at when a body,
such as a stone or stick or bullet, is thrown or projected into the air,
it always falls to the earth again. This is due to the attraction of the
earth and the stone for each other. It has been proved experimentally
that if a stone and a weight are let fall from a height of 16 feet, they
would reach the earth in one second of time. Again, a feather, or cork,
or even a piece of iron would take exactly the same time falling through
the same space, provided that the feather or cork could be screened from
the resistance of the air.

The distance, however, through which a body falls in one second varies
at different parts of the earth's surface, being least at the equator,
and greatest at the North and South Poles. This is accounted for by the
fact that the polar diameter is only 7899 miles, while the equatorial
diameter is 7925 miles, thus the distance from the centre of the earth
to either pole is about 3950 miles, or 13 miles less than the equatorial
radius of the earth. Now the force of gravity decreases upwards from the
earth's surface inversely as the square of the distance from the earth's
centre of gravity, but decreases downwards simply as the distance from
the centre decreases. Thus if a ball were taken down 2000 miles, that is
half the distance to the centre, it would only weigh half-a-pound, while
if it were taken to the centre of the earth, it would have no weight at
all; while a pound weight at the equator would not weigh one pound at
the poles, because it would be nearer the centre of the earth by 13
miles.

Thus a pound weight is not always a pound weight. It varies as we carry
it to different parts of the earth's surface, depending upon its
relation to the centre of the earth for its exact weight. The point
which I wish to make perfectly clear, as it will be necessary for future
reference, is, that there is no such thing as weight apart from the
gravity of the earth; or, if we apply the principle to the solar system,
there is no gravitating force in that system apart from the gravitating
force of the central body, the sun, or the planets and other bodies
which form the solar system.

Let us look at this matter from another standpoint, in order to prove
this truth and make the same perfectly clear. If a pound weight were put
in a spring-balance, then at the surface of the earth it would weigh one
pound. Now, we will suppose that we have taken the weight to a height of
4000 miles above the s