CENTER. 
distances 6 n t!ie other side of I L, then C c 
vanishes, or the common center of gravity 
of all the bodies falls on the right line I L. 
Hence it is demonstrable that when any 
number of bodies move in right lines with 
uniform motions, their common center of 
gravity moves likewise in a right line with 
an uniform motion; and that the sum of their 
motions estimated in any given direction, is 
precisely the same as if ail the bodies in one 
mass were carried on with the direction and 
motion of their common center of gravity. 
Center of an hyperbola, a point in the 
middle of the transverse axis. 
Center <f magnitude, of any homoge- 
neal body, tlie same with the center of gra- 
vity. 
Center of motion, that point which re- 
mains at rest, while all the other parts of a 
body move about it. And this is the same 
in uniform bodies of the same matter 
throughout, as the ' center of gravity. 
Center of oscillation, that point in a 
pendulum in which, if the weight of the 
several parts thereof were collected, each 
vibration would be performed in the same 
time as when those weiglits are separate. 
This is the point from whence the length of 
a pendulum is measured, which in our lati- 
tude, in a pendulum that swings seconds, is 
39 inches and j|. 
The center of suspension is the point on 
which the pendulum hangs, 
A general rule for finding the center of os- 
cillation. If several bodies be fixed to an 
inflexible rod suspended upon a point, and 
each body be multiplied by the square of 
its distance fronj the point of suspension, 
and then each body be multiplied by its 
distance from tlie same point ; and all tire 
former products vvlien added together, be 
divided by all the latter products added to- 
gether, the quotient which shall arise from 
thence, will he the distance of the center 
of oscillation of these bodies from the said 
point. 
Thus, if C F (fig. 8 ) be a rod qn which 
qre fixed the bodies A, B, D, &c. at the scr 
veral points A, B, D, &c. and if the body 
A be multiplied by the square of the dis- 
tance C A, and B be multiplied by the 
square of the distance C B, and so on for 
(he rest ; and then if the body A he multi- 
plied by the distance C A, and B be multi- 
plied by the distance C B, and so on for the 
rest ; and if the. sum of the products arising 
in f.ie former case be divided by the sum of 
those which arise in tlie latter, the quotient 
will give C Q, the distance of the center of 
oscillation of the bodies A, B, D, &c. from 
the point C. To determine the center of 
oscillation of the rectangle R I H S (fig. 9) 
suspended on the middle point A of the side 
RI, and oscillating about its axis R I. 
Let R I = S H = ff, A P — X, then will 
P p, = d x and the element or the area, 
consequently one weight =:« d x and its 
momentum a xdx. Wherefore s ax^ dx i 
s ax dx=: a : i u x ^ | x, indefinite- 
ly expresses the distance of tiie center 
of oscillation from the axis of oscillation in 
the segment R C D I. If then for x be 
substituted the altitude of the whole rec- 
tangle R S = 6, the distance of the center 
of osciliation from the axis will be found 
= 16 . 
The center of oscillation in an equilateral 
triangle S A H oscillating about its axis 
R I, parallel to the base S H, is found at a 
distance from the vertex A equal to | A E 
the altitude ot the triangle. 
The center of oscillation in an equilateral 
ti-iangle SAH oscillating about its base 
S H, is found at a distance from the ver- 
tex A =:i A E. 
For the centers of oscillation of parabolas 
and curves of the like hind o.scillating about 
their axis parallel to their bases, they are 
found as follows. In the apollonian parabo- 
la, the distance of the center of oscillation 
from the axis = i A E, 
In the cubical paraboloid, the distance of 
the center from the axis A E. In a bi- 
quadratic paraboloid, tlie distance of the 
center from the axis = A E, 
Center of percussion, in a moving body, 
that point wherein the striking force is 
greatest, or that point with which if the 
body strikes against any obstacle, no shock 
shall be felt at the point of suspension.. 
The center of percussion, when the 
striking body revolves round a fixed point, 
is the same with the center of osciliation, 
and consequeutly may be determined by 
the same rule. 
Hence a stick of a cylindrical figure, sup- 
posing the center of motion at the hand, 
will strike the greatest blow at a distance 
about two-thirds of its length from the 
hand. 
The center of percussion is the same with 
the center of gravity, if all the parts of the 
striking body be carried with a parallel 
motion, or with the same celerity. 
Center of a parallelogram, or polygon, 
the point in which its diagonals intersect. 
Center of a sphere, a point in the mid- 
dle, from which all lines drawn to tlie sur- 
