GUN.NERY. 
113 
Bad juftly enough deferibed the feveral parabolic lines, 
according to the different degrees of the elevation of the 
piece ; but that pradtice had convinced him there was 
no theory in the effect of gunpowder; for having endea¬ 
voured, with the greateft precifiofi, to point a mortar 
according to thefe calculations, he had never been able 
to eftablifli any folid foundation upon them,” One in- 
ffance only occurs in which D. Bernouilli applies the 
dodtrine of Newton to the motions of projedtiles, in the 
Com. Acad. Petrop. tom. ii. p.338, &c. Befides which 
no further enquiry Was made, into the dodtrine of mili¬ 
tary projedtiles, till the time of Mr. Benjamin Robins, 
above-mentioned, who in 1742, publifhed his Principles 
of Gunnery, in which he treated particularly not only 
of the reliftance of the atmofphere, but alfo of the force 
and properties of gunpowder, the nature and effedts of 
different guns, and almoft every thing elle relating to 
the flight of balls, and the theory and pradtice of 
gunnery. 
The firft thing confidered by Mr. Robins, and which 
is indeed the foundation of military projedtiles, is the 
explofive force of gunpowder. M. de la Hire, in the 
Hiltory of the Academy of Sciences for 1702, fuppofed 
that this force may be owing to the increafed elafticity 
of the air contained in and between the grains, in confe- 
quence of the heat produced at the time of the explo- 
fion : a caufe not adequate to the 200th part of the 
eflredt. On the other hand, Mr. Robins determined, by 
irrefragable experiments, that this force was'owing to 
an elaftic fluid, fimilar to our atmofphere, exiftingin the 
powder in an extremely condenfed ftate, which, being 
fuddenly freed from the powder by the cornbuftion, ex¬ 
panded with an amazing force, and violently impelled 
the ball, or whatever might oppofe its expanflon. 
The intenfity of this force of exploded gunpowder 
Mr. Robins afcertained in different ways, after the ex- 
ample of Mr. Hawkfbee, related in the Philof. Tranf. 
No. 295, and in his Phyfico-Mechan. Exper. p.81. One 
of thefe is by firing the powder in the air thus : A fmall 
quantity of the powder is placed in the upper part of a 
glafs tube, and the lower part of the tube is immerfed 
in water, the water being made to rife fo near the top, 
that only a fmall portion of air is left in that part where 
the powder is placed : then in this fituation the commu¬ 
nication between the upper part of the tube and the ex¬ 
ternal air being clofed, the powder is fired by means of 
a burning lens, or otherwife; the water defcends upon 
the explofion, and ftands lower in the tube than be¬ 
fore, by a fpace proportioned to the quantity of powder 
fired. 
Another way was by firing the powder in vacuo, viz. 
in an exhaufted receiver, by dropping the grains-of pow¬ 
der upon a hot iron included in the receiver. By this 
means a permanent elaftic fluid Was generated from the 
■fired gunpowder, and the quantity of it was always in 
proportion to the quantity of powder that was ufed, as 
was found by the proportional finking of the mercurial 
gauge annexed to the air-pump. The relult of thefe ex¬ 
periments was, that the weight of the elaftic air thus 
generated, was equal to of the compound mafs of the 
gunpowder which yielded it; and that its'bulk, when 
cold and expanded to the rarity of common atmofpheric 
air, was about 240 times the bulk of the powder; and 
confequerttly in the fame proportion would Inch fluid 
at firit, if it were cold, exceed the force or elafticity of 
the atmofphere. But as Mr. Robins founds by another 
•ingenious experiment, that air heated to the extreme 
degree of the white heat of iron lias its- elafticity qua¬ 
drupled ; he thence inferred that the force of the elaftic 
air generated as above, at the moment of the explofion, 
is at leaft four times 240, or 960, or in round numbers 
about 1000 times as ft rang as the elafticity orprefture of 
the atmofphere on the fame fpace. 
Having thus determined the force of the gunpowder, 
or intenfity of the agent by which the projedtile is to be 
Vox.. IX. No. 570, 
urged, Mr. Robins next proceeds fo determine the ef~ 
feels it will produce, or the velocity with which it wil* 
impel a fhot .of a given weight from a piece of ordnance 
of given dimenfions; which is a problem ftridtly limited, 
and perfectly folvable by mathematical rules, and is in 
general this : Given the firft force, and the law.of its 
variation, to determine the v'elpcity with which it will 
impel a given body in palling through a given fpace, 
which is the length of the.bore of the.gun. 
In the foliation of this problem, Mr. Robins aftumes 
thefe two poftulates, viz. 1, That the adtion of the pow¬ 
der on the ball ceafes as foon as the ball is out' of the 
piece; and 2d, That all the powder of the charge is 
fired and converted into elaftic fluid before the ball is 
fenfibly moved from its place: affumptions which, for 
good reafons, are found to be in many cafes very near 
the truth. It is'to be noted alfo, that the law by which 
the force of the elaftic fluid varies is this, viz. that-its 
intenfity is diredtly as’ its denfity, or reciprocally pro¬ 
portional to the fpace it occupies, being fo much the 
ftronger as the fpace is lefs: a principle well known, 
and common to all elaftic fluids. Upon thefe principles 
then Mr. Robins refolves this problem, by means of the 
39th prop, of Newton’s Principia, in a diredt way, and 
the refult is equivalent to this theorem, when the quan¬ 
tities are expreffed by algebraic fymbols; viz. the velo¬ 
city of the ball 
I 10a , b 
v — 27130^— x log.— 
Iiz^ad 2 , b 
or == ioo^J ———x log.-; 
where v is the velocity of the ball, 
a the length of the charge of powder, 
b the whole length of the bore, 
c the fpec. grav. of the ball or wt. of a cubic foot, 
of the fame matter in ounces, 
d the diam., of the bore, 
w the wt. of the ball in ounces. 
For example, Tuppofe a 2f inches, b— 45 inches, 
c ==. 11345 oz. for a ball of lead, and d = \ inches ; 
then v == 27130^— ^ x log.—^=1674 feet per fecend, 
the velocity of the ball. 
Or, if the' wt. of the ball be w-- i^-oz. = %% oz. 
Then v = 100 J-—- x log. -—= 1674 feet, as 
^ 29X32 7 
before. 
“ Having in this propofition (fays Mr. Robins) fliewn 
how the velocity which any ball acquires from the force 
of powder, may be computed upon the principles of the 
theory laid down in the preceding propofitions, we (hall 
next fhew, that the adtual velocities with which balls of 
different magnitudes are impelled from differept pieces, 
with different quantities of powder, are really the fame 
with the'velocities affigned by thefe computations ; and 
confequently that this theory of the force of powder, 
here delivered, does unqueftionably afeertain the true 
action anA-ifiddification of this enormous power. But 
in order tqkompare the velocities communicated to balls 
by the explofion with the velocities refulting from the 
theory by.'computation, it is neceftary that the adtual 
velocities, with which balls move, ftiould be capable of 
being difedvered, which is impofiible to be done by any 
methods yet made public. The only rfteans hither.tq 
pradtifed by otherp for that purpofe, have been either 
by obferving the time of the flight of thd fhot through 
a given fpace, or by meafuring the range of the Ihot at 
a given elevation, and thence computing on the para¬ 
bolic hypotheiis what velocity would produce tli^s range. 
The firft method labours under this infurmountable dif¬ 
ficulty,,that the velocities of thefe-bodies ale often fo 
G g fwiff. 
