IX
tralized and the whole body may be supported, or the point,
round which the molecules of a body are equally arranged.
If the mass of a body is not homogeneous, the centre of gravity
will be found in the direction of those parts possessing the
greatest specific weight.
§ 27. The way in which this point may be found. 95. If
the mass of a body is homogeneous and its substance equally
distributed, the centre of gravity may be decided by mathe
matical calculations, it will be
1) For a Triangle in the point of intersection of two lines
drawn from two corners to the middle of the opposite sides.
2) For a three-edged Pyramid in the point of intersection
of two lines drawn from two corners to the centre of gravity of
the opposite triangles.
3) For a Prism in the middle of a line connecting the cen
tres of gravity of both bases; hence for a cylinder in the middle
of its axis.
4) For a Circle in its centre.
5) For an Arc on its besecting radius at a distance from the
centre of the circle equal to SR/B (B being the arc, S the chord
belonging to it and R the radius).
For some bodies the centre of gravity lies outside their
masses (in a hollow ball, a hoop, an empty cask etc.).
Remark, Archimedes was the first physicist, who decided the centre
of gravity by mathematical operations.
§ 28 Stable, unstable and neutral equilibrium, as seen
in the pendulum of a clock, in a stick balanced upright on the
finger, and in a wheel. 95.
When the centre of gravity is supported the action of gravity
is neutralized and the body stands firm or remains in equili
brium. 96–108.
