116 GUNNERY. 
projected in ; and that fo much as 300 or 400 yards in 
a range of a niilej or almoft ^th of the range, which is 
pearly a deflection of an angle of fifteen degrees. 
“ jo. Finally, thefe experiments fur-nifti us with the 
following concomitant data, to a tolerable degree of ac¬ 
curacy, namely, the dimenfions and. elevation of the 
gun, the weight and dimenfions of the powder and ftiot, 
with the range and time of flight, "and the firft veloci¬ 
ty of the ball. From which it is to bejtoped, that the 
sneafure of the refiftance of the air to projectiles may be 
determined, and thereby lay the foundation for a true 
and practical fyftem of gunnCry, which may beTufeful 
in fervice as well as in theory.” 
“ Since the publication of thofe TraCts, (fays Dr. 
Hutton,) we have profecuted the experiments hill far¬ 
ther from year to year, gradually extending our aim to 
more objeCts, and enlarging the guns and machinery, 
till we have arrived at experiments with the 6-pounder 
guns, and pendulums of j8oo pounds weight. One of 
the new objects of enquiry was the refiftance fhe atmo¬ 
fphere makes to military projeCtiles; to obtain which, 
the guns have been placed at many different diftances 
. from the pendulum againft which they are fired, to get 
the velocity lo.ft in pafling through thofe fpaces of air; 
by which, and the ufe of the whirling machine, de- 
fcribed near the end of the ift vol. of Robins’s TraCts, 
for the flower motions, I have inveftigated the refift¬ 
ance of the air to given balls moving with all de¬ 
grees of velocity, from o up to zooo feet per fecond ; 
as well as the refiftance, for m'any degrees of velocity, to 
planes and figures of other fliapes, and inclined to their 
path in all varieties of angles; from which I have de¬ 
duced general laws and formulas for all fuch motions. 
“ Mr. Robins made alfo fimilar experiments on the 
refiftance of the.air; but being only with mufket-bul- 
lets, on account of their fmallnefs, and of their change 
of figure by the explofion of the powder, I find they 
are very inaccurate, and confiderably different from 
thofe above-mentioned, which were accurately made 
with pretty confiderable cannon balls, of iron. For 
this reafop we may omit here the rules and theory de¬ 
duced from them by Mr. Robins, till others more cor- 
reCl fliall have been eftablifhed. All thefe experiments 
indeed agree in evincing the very enormous refiftance 
the air makes to the fwift motions of military projec¬ 
tiles, amounting in fome cafes to twenty or thirty times 
the weight of the ball itfelf; on which account, the 
common rules for projectiles, deduced from the para¬ 
bolic theory* are of little or no ufe in real practice; for 
from thefe experiments it is clearly proved, that the 
track defcribed by the flight even of the heavieft fhot 
is neither a parabola, nor yet approaching any thing 
near it, except when they are projected with very fmall 
velocities ; in fo much that fome balls, which in the 
air rangb only to the diftance of one mile, would, in va¬ 
cua, when projected with the fame velocity; range above 
ten or twenty times as far.” 
Sir Benjamin Thompfon (now count Rumford) infti- 
tuted a very confiderable courfe of experiments of the 
fame kind as thofe of Mr. Robins, with muflcet barrels, 
which were publilhed in the Philofophical TranfaCtionsy 
vol. 71, for the year 1781. In thefe experiments, the 
conclulions of Mr. Robins are for the moft part confirm¬ 
ed. This gentleman alfo purfues a hint thrown out by 
Mr. Robins, relative to the determining the velocity of 
a ball from the recoil of the pendulpus gun itfelf. Mr. 
Robins, in prop. 11. remarks, that the eft'eCt of the ex¬ 
ploded powder upon the recoil of the gun, is the fame 
whether the gun is charged with a ball or without one ; 
and that the chord, or velocity, of recoil with the pow¬ 
der alone, being lubtraCted from that of the recoil 
when charged with both powder and ball, leaves the 
velocity which is due to the ball alone. From thence 
fir Benjamin obfer.ves, that the inference is obvious, 
viz. the momentum thus communicated to the gun 
by the ball alone, being equal'to the momentum of the 
ball, this becomes-known ;- and therefore being divided 
by the known'weight of the ball, the quotient will be 
its velocity. In the experiments however contained in 
Dr. Hutton’s TraCts, a great multitude of thofe .cafes 
are compared together, and the inaccuracy of that rule 
is fllewn. 
Having in the 9th prop, compared together a number 
of computed and experimented velocities of balls, to 
verify his theory ; Mr. Robins, in the 10th prop, allign? • 
the changes in the force of powder, which arife from 
the different ftate of the atmofphere, as to heat and 
moifttire, both which he finds have fome effect on it, 
but efpecially the latter. In prop. 11. he i-nveftigates 
the,velocity vvhich-the flame of gunpowder acquires by 
expanding itfelf, fuppofing it fired in a given piece of 
artillery, without either a bullet or any other body be¬ 
fore it. This velocity he finds is upwards of 7000'feet 
per fecond. But the celebrated Euler, in his commen¬ 
tary on this part of Mr. Robins’s book, thinks it may 
be ftill much greater; and in this propofition too it is, 
that Mr. Robins declares his opinion above alluded 
to, viz, that the effeCt of the powder upon the recoil 
of the gun is the fame in all cafes, whether fired with 
a ball or without one. In prop. 12. he afcertains the 
manner in which the flame of powder impels a ball 
which is laid at abonfiderable diftance from thecharge; 
fhowing here that the fudden accumulation and denfity 
of the fluid againft the ball is the reafon that the bar¬ 
rel is fo often burft in thofe cafes. 
Mrf’Robins, in eight other propofitions, treats “of 
the refiftance of the air, and of the track defcribed by 
the flight of fhot and fhells.” And of thefe, prop. 1. 
defcribes the general principles of the refiftance of fluids 
to folid bodies moving in them. Here Mr. Robins dif- 
criminales between continued and comprefled fluids, 
which immediately rufh into the fpace quitted by a 
body moving in them, and whole parts yield to the im- 
pulle of the body without condenfing and accumulating 
before it; and fuch fluids as are imperfectly comprefll 
ed, rufiring into a void fpace, with a limited velocity, 
as in the cafe of our atmofphere, which condenfes more 
and more before the ball as this moves quicker, and alfo 
prefles the lefs behind it, by following it always with 
only a given velocity : hence it happens, that the for¬ 
mer fluid will refill moving bodies in proportion to the 
fquare of the velocity, while the latter refills in a higher 
proportion. Prop. 2. is “ to determine the refiftance of 
the air to proje&iles by experiments.” One of the me¬ 
thods for this purpofe is by the balliftic pendulum, pla¬ 
cing the gun at different diftances from it, by which he 
finds the velocity loft in pafling through certain fpaces 
of air, and confequently the force of refiftance to fuch 
velocities^ as the body moves within the feveral parts 
of its path. And another way was by firing balls, 
with a known given velocity, over a large piece of wa¬ 
ter, in which the fall and plunge of the ball could'be 
feen, and confequently the fpace it palled over in a. 
given time. By thefe means Mr. Robins determined 
the refinances of the air to feveral different velocities, 
all which (howed that there was a gradual increafe of 
the refiftance, over the law of the fquare of the veloci¬ 
ty, as the body moves quicker. In the remaining pro¬ 
pofitions he proceeds a little farther in this fubjeCt of 
the refiftance of the air; in which he lays down a rule 
for the proportion of the refiftance between two afligned 
velocities ; and he fttows, that when a twenty-four pound 
ball, fired with its full charge of powder, firft iflites 
from the piece, the refiftance it meets with from the air 
is more than twenty times its weight. He farther fttows, 
that “the track defcribed by the flight of fhot or fltells 
is neither a parabola, nor nearly a parabola, unlefs they 
are projected with fmall velocities ;” and that “bullets 
in their flight are not only deprefled beneath their ori¬ 
ginal direction by the aCtion of gravity, but are alfo 
frequently 
