ith great
accuracy. Let it swing for 10,000 oscillations, and measure the time
that these oscillations have consumed. The arc through which the
pendulum swings may not have remained quite constant, but this does not
appreciably affect the _time_ of its oscillation. Suppose that an error
of a second is made in the determination of the time of 10,000
oscillations; this will only entail an error of the ten-thousandth part
of the second in the time of a single oscillation, and will afford a
correspondingly accurate determination of the force of gravity at the
place where the experiment was made.

Take a pendulum to the equator. Let it perform 10,000 oscillations, and
determine carefully the _time_ that these oscillations have required.
Bring the same pendulum to another part of the earth, and repeat the
experiment. We have thus a means of comparing the gravitation at the two
places. There are, no doubt, a multitude of precautions to be observed
which need not here concern us. It is not necessary to enter into
details as to the manner in which the motion of the pendulum is to be
sustained, nor as to the effect of changes of temperature in the
alteration of its length. It will suffice for us to see how the time of
the pendulum's swing can be measured accurately, and how from that
measurement the intensity of gravitation can be calculated.

The pendulum thus enables us to make a gravitational survey of the
surface of the earth with the highest degree of accuracy. We cannot,
however, infer that gravity alone affects the oscillations of the
pendulum. We have seen how the earth rotates on its axis, and we have
attributed the bulging of the earth at the equator to this influence.
But the centrifugal force arising from the rotation has the effect of
decreasing the apparent weight of bodies, and the change is greatest at
the equator, and lessens gradually as we approach the poles. From this
cause alone the attraction of the pendulum at the equator is less than
elsewhere, and therefore the oscillations of the pendulum will take a
longer time there than at other localities. A part of the apparent
change in gravitation is accordingly due to the centrifugal force; but
there is, in addition, a real alteration.

In a work on astronomy it does not come within our scope to enter into
further detail on the subject of our planet. The surface of the earth,
its contour and its oceans, its mountain chains and its rivers, are for
the physical