RES 
RES 
to be sure, by many previous trials, that the 
velocity of the bail could not differ by 20 
feet in l" from its medium quantity. He 
then fired it against a pendulum, placed at 
25, 75, and 125 feet distance, &c. from the 
mouth of the piece respectively. In the 
fiist case it impinged against the pendulum 
with a velocity of 1670 feet in 1''; in the se- 
cond case, with a velocity of 1550 feet in 
1"; and in the third case, with a velocity of 
1425 feet in l"; so that in passing through 
50 feet of air, the bullet lost a velocity of 
about 120, or 125 feet in l"; and the time 
of its passing through that space being about 
j'j or jL of 1 ", the medium quantity of resis- 
tance must, in these instances, have been 
about 120 times the weight of the ball; 
which, as the ball was nearly of a pound, 
amounts to about tOlb. avoirdupoise. 
Now if a computation be made, accord- 
ing to the method laid down for compressed 
fluids in the thirty-eighth Propos. of lib. 2. 
of Sir Isaac Newton’s Principia, supposing 
the weight of water to be to the weight of 
air as 850 to 1, it will be found that the 
resistance of a globe of three quarters of an 
inch diameter, moving with a velocity of 
about 1600 feet in l", will not, on those 
principles, amount to anymore than a force 
of mb. avoirdupoise ; whence we may con- 
clude (as the rules in tliat proposition for 
slovv motions are very accurate) that the 
resisting power of the air in slow motions is 
less than in swift motions, in the ratio of 
to 10, a proportion between that of 1 and 2, 
and 1 to 3. 
Again, charging the same piece with equal 
quantities of powder, and balls of the same 
weight, and firing three times at the pendu- 
lum, placed at 25 feet distance from the 
mouth of the piece, the medium of the velo- 
cities with which the ball impinged was 
1690 feet in 1'". Then removing the piece 
175 feet from the pendulum, the velocity of 
the ball, at a medium of five shots, was 1300 
feet in l". Whence the ball, in passing 
through 150 feet of air, lost a velocity of 
about 390 feet in 1 and the resistance, 
computed from these numbers, comes put 
something more than in the preceding in- 
stance, amounting to between 11 and 12 
pounds avoirdupoise: whence, according to 
these experiments, the resisting power of 
the air to swift motions is greater than in 
slow ones, in a ratio which approaches 
nearer to the ratio of 3 to 1, than in the 
preceding experiments. 
Having thus ascertained the resistance to 
31 velocity of near 1700 feet in 1 ", he next 
proceeded to examine this resistance iit 
smaller velocities : the pendulum being 
placed at 25 feet distance, was fired at live 
times, and the mean velocity with which 
the ball impinged was 1180 feet in 1". 
Then removing the pendulum to the dis- 
tance of 250 feet, the medium velocity of 
five shot at this distance, was 950 feet in l""; 
whence the ball, in passing through 225 
feet of air, lost a velocity of 230 feet iu 1'", 
and as it passed through that interval in 
about ^ of 1 "", the resistance to the middle 
velocity will come out to be near 33i times 
the gravity of the ball, or 216. lOoz. avoir- 
dupoise. Now the resistance to the same 
velocity, according to the laws observed in 
slower motions, amounts to ^ of the same 
quantity ; whence in a velocity of 1065 feet 
in l", (the medium of 1180 and 950) the 
resisting power of the air is augmented in no 
greater proportion than of 11 to 7 ; where- 
as in greater degrees of velocity, as before, 
it amounted very near the ratio of 3 to 1. 
That this resisting power of the air to 
swift motions is very sensibly increased be- 
yond what Sir Isaac’s theory for slow mo- 
tions makes it, seems hence to be evident. 
It being, as has been said, in musket, or 
cannon-shot, with their full charge of pow- 
der, nearly three times the quantity assign- 
ed by that theory. 
The resistance of a bullet of three quar- 
ters of an inch diameter, moving in air with 
a velocity of 1670 feet in 1", amounting, as 
we said, to 1 015. the resistance of a cannon- 
ball of 2416. fired with its full charge of 
powder, and thereby moving with a velo- 
city of 1650 feet in l"", may hence be de- 
termined. For the velocity of the cannon- 
ball being nearly the same as the musket-bul- 
let, and its surface above 54 times greater, 
it follows that the resistance on the cannon- 
ball will amount to more than 54016. which 
is near 23 times its own weight. And from 
hence it appears how rash and erroneous 
the opinion of those is, who neglect the 
consideration of the resistance of the air as 
of no importance in the doctrine of pro- 
jectiles. See Robins’s Tracts; Hutton’s Dic- 
tionary, article Resistance. 
RESOLUTION, or Solution, in ma- 
thematics, is an orderly enumeration of 
several things to be done, to obtain what is 
required in a problem. 
Resolution, in algebra, or algebraical 
resolution, is of two kinds ; the one practis- 
ed in numerical problems, the other in geo- 
metrical ones. 
In resolving a numerical problem alge» 
