576 
Initial _ the dimensions of the piece of artillery from which it is 
Velocity of thrown, are known. 
Projectiles. “Phe solution of this problem depends upon the two 
Robins’ following principles. 
denies of 1. That the settee of the powder upon the ball 
the force of ceases as soon as it is out of the piece. 
gunpowder. 9 That all the powder is converted into an elastic 
fluid before the ball is sensibly moved from its place. 
The first of these principles is sufficiently manifest 
from the consideration, that the flame will very sudden-~ 
ly extend itself in every direction when it reaches the 
mouth of the gun, and therefore its force on the bullet 
will be completely extinguished. ; 
The second principle, though less obvious, is equally 
certain. If the powder was fired successively, and not 
all at once, it occurred to Mr Robins, that by using two 
or three bullets instead of one, a greater quantity of 
powder would be fired, since a heavier weight would 
require a longer time to pass through the barrel. Hence 
two or three balls should be impelled with a much 
ater force than one. This, however, is by no means. 
the case. Mr Robins found from experiment, that the 
velocities with which different numbers of balls were 
discharged were reciprocally in the subduplicate ratio 
of the number of balls; that is, if one ball was dis- 
charged with a velocity of 1700 feet per second, the 
same charge would impel two balls with a velocity of 
from 1250 to 1300 feet per second, and three balls with 
a velocity of from 1050 to 1110. But when bodies, 
containing different quantities of matter, are successive- 
ly impelled through the same space, with the same 
power acting at each point of that space with a given 
force, then the velocities communicated to these different 
bodies should be reciprocally in the subduplicate ratio 
of their quantities of matter. Hence, since the veloci- 
ties are in the subduplicate ratio of the number of balls, 
the action of the powder must, in all these cases, have 
been nearly the same, and consequently the truth of 
the principle is established. « 
PLATE Let us now suppose that AB, Fig. 5. is the axis of the 
CCLXXXVl, gun, DCGE the part of the cavity filled with powder, and 
Fig: 5 ‘that the hinder surface of the ball lies at GE. Then 
if we take FH to represent the force with which the ball 
is impelled at the point F, and if through H we draw 
a hyperbola KHNQ to the asymptotes AI, AB forming 
a right angle, the ordinate MN will represent the force 
with which the ball is impelled at M; for since the 
densities of the elastic fluid at the points F and M are as 
AM to AF, or as FH to MN, the forces will be in the 
same ratio, Take EL to FH as the force which im- 
pels the ball at F is to the weight of the ball, and draw 
LP parallel to EB. Then the equal lines LF, RM, &c. 
will be to the corresponding ordinates FH, MN as the 
gravity of the ball is to the force with which it is im- 
pelled at the points F and M. But by Prop. 39. Book I. 
of Newton’s Principia, the areas FLPB, FHQB are as the 
squares of the velocities which the ball would acquire 
when acted upon by its own gravity through the space 
EB, and when impelled through the same space by the 
force of the gunpowder. Hence we shall have 
V=,/ FHQB x (Vel. of falling through FB): 
~FLPB~ 
If we therefore put 
Soe eaech’, of the ball. 
=length of the charge of powder. 
B = length of the eR, hig 
S = specific gravity of the ball, 
D = the diameter of the bore, and 
GUNNERY. 
_ slide vertically up and down a groove in a heavy block 
W = the weight of the ball in ounces, we shall have Jn 
V = 27130 10L B 
7 it Sp x Log. L’ or 
V = 100,/ 223 LD* Le 
af Ww. x Log. L 
Thus making L = 24 inches. 
B= 45 inches. 
S = 1.345 for a leaden ball. \ 
D = tof an inch. ty 
Then we shall have 4 
7 120 : 
V=27130 2269 X log. = = 1674 for the ves 
locity of the ball per second; or if the weight of the 
ball W = 1,02. or 32 oz, theny =  * : 
1115 x 189 <> 120 
V= 100 29 x 52% ay AY, Phe 1674 feet, as 
formerly. 
Having thus determined theoretically the initial velo- 
cities of projectiles, Mr Robins was anxious to compare 
his theory with experiment. He was thus led to the 
invention of the ballistic pendulum, by which the real 
velocities may be measured with such a degree of ex- 
actness, that in a velocity of 1700 per 1”, the error will 
never exceed the 500th part. 
CHAP. III. 
On the Methods of determining Experimentally the Velo« 
cities of Projectiles at.any Distance from the. Gun from ; 
which they are Discharged. { 
Tue ballistic pendulum, which Mr Robins invented * 
for measuring the initial velocity of projectiles, is shewn ;? 
in Plate CCLXXXV. Fig. 12. where ABCD listic 
the body of the machine consisting of three poles B, CD, lum. 
joined at A. On the sockets R, S screw 
these poles, rests the horizontal axis EF, which sus- 
pends a pendulum GHIK, made of iron, with a broad 
surface at its extremity. A thick piece of wood 
GHIK is fastened by screws to the broad surface of 
the iron. A little below the bottom of the pendulum 
is a brace OP, joining the two poles B, C; and on this 
brace is fastened a contrivance MNU, made somewhat 
like a drawing pen, with two edges of steel, bearing on 
e line UN, the pressure of these . 
each other in 
being regulated by a screw Z. To the bottom HI of 
the pendulum is fastened a narrow ribbon LN, which 
passes between the steel edges, and which loosely 
down, as at W, through an opening cut in lower 
piece of steel. # 
Dr Hutten made some considerable improvements Hutton 
on the ballistic pendulum. At first, he used a nar. prove 
row tape divided into inches and tenths, to which he ‘ 
adapted a contrivance different from that of Mr Ro- autumn, 
bins. From the bottom of the pendulum proceeded iP 
a tongue of iron, which was raised or depressed by 
means of a screw. This tongue was cloven at the 
bottom.to receive the end of the tape, and the tips 
were pinched together by a screw. Immediately be- 
low this, the tape was passed between two slips of 
iron, which could be brought to any degree of ap- 
proach by two screws. These pieces were made to 
wu PLA 
pon two of tae 
Fig, 1 
a screw. 
of wood, and d be fixed at egies gt ‘ 
This method of measuring the of the arc of vi« 
