659. We come now to the most important practical application of the
pendulum. The vibrations being always isochronous, it follows that,
if we count the number of vibrations in a certain time, we shall
ascertain the duration of that time. It is simply the product of the
number of vibrations with the period of a single one. Let us take a
pendulum 39·139 inches long; which will vibrate exactly once a second
in London, and is therefore called a seconds pendulum (See Art. 607).
If I set one of these pendulums vibrating, and contrive mechanism by
which the number of its vibrations shall be recorded, I have a means of
measuring time. This is of course the principle of the common clock:
the pendulum vibrates once a second and the number of vibrations made
from one epoch to another epoch is shown by the hands of the clock.
For example, when the clock tells me that 15 minutes have elapsed, what
it really shows is that the pendulum has made 60 × 15 = 900 vibrations,
each of which has occupied one second.
660. One duty of the clock is therefore to count and record the number
of vibrations, but the wheels and works have another part to discharge,
and that is to sustain the motion of the pendulum. The friction of
the air and the resistance experienced at the point of suspension are
forces tending to bring the pendulum to rest; and to counteract the
effect of these forces, the machine must be continually invigorated
with fresh energy. This supply is communicated by the works of the
clock, which will be sufficiently described presently.
661. When the weight driving the clock is wound up, a store of energy
is communicated which is doled out to the pendulum in a very small
impulse, at every vibration. The clock-weight is just large enough to
be able to counterbalance the retarding forces when the pendulum has
a proper amplitude of vibration. In all machines there is some energy
lost in maintaining the parts in motion in opposition to friction and
other resistances; in clocks this represents the whole amount of the
force, as there is no external work to be performed.