History. was too 
—_—" amount, by the calculation, to that enormous degree 
564 
eat to. be overlooked; though it did not 
which was afterwards deduced from, direct experiment, 
Newton has not attempted to investigate, in a direct 
manner, the path which a body will describe when pro- 
jected into the atmosphere with a given velocity, and 
in a given direction. He shews, however, the particu- 
lar state of density in the air, which will agree with the 
motion of a body in any curve whatever; and, by the ap- 
plication of the principle to curves, which have some 
resemblance to the path of a projectile, he finds it. 
differing little from what may be considered as the 
path of a body projected in our atmosphere. In the 
second edition of the Principia, which appeared in 
1713, he corrects some of the oversights into which he 
had formerly been led; and he shews that a projectile, 
moving in a medium, whose density yaries according 
to certain laws, and acted upon by a force directed to the 
centre of the earth, will describe an eccentric spiral, 
whose properties he describes. . 
The complete solution of this problem was not obtain- 
ed till Dr Keill challenged John Bernoulli to determine 
the curve described by a body projected through a me- 
dium resisting as the square of the velocity. ‘The Swiss 
geometer very soon gave a much more general solution 
than was demanded, independent of any limitation of 
the law of resistance, of the law of gravity, or of the 
law of density, provided that they were capable of be- 
ing expressed algebraically. _Dr Brook Taylor gave a 
solution of the problem in its limited form, 
In the year 1690, the celebrated Huygens published 
a treatise on Gravity, in which he endeavoured to 
prove, from a series of experiments, that projectiles 
discharged through the air with great velocity, described 
paths very different from a parabola. The inconsist- 
ency of the Galilean theory, with the practice of artil- 
Jery, was now particularly noticed by M. Ressons, a 
French artillery officer, who drew up a memoir on the 
subject, and presented it to the Academy of Sciences. * 
In this memoir, which was entitled Methode pour tirer 
les bombes avec succes, he attempts to shew that the 
theory is of very little service in the use of mortars, 
and that the theoretical path of projectiles is justly 
described in the works of Blondel; yet by directing 
mortars according to that theory, he could never ob- 
tain results that had the slightest agreement with it. 
In the year 1736, a series of experiments was made 
at Woolwich, in order to determine the length of can- 
non that could enable them to shoot most efficaciously. 
These experiments were made with six 24 pounders, 
cast on purpose, and of the same weight, but varying 
in length from 8 feet to 103 feet. Thes ieces were’ 
all loaded alike, with allotments of powder equal to 
half the weight of the bullet; and. five shot were fired 
from each, at an.elevation of 74°, The following are 
the results which were obtained: 
June Ist) dune 16ch, aly © A : 
Length  T hapeerndias i one ap Kart and to 45°, Experiments were also made with a 24 
Five Ranges. | Three Ranges. | Three Ranges. | pounder, at different elevations, from4® to 45°,.and the * 
- following results were obtained with a charge of nine 
ae: Yards. Yards, Yards. libs of powder, 
108 qa56 2614 2406 Angleof | Actual Ranga, |) Angle of” 
2570. 2552 2486 Elevation. ‘Yards.|} Elevation. 
93 2633 2560 2500 4 te aeie re 4100)}20, . . 
9 2790 2494 2563 BR. sed kee MO4FOH TS oi 
} "84 2586 2490 2466 80... w]e st pgaOlta coke 
8 2438 2473 2452 RB... | » + 4! 3650 ; 
GUNNERY. 
‘committee, however, seem to have made some mistake; 
de Borda. They were made with the usual pieces of La Fereb 
_ 
From the average range of these five shot, the effects ston 
of the different lengths were supposed to be deduci a 
The result of the experiments was, that the pieces of 9 Boat 
and 94 feet had the greatest range. Mr Robinshhas, hows woo) 
ever, shewn that these experiments,are by no means in- jn 1736, 
consistent with his opinion, thatthe largest piecesought = 
to have the greatest range. The ranges. withthe 9 and 
93 feet guns ought net to differ more than 35 yards from 
the ranges of the 8 and the 103 feet guns, according ? 
to his theory; and yet with two subsequent trials — 
with the 9 feet gun, the ranges differ no less than 650 
yards; and the average ranges made in these succese 
sive days differ from each other $00 yards. Hence it 
is obvious that these experiments differ so much from 
each other, that they are not sufficient to decide the 
point for which they were undertaken, } 
No step a SmpaTeanee seem: to ee: been made in Experi 
nnery till the year 1742, when jurin proposed ments of — 
PA questions, which the Royal Society appointed a ‘he Rey: 
committee to investigate. The first of these i ako 
was, ther all the powder of the charge be > 
2d,-Whether all the powder that is fired, be fired before 
the bullet is sensibly moved from its place? And 
3dly, Whether the distance to which the bullet. is 
thrown may not become greater or less by changing 
the form of the chamber, though the charge of powder 
and all other circumstances remain unchanged? The 
committee, after numerous experiments, found that all 
the powder was not fired ; that the bullet was sensibly 
moved from its place, before all the powder that was 
fired had taken fire; and that a change in the form of 
the chamber would produce a change in the distanee 
to which the bullet is thrown ; the largest chamber of 
equal capacity always driving the ball farthest. + The 
- 
for Mr Robins afterwards proved, that the ball has not 
sensibly changed its place when the powder is fired. 
Several experiments were about this time made in 
France on the ranges of cannon. M. St Remy has 
given us an account of a series made with pieces of 
cannon 10 feet in length, of the usual calibre, and ele- 
vated at an angle of 45°. The following were his re- 
sults, the quantity of powder being two-thirds of the 
weight of the bullet. ; 
Range in Yards. Range in Yards. 
24 Pounder. . 4490 8Pounder. . . 3820 
16 Ditto. . . . 4040 4Ditto. . . . 8040 
12 Ditto. . 3740 
Pieces of the same calibre as the preceding, but some- 
what shorter, had almost the same ranges when fired 
with only one-half the former , or one-third of 
the weight of the ball in powder, See Remy's Me- 
moirs of Artillery, vol. i. p. 69. 
Another series of experiments was made at La Fere, ,. 
in the year 1739, under the direction of the Chevalier jrents at " 
all the preceding calibres, and were charged with va~ Borda in ~ 
rious quantities of powder, and elevated to 4°, to 15°, 173% 
* See Mem, Acad. Par, 1716, -p. 79: 
+ See Phil, Trans. 1742, Vol. xlii. p. 172 
