]{4 GUN! 
Iwift, and confequently the time obferved is fo (hort, 
that an imperceptible error in that time may occafion an 
error’in the velocity thus found, of 2, 3, 4, 5, or 600, 
feet in a fecond. The other method is fo fallacious, 
by reafon of . the refiftance of the air, (to which inequa¬ 
lity the firft is alfo liable,) that the velocities thus af- 
figned may not be perhaps the tenth part of the actual 
velocities fought. To remedy then thefe inconvenien¬ 
ces, IJiave invented a new method of finding the real 
velocities of balls of all kinds; and this to fuch a de¬ 
gree of cxa&nefs (which maybe augmented too at plea- 
fut e), that in a ball moving with the velocity of 1700 feet 
in one fecond, the error in the eftimation of it need ne¬ 
ver amount to its 500th part ; and this without any ex¬ 
traordinary nicety in the conftrudlion of the machine.” 
Mr. Robins then proceeds to defcribe the machine by 
which he meafures the velocities of the balls, which 
machine is fimply a pendulous block of wood, fufpend- 
ed freely by a horizontal axis, againft which block are 
to be fired the balls whofe velocities are to be deter¬ 
mined. “ This inftrument thus fitted, if the weight of 
the pendulum be known, and likewife the refpedtive 
diftances of its centre of gravity and of its centre of of- 
ciilation from its axis of fufpenlion, it will thence be 
known what motion will be communicated to this pen¬ 
dulum by the percuflion of a body of a known weight 
moving with a known degree of celerity, and ftriking it 
in a given point; that is, if the pendulum be fuppofed 
at reft before the percuffion, it will be known what vi¬ 
bration it ought to make in confequence of fuch a deter¬ 
mined blow; and, on the contrary, if the pendulum, 
bein^ at reft, is (truck by a body of a known weight, 
and The vibration which the pendulum makes after the 
blow is known-, the velocity of the ftriking body may 
from thence be determined. Kence then, if a bullet of 
a known weight (trikes the pendulum, and the vibration 
which the pendulum makes in confequence of the ftroke 
be alcertained, the velocity with which the ball moved 
is thence to be known.” 
Mr. Robins next explains his method of computing 
velocities from experiments with this machine; but 
which is rather perplexed, as well as the rules of Euler 
and Antoni, who followed him in this inveftigatiom A 
much plainer rule is given in Dr. Hutton’s Tradts, vol. i. 
p. 119,- where fuch experiments are explained at full 
length, and this rule is exprelTed by either of the two 
following formulas : 
r= 5-6mcg X 6i^s,%cg Xjgp the velo¬ 
city ; where v denotes the velocity of the ball when it 
ftrikes the pendulum, p the weight of the pendulum, b 
the weight of the ball, c the chord ot the arc defcribed 
by the vibration to the radius r, g the diftance below 
the axis of motion to tlie centre of gravity, 0 the dif¬ 
tance to the centre of ofcillation, i the diftance to the 
point of impact, and n the number of ofcillations the 
pendulum will perform in one minute, when made to 
ofcillate infmal) arcs. The latter of thefe tjvo theorems 
is much the eafieft, both becaufe it is free of radicals, 
and becaufe the value of the radical 4/0, in the former, 
is to be.firft computed from the number*, or number of 
ofcillations the pendulum is obferved to make. 
With fuch machines Mr. Robins made a great num¬ 
ber of experiments, with mufket-barrels of different 
lengths, with balls of various weights, and with different 
charges or quantities of powder. He has fet down the 
refufts of iixty-one of thefe experiments, which nearly 
agree with die correfponding velocities as computed by 
his theory of the force of powder, and which therefore 
eftablilh that theory o n *a lure foundation. 
From thefe experiments, as well as from the preced¬ 
ing theory, many important conclufions were deduced 
by 3 Mr. Robins ; and indeed by means of thefe it is ob= 
r E R Y. 
vious that every thing may be determined relative both 
to the true theory of projectiles, and to practical gun¬ 
nery : for, by firing a piece of ordnance charged in a. 
fimilar manner againft fuch a balliftic pendulum from 
different diftances, the velocity loft by paffing through 
fuch fpaces of air will be found, and confequently the 
refiftance of the air,, the only circumftance that was 
wanting to complete the theory of military projectiles; 
and of this kind Dr. Hutton profeftes to have made a 
great number of experiments with cannon-balls, and 
thereby obtained the whole feries of refiftances to fuch a 
ball when moving with every degree of velocity, from 
o up to 2000 feet per fecond of time. In the ftniCture 
of artillery, they may likewife be of the greateft ufe r 
for hence may be determined the belt lengths pf guns; 
the proportions of the (hot and powder to the feveral 
lengths; the thicknefs of a piece, fo as it may be able 
to confine, without burfting, any given charge of pow¬ 
der; as alfo the effedt of wads, chambers, placing.of the 
vent, ramming the powder, &c. For the many other 
curious circumftances relating to this fubjeft, and the 
various other improvements in the theory and pradtice 
of gunnery made by Mr. Robins, confult the firft volume 
of his Tracts, collected andpubliffied by Dr. Wilfon, 
in 1761, where ample information may be found. 
Soon after the firft publication of Robins’s Principles 
of Gunnery, in 1742, the learned in feveral other na¬ 
tions, treading in his fteps, repeated and farther ex¬ 
tended the fame fubjeCt, fometimes varying and enlarg¬ 
ing the machinery; particularly Euler in Germany, 
D’Antoni in Italy, and D’Arcy and Le Roy'in France. 
But mod of thele, like Mr. Robins, with fmall fire¬ 
arms only, fuch as mu fleets and fufils. “ But, fays Dr. 
Hutton, (Phil. DiCt. p.556,) in the year 1755, in con¬ 
junction with feveral able officers of the royal artillery, 
and other ingenious gentlemen, I undertook a courfe of 
experiments with the balliftic pendulum, in which we 
ventured to extend the machinery to cannon-ffiot of one, 
two, and three, pounds weight. An account of thefe 
experiments was publiffied in the Philof.Tranf. for 1778, 
and for which the Royal Society honoured me’with the 
prize of the gold medal. Thefe were the only experi¬ 
ments that I know of which had been made with can¬ 
non-balls for this purpole, although the conclufions to 
be deduced from fuch are of the greateft importance to 
thofe parts of natural philofophy which are dependent 
on the effeCts of fired gunpowder; nor do I know of 
any other practical method of afeertaining the initial 
velocities within any tolerable degree of the truth. The 
knowledge of this velocity is "hf the utmoft confequence 
in gunnery : by means of it, together with the law of 
the refiftance of the medium, every thing is determi¬ 
nable relative to that bufinefs; for, befides its being an 
excellent method of trying the ftrength of different forts 
of powder, it gives us the law relative to the different 
quantities of powder, to the different weights of (hot, 
and to the different lengths and (izes of guns. Befides 
thefe, there does not feem to be any thing wanting to 
anfwer any inquiry that can be made concerning the 
flight and ranges of (hot, except the effeCts arifing from 
the refiftance of the medium. In thefe experiments the 
weights of the pendulums employed were from 300 to 
near 600 pounds. In that paper is defcribed the method 
of conftruCting the machinery, of finding the centres of 
gravity and ofcillation ofthe pendulum, and of making 
tlie experiments, which are ail fet down in the form of 
a journal, with all the minute and concomitant eirc.um- 
ftauces;. as alfo’ the inveftigation of the new and eafy 
rule, fet down juft above, for computing the velocity 
of the ball from the experiments. The charges of pow¬ 
der were varied from two to eight ounces, and the (hot 
from one to near three pounds. And from the whole 
were clearly deduced thefe principal inferences, viz. 
“ 1. That gunpowder--fires almoft inftantaneoufly. 
z. That 
