s to be reduced to what it would
be were it removed to a distance of 4,000 miles. This can fortunately be
effected by a simple calculation depending upon the general law that the
intensity of gravitation varies inversely as the square of the distance.
We can thus, partly by calculation and partly by experiment, compare the
intensity of the attraction of the leaden sphere with the attraction of
the earth. It is known that the attractions are proportional to the
masses, so that the comparative masses of the earth and of the leaden
sphere have been measured; and it has been ascertained that the earth is
about half as heavy as a globe of lead of equal size would be. We may
thus state finally that the mass of the earth is about five and a half
times as great as the mass of a globe of water equal to it in bulk.

In the chapter on Gravitation we have mentioned the fact that a body let
fall near the surface of the earth drops through sixteen feet in the
first second. This distance varies slightly at different parts of the
earth. If the earth were a perfect sphere, then the attraction would be
the same at every part, and the body would fall through the same
distance everywhere. The earth is not round, so the distance which the
body falls in one second differs slightly at different places. At the
pole the radius of the earth is shorter than at the equator, and
accordingly the attraction of the earth at the pole is greater than at
the equator. Had we accurate measurements showing the distance a body
would fall in one second both at the pole and at the equator, we should
have the means of ascertaining the shape of the earth.

It is, however, difficult to measure correctly the distance a body will
fall in one second. We have, therefore, been obliged to resort to other
means for determining the force of attraction of the earth at the
equator and other accessible parts of its surface. The methods adopted
are founded on the pendulum, which is, perhaps, the simplest and
certainly one of the most useful of philosophical instruments. The ideal
pendulum is a small and heavy weight suspended from a fixed point by a
fine and flexible wire. If we draw the pendulum aside from its vertical
position and then release it, the weight will swing to and fro.

For its journey to and fro the pendulum requires a small period of time.
It is very remarkable that this period does not depend appreciably on
the length of the circular arc through which the p