Initial Ve- 
locities of 
Projecti 
Method of 
578 
initial velocity by the methods already described, and 
let it be 1000 feet, then v = 1000. Let the same piece 
be then loaded as before, and fired into the butt, and 
let its penetration be 12 inches, or 1 foot, = p. Then 
since’b p = dv?, we shall have p X t= ts X 10002, 
or p X 83333. Substituting then, in the formula, 
bp =dv*, we have 83333 F =dv*, The consistency 
of the butt being thus found, place the great gun, the 
initial velocity of whose shot is renee, and having 
fired several rounds in a horizontal direction against 
the butt, let the mean of the different of pe- 
netration be 7 = p, and let d, the diameter of the shot, 
be equal 4 inches, then we have 83333 x 7= +, v’, 
Gale an Pr sea x 7x 12 
4 = 1323, the initial velo- 
city required. . 
The second method proposed by Antoni of deter- 
determining mining initial velocities, consists in analysing and re- 
initial velo- 
cities by an- 
alysing the 
curve. 
PLATE 
GCLXXxvI- 
Fig. 7. 
Methodof 
deducing 
the initial 
velocities 
from the 
thicknéss 
of the me- 
tal, 
solving into its simple movements the curve described 
by the projectile on quitting the piece. In order to 
effect this, a gun AB, Fig. 7, mounted on its carriage, 
and laid on an even and solid platform, is placed 
with its axis in a horizontal direction AC, so that the 
shot, at its, first graze, may touch the earth in the point 
C of the horizontal line DF, The vertical distance KG 
is obviously the space through which ‘the shot has de- 
scended by the action of gravity, which may be called 
s, and the Intervene distance AK or DG is the space 
which it has 
of the impulsive or projectile force. 
_ 32.18 2 
Then since 
» and pee/ ae we have, by substi- 
tating KG for s, t= 4/, bd Ss <= the the in which the 
shot is impelled from A to K. Having obtained DG 
accurately from the mean of several trials, call it r, and 
considering it as uniformly passed over, say, as ¢; r= 
1: — the initial velocity or the space through which the 
shot would move in a second, without considering the 
air’s resistance. Let KG = four feet, then we have 
4 inf mre ae m cctonidyand if DG = 700 feet, we 
32.18 
Pe 
T 2X4 ake 
have as orv= mais = 1400 feet, the initial ve- 
locity required, 
As the initial velocity thus determined is not abso- 
Jutely correct, on account of the resistance of the air, a 
more accurate result may be obtained, by placing a butt 
LMN nearer the gun. Let aline be drawn on the butt 
at.M, where it is cut by the horizontal line of direction 
AM, and by firing several shot at the butt, the vertical 
distance MH=s will be ascertained. By measuring the 
distance DL, and using the formule already given, the 
initial velocity » will again be found. The nearer the 
gun is brought to the butt, the more correct will the 
mitial velocity be found. Both these methods may be 
applied to guns of all lengths and calibres. , 
he third method of determining initial velocities, is 
by deducing them from the thickness of the metal of the 
fire arm win it is in equilibrio with the pressures of 
the elastic fluid in every point of its length. This me- 
thod, however, is not applicable to guns of large cali- 
bre fired with the common charges of powder, but only 
to fusils and pieces of small callie, Antoni informs 
sed through in the same time, in virtue © 
GUNNERY. 
us, that in Piedmont musket barrels are proved, by Init 
charging them with 17 drachms of common cannon 1 
wder, over which is puta very high wad of hard tow, 
which is with difficulty pressed into the barrel, and 
which is afterwards rammed down with all the force 
which the armourer can exert. A leaden bullet, weigh. 
ing 18 drachms, is then put in, and wadded as before. 
The barrels being placed with their breach upon a 
strong beam of Weed. are each fired twice. Many of 
them burst, sotnetimes at the breach, and sometimes in. 
the middle ae the bore, er heagane tier the muzzle; 
but as the bursting never happened more frequently on 
one than another, the officers and peso A 
rers did not consider it as n to make any chan 
in the thickness of the metal. Hence in guns of this 
kind, the thickness of the metal may be considered as 
proportional to the pressure of the elastic fluid in every 
part of their length. i. 
As this method is not likely to be of much use, we 
shall merely refer the reader to Antoni’s Treatise on 
Gunpowder, translated by Thomson, p. 87, 88, 165, &e. 
CHAP. IV. rural 
Comparison of the Initial Velocities of Bullets, as com- 
puted from the Theory, mith the actual Velocities, as 
determined by the Ballistic Pendulum, : 
In determining the initial velocity of bullets, Mr 
Robins used a musket barrel, nearly as thick at the 
muzzle as at the breach, and its thickness was made 
equal to the diameter of its bore. It was always char- 
ged with a laddle, as in the case of cannon, and the 
wadding was never greater than was necessary to con 
fine the powder to its propes place. In order to pre- 
vent the impulse of the flame from actin the 
pendulum, the mouth of the musket should be sixteen _ 
or eighteen feet from it, when the is half an 
ounce of powder. With larger charges, Mr Robins has 
often found the impulse to be sensible at the distance 
of twenty-five feet. =a 
His first set of experiments was made with a musket 
45 inches long ; the diameter of the ball was ths of an 
inch, and the ey ees the powder was 2{ 
inches, which, as barrel pret 9 the bullet by 
about the 40th of an inch, contained exactly 12 penny+ 
weights of powder. This barrel we shall call A. 
The weight of the whole pendulum was 52 )b. 3 oz. 
The distance of the centre of gravity from the axis of 
suspension was 52 inches ; 200 of its small swings were 
performed in 253 seconds, and therefore the distance of - 
Its — of oscillation from the axis of suspension, was 
622 inches. 4 
The following results were obtained with 
dulum and the barrel A. 
: 
this pen- 
ka) 
a ed Chord of its As- ; 
2 R= | E = Quantity. } cending Arch ig ay aie of 
& |S & jof Powder |measured on the 
. a al 5 Ribbon. Theory. | Theory. 
Dwts. 
1/A]| ie 18.7 19.0 | 4.3 
21A 12 19.6 19.0 — 
3 \A 6 13.6. 13.4 —2 
Another set of experiments was made with the same 
barrel, but with a pendulum exceeding a little the 
