(150.) An enquiry is here suggested: does the direction of the
equivalent force thus determined depend on the position of the body
with respect to the surface of the earth, and how is the direction
of the equivalent force affected by a change in that position? This
question may be at once solved if the body be suspended by different
points, and the directions which the suspending thread takes in each
case relatively to the figure and dimensions of the body examined.
The body being suspended in this manner from any point, let a small
hole be bored through it, in the exact direction of the thread, so that
if the thread were continued below the point where it is attached to
the body, it would pass through this hole. The body being successively
suspended by several different points on its surface, let as many small
holes be bored through it in the same manner. If the body be then cut
through, so as to discover the directions which the several holes have
taken, they will be all found to cross each other at one point within
the body; or the same fact may be discovered thus: a thin wire, which
nearly fills the holes being passed through any one of them, it will be
found to intercept the passage of a similar wire through any other.
This singular fact teaches us, what indeed can be proved by
mathematical reasoning without experiment, that there is _one_ point in
every body through which the single force, which is equivalent to the
gravitation of all its particles, must pass, in whatever position the
body be placed. This point is called _the centre of gravity_.
(151.) In whatever situation a body may be placed, the centre of
gravity will have a tendency to descend in the direction of a
line perpendicular to the horizon, and which is called the _line
of direction_ of the weight. If the body be altogether free and
unrestricted by any resistance or impediment, the centre of gravity
will actually descend in this direction, and all the other points of
the body will move with the same velocity in parallel directions,
so that during its fall the position of the parts of the body, with
respect to the ground, will be unaltered. But if the body, as is most
usual, be subject to some resistance or restraint, it will either
remain unmoved, its weight being expended in exciting pressure on the
restraining points or surfaces, or it will move in a direction and
with a velocity depending on the circumstances which restrain it.
Public-domain text, read in full here on John Shaqi.
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