DYNAMICS. 
Cqnal to that which it had acquired on reach- 
ing the bottom of the curve. Therefore a 
body falling from O, fig. 8, to tire bottom 
P of the ciirve OPS, would have power 
to reascend (excluding friction) to S, which 
is level with O; and it would rise from 
P to S in the same space of time it occu- 
pied in falling from O to P; in either case 
the time occupied would be the same as 
from X to P. When treating of the pen- 
dulum this will be more obviously demon- 
strated. 
Tt was for a long time supposed that a 
body would move more rapidly in a direct 
line, not being vertical, than b}' any other 
course ; but it has been ascertained that 
any curve, not exceeding 60 degrees, is a 
quicker descent than its chord ; and that a 
cui-ve of 90 degrees is a quicker descent 
than any tangent laying between the same 
parallels. Thus, in fig. 9, the curve ABC 
is of quicker descent than the chord A C, 
and the curve M A B C gives a quicker de- 
scent than the tangent F G, or H I, or 
K L, laying between the same parallels 
M K, and C D. 
With regard to the motions of projec- 
tiles, we refer the reader to that article. 
Of central forces we have already given 
an ai-ticle, but shall observe here, in ad- 
dition, that all bodies, when put in motion, 
would preserve their respective velocities, 
and their original directions, were they not 
acted upon by other forces. When a force 
acts equally for a limited distance, and then 
is superseded by the actions of another 
force, the body will describe a polygon 
in its track ; but if the original force be 
gradually weakened, the body will then 
describe a curve, bending towards the 
centre of attraction, resulting from the 
operation of a deflecting force, which, 
by its pressure, causes the body to bend 
from its original direction. When a body is 
constantly attracted towards a centre, it is 
under the influence of a centripetal force ; 
and when it is disposed to fly from that cen- 
tre, it is under the bias of a centrifugal 
force. These two latter constitute what 
are termed central forces. The projectile 
force is the original direction of an impelled 
body, forming a tangent with the curve 
occasioned by the deflecting force. The 
track of a body under the influence of a 
centripetal force, is called its trajectory, or 
orbit. The radius vector is a line drawn 
from the centre to which the force is re- 
ferred, or wherein it is supposed to act, to 
any point in the trajectory where the body 
is found. A body moving regularly on a 
trajectory, or orbit, which returns into it- 
self, is, on its return to the incipient point 
whence the motion began, said to have 
made a period ; and the time occupied is 
called its periodical time. It must be under- 
stood, that a body can neither set itself in 
motion, nor avert its own course ; such 
effects must be the result of forces exteriorly 
applied ; also we must state, that the mo- 
tion of each body is naturally in a right 
line, but by the impulse of some one or 
more powers, its course will deviate into a 
curve. Thus a pebble in a sling, or a full 
glass of water, placed within a hoop that 
is turned swiftly round, will follow the 
course of the sling or hoop, respectively; 
but when liberated, or improperly check- 
ed, they will fly off in a right line, which 
they must preserve, if not opposed by the 
air, &c. 
We invariably find, that, when a boat is 
pushed off from the shore, a certain bias 
towards the place quitted is felt by every 
person on board. If any thing should be 
overset at that instant, unless pressed tOr 
wards any other point, it will fall towards 
that shore. On arriving at the opposite 
bank, if the boat is allowed to run against 
it, a disposition to fall towards that bank 
will be manifested by every person, and by 
every matter, at liberty, within the boat. 
Hence we find, that all loodies at rest are 
disposed to remain so ; and that, when bo- 
dies are set in motion, they would continue 
to move, were they not obstructed by ei- 
ther a mechanical, or an invisible, agent. 
All bodies moving in orbits have a dispo- 
sition to fly out of them ; and those which 
describe orbits of tiie smallest diameter have 
rotatory motions quicker than those which 
take a greater range. If one body moves 
round another, both will describe curves 
round their common centre of gravity. The 
centrifugal force of a revolving body is in 
direct proportion to the quantity of matter, 
multiplied into the velocity. The centri- 
petal forces in circles are as the squares of 
the velocities directly, and of the radii in- 
versely ; therefore when the centripetal 
force, and the distance from the centre are 
given, the velocity is given. The mutual 
attraction of bodies does not affect their 
centre of gravity : and if, while two bodies 
act on each other, they be projected in op- 
posite and parallel directions, with velocities 
in proportion to their respective distances 
from the centre of gravity, they will de- 
scribe similar figures around that centre. It 
