38ß Molesworth’s pocket-book
Centre of Gbavity (Homogeneous Substances).
P = The volume of any particle.
d = The distance of P from any given plane.
2 — Sum.
x — The distance of the centre of gravity of the
whole mass from a given plane.
S (P d) P c? -f- P. cZj -f- P2 -f-
X = ----—---------—----i;--r~-----------
2P ~ ”P + PI+P2 + &c.
TO FIND THE CENTRE OF GRAVITY IN A TRIANGLE.
Bisect the base B C at D, and join A D. The
centre of gravity lies in the line
AD at E, DE being Irdof AD;
or bisect each side and join each
apex with, the centre of the oppo-
site side. The intersection of
these lines will give the centre of gravity.
IN A PARALLELOGRAM, OB ANY FOUR-SIDED FIGURE.
In a parallelogram the in-
tersection of the diagonals
gives the centre of gravity.
In any four-sided figure
ABCD draw the diagonals
intersecting at E. Lay off
D F — B E, and join F A,
F 0; then the centre of gra-
vity of the triangle F A C is
also the centre of gravity of
the figure AB CD.
CO-ORDINATES OF THE CENTRE
OF GRAVITY.
1/. _ AB \
C/2A + B
3/ = '
A + B