nearly in the middle ratio between the two. 
4, The range increases in a much less ratio than 
the velocity, and indeed is nearly as the square root of 
the velocity, the gun and elevation being the same. 
And when this is compared with the property of the 
velocity and length of gun in the foregoing para- 
graph, we perceive that very little is gained in the 
range by a great increase in the length of the gun; 
the charge being the same. 
And, indeed, the range is nearly as the, 5th root of 
the length of the bore, which is so small an increase, 
as to amount only to about one-seventh part more range 
for a double length of gun. f 
5. It appears also: that the time of therball’s. flight is 
nearly as the range; the gun and the elevation being the 
same. ; 
G6. It appears that there is no sensible difference 
caused in the velocity or tange, by varying the weight 
of the gun, nor by the use of wads, nor by different 
degrees of ramming, nor by firing the charge of pow=' 
der in different parts of it. 
7. But a great’ difference in the velocity arises from 
a small degree of windage. Indeed;: with the usual 
-established windage only, namely, about 1-20th of the 
calibre, no less than between 1-3d and 1-4th of the 
powder escapes and is lost. .And.as the balls are often 
smaller than that size, it frequently happens that half 
the powder is lost by unnecessary windage. 
8. It appeats that the resisting force of wood to 
balls fired into it, is not constant. And that the depths 
penetrated by different velocities or charges are nearly 
as the logarithms of the charges, instead of being as 
the charges themselves, or, whicli is the same thing, as 
the square of the velocity. 
9, These, and most other experiments, shew, that 
balls are tly deflected from the direction they are 
projected in, and that so much ds 300 or 400 yards in 
arange of a mile, or almost 1-4th of thé range, which 
is nearly a deflection of an angle of 15°. 
10.. Finally, these experiments furnish us with the 
following data to a tolerable degree of accuracy, viz. 
the dimensions and elevation of the gun, the weight 
and dimensions of the powder and shot, with the 
a and time of flight, aiid the first velocity of the 
The experiments made by Dr Hutton in the years 
1787,.1788, 1789, and 1791, were principally intend. 
ed to ascertain the resistance of the air to military pro- 
jectiles. Balls of 2 inches, 2.78 inches, and:3.55 inches 
in diameter, were employed, to determine the resistance 
of very high velocities. They were discharged with 
velocities from 300 to 2000 feet per second, and were 
made to strike the pendulum at several different dis- 
tances from the guns. In all these experiments, the 
resistances varied nearly as the 2y',th power of the ve- 
locity, the exponent being 2.028 for a velocity of 
200 feet per second, and increasing gradually to 2.136, 
— reached when the velocity was 2000 feet per 
GUNNERY, 
- Col, Grobert ; and avery favoura 
In the year 1804, a new machine forme : 1 
initial velocity of projectiles was and used by = 
was made to the National Institute of France, by Messrs P™ 
B and Monge. The apparatus consists of a hori- the 
‘revolving axis about 34 decimetres long, having vek 
at each of its extremities a circle or disc of tehoatel 
Sete at ‘ 4 
yoo cated to the axes, and consequently to the 
discs, by means of a weight suspended at the extremi 
of a rope, which, panting over a pulley 10 or 12 yar 
above the ground, coils itself about the arbor 
wheel and axle fixed at the same level as th 
The motion given to the wheel and axle by the 
of the weight is communicated to the axis of the 
by an en ne chain nena, Need eee 
and also round a pulley on the axis of the discs, 
instrument being thus constructed, let us suppose 
a ball traverses two discs when in motion, in a 
rection parallel to their axes. It is obvious that. 
hole in each dise will not coincide with one. 
% 
2 
Hl 
z 
E 
eF 
FEES 
accurately the arch spewed over by the second dise dur~ 
ing the transit of the é 
In the experiments which were made with this machine,’ 
the motion becanie sensibly uniform when the weight; 
had arrived nearly. at the half of thé: vertical space: 
which it traversed, The following is the formula for 
calculating the velocity of the ball. 
Qan fr 
Vv= Te. ~ ant 6, or 
6.282n 7r,. 3 Z 
V= ki ene $n 
V=the velocity of the ball between the discs, consi- 
* dered as uniform ; . , 
*=3.141, the ratio of the circumference to the di- 
ameter of a circle ; 
k=the ratio between the respective numbers of the’ 
turns made at the same time by the wheel of 
the axle, and the pulley of the axis of the discs, 
which in the following experiments was 7R75 
=the time eriployed by the wheel of ‘the axle to 
make » number of turns ; 
r==the distance of the hole made by the ball in the 
second dise from the axis of the discs ; 
a=the are passed over by that hole while the disc 
goes from the one to the other ; ; 
b=the distance between the two discs. — 
The following experiments were made with a horse 
musketoon, 0.765 metres of interior length. The weight 
of the ball was 24.7 grammes, and it was projected with 
half its weight of powder. The mean velocity deduced 
from these i s is $90.47; whereas the mean 
velocity found from riments with the common in- 
fantry musket, 1.187 metre of interior length, was 428, 
exceeding the former in the ratio of 11 to 10. All the 
values of a are referred to that ofr == 1 metre. i? 
