ner] Values of oe the time io} Wal¥ee of @s | Vajues of 
; va nae which the sagen by V, or the 
‘the wheel] DUMP OF tine holein the "elocty OF 
cpap ade. | second dise. | "* **! 
Seconds, Metres. Metres. 
ts 8 10 0.3510 402.3 
2 8 10 . 0.3800 871.7 
8 8 10 0.368 $62.5 
4 15 22 0.296 3884.1 
3B. 15 22 0.264 | 430.7 
6 10 18 0.268 345.7 
7 15 16 0.392 $98.8 
8 15 16 0.392 398.8 
9 15 16 0.416 375.8 
10 15 16 0.360 434.3 
In order to afford the means of traversing the discs 
by throwing balls in different directions from 0° to 45°, 
Colonel Grobert gives to each disc a parti 
tal axis, to which a pulley is affixed ; and the rotato) 
motion ——_ unicated by an eee chain to both 
axes, so that they may perform the same number of re- 
volutions in the same pe The supporter of the 
second disc is capable of rising vertically, and fixing it- 
self at different heights. The adjustment of this appa- 
ratus must, however, be attended with great di ty. 
CHAP. I. 
On the Parabolic Theory of Gunnery. * 
In the process of our examination of the motions in 
the solar system, it appears that terrestrial gravity, or 
the heaviness of common sublunary bodies, is only a 
icular case of the mutual tendency of all matter to- 
wards all matter. It further appears, that a body on 
the surface of our globe gravitates in a line that is di- 
rected very nearly to the centre of the earth ; and that 
the intensity of this gravitation is inversely proportional 
to the square of its distance from this centre. 
Bodies let fall, or projected in any direction on the 
surface of this earth, move under the influence of this 
force ; and their motions may be computed from the ge- 
neral doctrines of dynamics in the same manner as we 
computed the motions of the planets. will either 
fall in the direction of gravity, or will rise in the oppo-« 
site direction, or will describe a curve line concave to- 
ward the earth, which will be an ellipsis, parabola, hy- 
perbola, or circle, according as the velocity and direc« 
tion of the projection may have been combined. 
But, in the greatest projections that we can make, 
the force of gravity is so nearly the same in every point 
of the path, that we may suppose it to be ly so, 
without any sensible error, were it ten times greater 
than it is. Therefore in all disquisitions about projec 
tiles, it would be useless affectation to embarrass ours 
selves with the variations. None of our projectiles rise 
a mile in the air, which is about 5, of the mean ra- 
dius of the earth, and will occasion a diminution of gra« 
Coxe equal to ry35, 4 quantity altogether insig- 
t. 
GUNNERY. 
.on this than on any other part of mechani 
569 
For the same reasons, although the directions of 
vity in the different points of the projectile’s fight, ate 
lines converging nearly to the centre of the earth, we 
may consider them as all lel, because none of our 
projectiles fly four miles, which produces a convergency 
of nearly four minutes, a deviation from parallelism 
which needs not be regarded. 
_ In general, therefore, we may consider all such pro- 
a as under the influence of equal gravity acting in 
es e] to the vertical or plumb-line drawn through 
the of projection. This reduces the theory of pro- 
j to a great degree of simplicity. 
"Accordingly, this is the first peo rate of mecha- 
nical phi y which first received improvenient by 
the application of mathematical knowledge. We are 
indebted for this fortunate introduction of mathematics 
into the doctrines of motion, to the celebrated Floren- 
tine, Galileo Galilei. This excellent philosopher read 
his discourses on local motion, about the beginning of 
the 17th century, Those lectures contain the whole of 
this doctrine, nearly in the state in which it continued 
till about the: middle of last century. There is no 
branch of natural philosophy that has met with so much 
assistance and encouragement, it having been consider- 
ed in all nations as the foundation of the art of gunnery; 
an art unfortunately too much connected with the se- 
curity of every nation. It has therefore been ised 
by princes and magistrates—most costly establishments 
have been made for its cultivation ; the mathematicians 
have occupied themselves with its problems, and more 
numerous and expensive volumes have been published 
philoso- 
phy Yet there is none in which so little improvement 
as been made. Galileo’s lessons contain every thing 
that has been done in a scientific way, till M. Robins, in 
1742, gave it a form altogether new. 
We shall first consider the dicular ascents and 
descents of heavy bodies ; and in the next place, their 
curvilineal motion when projected in directions devia. 
ting from the vertical. . 
he motion of a falling body is uniformly accelerated, 
and that of a body thrown straight upward is uniformly 
retarded. 
For the accelerating or retarding force is constant, 
and therefore the motions are such as were considered 
in Dynamics. 
All the characteristic phenomena of these motions 
having already been sufficiently considered, all that is 
wanted for the application to this class of mechanical 
phenomena, is merely one experimental determination 
of the accelerative power of gravity, that is, the veloci- 
ty, or increment of velocity, which gravity will generate 
ina ean acting on it uniformly during some given 
time. ileo, who first demonstrated that an invaria- 
ble gravity must produce a uniformly accelerated mos 
tion, was also among the first who appealed to i 
ment in all inquiries, We now think lightly of this, 
and wonder that a man shall think of another argument 
who has this in his power. But when Galileo began 
to communicate his alee to the world, this was 
the last sw that a philosopher would think of, 
They had received a parcel of topics from their master, 
which had been handed down in the schools durin 
many ages; and from these was every thing accoun’ 
* This valuable Chapter was written by the late John Robison, LL.D. F.R.S.E. It was intended to form a patt of his System of 
Mechanical Philosophy, and was the last 
sion of Mr Murray the proprietor of the 
VOL. X. PART II, 
ction of that eminent philosopher, It is now ' the permis- 
‘SS, and will appear in pater Nae he oy oh hr wie pee now in the prese, 
c 
for the first time, with the 
Parabolic 
Theory of 
Gunnery. 
