of 16 at the end of the first se- 
nd velocity 128. 
‘of the fourth second it will be 32, and at the 
five seconds it will stop, and begin to fall. 
_ The times of the rise and the subsequent fall are 
II. Since the heights are as the squares of the times 
of the fall or ascent, we have 
eli 1”7:P = 16: 162 
and h = 16 and ,/h = 41, 
by, ae sho. # 22-5 cadion 
16° tom AN 
Wau 
: A heavy body, falling during four seconds, falls 256 
eet. 
A body rising straight upwards 144 feet employs 3 
Seo Because th ‘peigh allah Uiarscigh ie lic ph 
IIL. e heights fallen are a 
portional to the squares of the velocities acquired athe 
end of the fall, we have ' 
‘ $22: 7% = 163% 
16 ea Si 
8 
and, conversely, v = 8 4/ h, and v? = 64h. 
_ All questions co: ing the perpendicular ascents 
and descents of heavy bodies may be solyed by means 
of the two equations 
Lhe v= 32t=gt 
P h=16P = het : 
An easy mode of extempore computations is had, by 
eeenking, that since a heavy body falls 16 feet in a se- 
cond, acquires the velocity 32, it falls 1 foot in 1th 
of a second, and acquires the velocity 8. 
._ In every second of the fall, the velocity is increased 
by 32, and in every foot of the fall, the square of the 
velocity is increased by 64. ; 
_ In many questions, particularly in hydraulics, it is 
_ convenient to have the measures in inches. 
Now, “193: “1 = 386: 27,785. Therefore a heavy 
body by falling one inch acquires the velocity 27,785 
aie aries tin ro aenly alon 
i wity impel a body uni a space 
ual roti fadttised the earth, it wonid geuhaan the 
be , which would enable the body to describe a pa- 
rabola, having the centre of the earth for its focus. If 
projected straight upwards with this velocity it would 
never return. 
~ Now “16: “Earth's phy ro yrctaed feet. Thi 
is the velocity now spoken of. ppose the earth uni- 
ee eatin: and , it to on 3 A eget hae d 
would acquire, ing down this pit, the velocity 
25,866. Trion velocities than either of these can be 
produced by forces which we know. Aurum fulminans 
‘expands with the velocity of at least 42 miles per se~ 
“cond. . 
It does not seem necessary to insist further on the 
‘rectilineal ascents and descents of heavy bodies, and 
therefore we proceed to consider their curvilineal mo- 
tions, gee sk a in any direction that deviates 
‘from the perpendicular. These are the motions which 
‘are understood to form what is called ProsrecriLes. 
These motions are not only interesting to the philo- 
sophical mechanist, as examples of a constant deflect- 
“ing force, and a uniform deflection in parallel lines, but 
also to the artillerist; because the motion of shot and 
GUNNERY. 
‘motion BH. 
‘By the composition of this with the motion CN, the 
571 
shells are cases of this question, which comprehend the Parabolic 
whole of his art. It has therefore been very much eul- Theory of 
tivated; and there is no branch of mechanical philoso. G2" 
phy on which so much has been written, or so many 
experiments made for its improvement. The experi- 
mental cultivation of this branch could scarcely be pro- 
secuted private persons; but, in all the states of 
Europe, there are public establishments for this pur- 
pose, and no expence has been for bringing -to 
ection an art in which the fate of nations un- 
ortunately much dependence. 
But, notwithstanding this liberal encouragement, and 
the numberless volumes which have been published on 
the subject, it cannot be said to have improved much 
as a science since it came out of the hands of its in- 
ventor, and his immediate pupil Tartaglia; and we 
shall be greatly disappointed if we look for that nice 
ent between the results of the most approved 
and what we observe in the flight of great shot 
and shells. The theory, however, is unexceptionable ; 
and the enormous deviations that we see in the actual 
performance of artillery, is owing to the resistance of 
the air. This was long considered as insignificant, 
even after Newton had given us sufficient information 
to the contrary. But the gentlemen of the profession 
made little account of the lations of a private phi- 
losopher, and continued to regulate their theories by 
notions of their own. They have been at last convinced 
of their mistake by the curious experiments and disco« 
veries of Mr Robins, and are improving their practice 
in some measure. But we now And, that the som of 
the motion of heavy bodies through a resisting fluid, is 
one of the most abstruse and difficult tasks that the me- 
chanician can take in hand. 
~ At present, we are about to consider this subject 
merely as'a particular case of motions regulated by 
gravitation, reserving’ the particular consideration of 
the modifications of these motions by the resistance of 
the air, ‘till we shall have made ourselves acquainted 
with the general laws of such resistance. 
Let a body (Plate CCLXXXVI. Fig. 1.) be project- pyar 
ed in any direction AB, which deviates from the verti- ccuxxxvr. 
cal AW. Then it would move on in this direction, Fig. 1. 
and _ equal noe eae, would tse the 
ual spaces AB, » HI, 1K, KL, &c. But su 4 
that when the body is at B it receives an peerrtayt< saad 
impulse in the direction of the vertical BB’, such that 
by this impulse it would describe the line Bd uniform. 
ly in the same time that it would have continued its 
motion along BH: Or, to more accurately, let 
the motion or velocity B 6 be compounded with the 
The body must describe the re ra 
BC of a parallelogram B 4 CH, and, at the end of this 
second moment, it must be in C, in the vertical line 
HCC’, and moving with the velocity BC. Therefore, 
in the third moment it would describe CN, equal to 
BC. But let another impulse in the direction of the 
vertical CC’ generate the velocity C c, equal to B 4. 
body will describe the di CD of the lo- 
Cc DN, and at the end of the third moment 
must be in D, moving in the direction and with the ve- 
lecity CD. It would describe DO equal to CD in the 
fourth moment. Another impulse of gravity;D d, in 
the vertical, and equal to either of the former impulses, 
will make the bed describe DE ; and an equal im- 
pulse E ¢ will deflect the body into EF ; and another 
impulse F f will deflect it into FG, &c. . 
Thus it is plain that the body, by the composition 
of these equal and parallel impulses, will describe the 
