81. In the last three lectures we considered forces in the abstract; we
saw how they are to be represented by straight lines, how compounded
together and how decomposed into others; we have explained what is
meant by forces being in equilibrium, and we have shown instances
where the forces lie in the same plane or in different planes, and
where they intersect or are parallel to each other. These subjects are
the elements of mechanics; they form the framework which in this and
subsequent lectures we shall try to present in a more attractive garb.
We shall commence by studying the most remarkable force in nature, a
force constantly in action, and one to which all bodies are subject, a
force which distance cannot annihilate, and one the properties of which
have led to the most sublime discoveries of human intellect. This is
the force of gravity.
82. If I drop a stone from my hand, it falls to the ground. That which
produces motion is a force: hence the stone must have been acted upon
by a force which drew it to the ground. On every part of the earth’s
surface experience shows that a body tends to fall. This fact proves
that there is an attractive force in the earth tending to draw all
bodies towards it.
[Illustration: FIG. 25.]
83. Let A B C D (Fig. 25) be points from which stones are let fall,
and let the circle represent the section of the earth; let P Q R S be
the points at the surface of the earth upon which the stones will drop
when allowed to do so. The four stones will move in the directions of
the arrows: from A to P the stone moves in an opposite direction to
the motion from C to R; from B to Q it moves from right to left, while
from D to S it moves from left to right. The movements are in different
directions; but if I produce these directions, as indicated by the
dotted lines, they each pass through the centre O.
84. Hence each stone in falling moves towards the centre of the earth,
and this is consequently the direction of the force. We therefore
assert that the earth has an attraction for the stone, in consequence
of which it tries to get as near the earth’s centre as possible, and
this attraction is called the force of gravitation.
85. We are so excessively familiar with the phenomenon of seeing bodies
fall that it does not excite our astonishment or arouse our curiosity.
A clap of thunder, which every one notices, because much less frequent,
is not really more remarkable. We often look with attention at the
attraction of a piece of iron by a magnet, and justly so, for the
phenomenon is very interesting, and yet the falling of a stone is
produced by a far grander and more important force than the force of
magnetism.
86. It is gravity which causes the weight of bodies. I hold a piece of
lead in my hand: gravity tends to pull it downwards, thus producing a
pressure on my hand which I call _weight_. Gravity acts with slightly
varying intensity at various parts of the earth’s surface. This is due
to two distinct causes, one of which may be mentioned here, while the
other will be subsequently referred to. The earth is not perfectly
spherical; it is flattened a little at the poles; consequently a body
at the pole is nearer the general mass of the earth than a body at the
equator; therefore the body at the pole is more attracted, and seems
heavier. A mass which weighs 200 lbs. at the equator would weigh one
pound more at the pole: about one-third of this increase is due to the
cause here pointed out. (See Lecture XVII.)
87. Gravity is a force which attracts every particle of matter; it
acts not merely on those parts of a body which lie on the surface, but
it equally affects those in the interior. This is proved by observing
that a body has the same weight, however its shape be altered: for
example, suppose I take a ball of putty which weighs 1 lb., I shall
find that its weight remains unchanged when the ball is flattened into
a thin plate, though in the latter case the surface, and therefore the
number of superficial particles, is larger than it was in the former.