tion by the tape, was however often attended with 
‘uncertainty ; and Dr Hutton adopted the following sim- 
ple contrivance. He took a block of wood, having its 
per surface formed into the are of a circle of nearly. 
the same radius as the extreme h of the pendulum, 
n the middle of this arch was a shallow groove three 
four inches broad, running slog the middle of the 
plock through its whole length, This groove was.fil- 
ed with a composition of so soap and wax, of about 
- the consistency of honey, or a little firmer, having its 
upper side smoothed off with the general surface of the 
broad arch. A sharp spear proceeded from the bottom 
of the pendulum, so as just to enter and scratch the sur- 
face of the composition in the groove, without havin 
its motion sensibly retarded, From the trace whi 
was thus left, the length of the cord of the arc of vibra- 
tion was easily measured. 
’ The pendulum being thus constructed, is used in 
following manner. The ball is discharged against 
the block of wood GHIK, which, in consequence of the 
impulse, vibrates through an arc of a certain extent, 
which of course increases with the velocity of the ball. 
The extent of the are of vibration is measured by the 
2 through which the ribbon LN is pulled out 
the edges UN. Hence, if the weight of the 
um is known, and also the distance of its centre 
of gravity and oscillation from its axis of suspension, it 
is easy to determine the extent of the are of vibration, 
the velocity with which itis struck by a body of a 
known weight entering it at a given point. In the 
investigation of the theorem for computing the velo- 
- of the ball, Mr Robins committed a trifling mis- 
a, which he corrected in the Philosophical Trans- 
actions for 1743, but which the editor of his works 
omitted to insert in the New Principles of Gunnery, 
‘published in. 1761. The theorem.of Robins is. 
mee iB sit dn ah Sagi 
» The theorem as corrected by Euler, is / 
wae PB g OFF 
hati ea hd ba 
.... The formula given by Antoni is _ 
4 4 . 
: Pgo+be* x pg+bi 
=cr/ 32.18 : tite 
emo san0 PO EE EE 
‘4 ae ~ ; egy CERN 
which is v=5.672700/ BEOtO Per" 
; The formula given by Dr Hutton is 
sed + 8:6727¢ 
PER 
toni’s, which he reduces to the following very sim- 
_ ple formula: 
my i- = 5.6727 gc. my 
_ which is within _..,,dth part of the true quantity, and 
willalways give the Seloclty within less than half’ foot, 
even when the velocities are greatest. In these formule, 
v = the initial velocity of the ball at the instant of 
i = weight of the ball. 
- p= weight of the pendulum. 
 g= distance to its centre of gravity. 
- @= the distance of its centre of oscillation. 
= the distance ‘to the point of im or. the point 
uck by the ball. ae ie 
VOL. X. PART II. » 
” pgo+biixpg +i, almost the same 
Pt Sing. 
GUNNERY. 
Initial Ve-. 
577. 
¢ = the chord of the arch:of vibration. 
r = its radius or distance to the ribbon, 
The machine of Mattei for measuring initial veloci- 
ties near the mouth of the gun, which we have alrea- 
dy briefly described, was employed by Antoni, It 
consists of a. horizontal wheel AB, mounted wu a 
vertical axis, and put in motion by the descent of a. 
weight Q suspended to the rope GG, and which can 
be raised into a state of activity by the winch fixed to the 
axis of the pulley P, A circular band of writin, 
AE, BF, about six inches high, is fixed round the cir- 
cumference of the wheel AB, so as to form a drum 10. 
feet in diameter. A butt or block of elm is placed about. 
two or three feet from the drum to receive the balls, 
The gun being fixed immoveably at the distance of 20 
feet, so that its axis produced would pass through an 
exact diameter of the drum perpendicular to GG, the 
machine is put in motion by the descent of the weight 
| The motion soon becomes uniform, and the velo- 
city of the drum is measured by a small eccentric wheel 
IL upon the axis CD, which at every revolution gives 
a vibratory horizontal motion to a tongue of wood, at 
the extremity of which is suspended a common us 
lum, which is shortened or lengthened till its vibrations 
are isochronous to those of the tongue. The time in 
which the wheel performs a revolution will be shewn 
by the length of the pendulum. When the pendulum 
and the tongue have acquired an isochronous motion, 
the gun is discharged, and the wheel stopped. The 
hole made in the drum at the first entrance of the ball 
will be easily distinguished from the other hole’ which 
it made at its exit, by the edges of the holes being 
turned to the point by which ch 
drum. A thread is then. stretched in the direction 
in which the ball was. fired, so as to pass through the 
centre of the first hole, and the point where the line 
cuts the drum is marked. The distance between this 
mark and the second hole is the distance through which 
the circumference of the drum has moved while the 
projectile was passing through.a space equal to its dia- 
meter. 
In order’to find the uniform velocity of the shot in a 
‘second of time,. call d:the-diameter of the wheel, c its 
circumference, ¢ the time in which the wheel performs 
one revolution, m-the distance through which a part of 
the circumference of the drum moves while the ball is 
traversing the distance D, and v,the initial velocity of 
the shot in a second of time: then m:d=c: ¢ = the 
space passed through by the shot with a uniform ve- 
locity ee a one revolution of the wheel: then as 
Tn using this machine, Antoni used wads of parch- 
ment torn in several places, that they might not injure 
the drum of paper. 
themselves will be given in the next Chapter. 
Antoni has given an account of other three methods 
of measuring the initial velocities of projectiles. The 
first consists in measuring their respective penetrations 
into a homogeneous butt of a. knewn consistency. If we 
call } the consistency of the butt, d the diameter of the 
shot, p the depth of its penetration, and v the initial * 
velocity, we shall have v = if f. In order to find 4, 
the consistency of the butt, fire a piece of small calibre, 
with an iron shot one inch in diameter, and measure its 
4D : 
locities of 
Projectiles. 
M ‘s 
machine for 
initial ~ 
Cities. 
e ball went out of-the. 
An account of the experiments . 
Methods of 
determining 
initial velo- 
cities by the 
penetration 
