503. The apparatus by which this important truth maybe demonstrated is
shown in Fig. 67. A part of it has been already employed in performing
the experiment of Galileo, but two other parts must now be used which
will be briefly explained.
504. At A a pendulum is shown which vibrates once every second; it
need not be connected with any clockwork to sustain the motion, for
when once set vibrating it will continue to swing some hundreds of
times. When this pendulum is at the middle of its swing, the bob
just touches a slender spring, and presses it slightly downwards.
The electric current which circulates about the magnets G (Art. 489)
passes through this spring when in its natural position; but when the
spring is pressed down by the pendulum, the current is interrupted.
The consequence is that, as the pendulum swings backwards and forwards,
the current is broken once every second. There is also in the circuit
an electric alarm bell C, which is so arranged that, when the current
passes, the hammer is drawn from the bell; but, when the current
ceases, a spring forces the hammer to strike the bell. When the circuit
is closed, the hammer is again drawn back. The pendulum and the bell
are in the same circuit, and thus every vibration of the pendulum
produces a stroke of the bell. We may regard the strokes from the bell
as the ticks of the pendulum rendered audible to the whole room.
505. You will now understand the mode of experimenting. I draw the
pendulum aside so that the current passes uninterruptedly. An iron
ball is attached to one of the electro-magnets, and it is then gently
hoisted up until the height of the ball from the ground is about 16'.
A cushion is placed on the floor in order to receive the falling body.
You are to look steadily at the cushion while you listen for the
bell. All being ready, the pendulum, which has been held at a slight
inclination, is released. The moment the pendulum reaches the middle
of its swing it touches the spring, rings the bell, breaks the current
which circulated around the magnet, and as there is now nothing to
sustain the ball, it drops down to the cushion; but just as it arrives
there, the pendulum has a second time broken the electric circuit, and
you observe the falling of the ball upon the cushion to be identical
with the second stroke of the bell. As these strokes are repeated at
intervals of a second, it follows that the ball has fallen 16' in one
second. If the magnet be raised a few feet higher, the ball may be seen
to reach the cushion after the bell is heard. If the magnet be lowered
a few feet, the ball reaches the cushion before the bell is heard.
506. We have previously shown that the space is proportional to the
square of the time. We now see that when the time is one second, the
space is 16 feet. Hence if the time were two seconds, the space would
be 4 × 16 = 64 feet; and in general the space in feet is equal to 16
multiplied by the square of the time in seconds.
507. By the help of this rule we are sometimes enabled to ascertain
the height of a perpendicular cliff, or the depth of a well. For this
purpose it is convenient to use a stop-watch, which will enable us to
measure a short interval of time accurately. But an ordinary watch will
do nearly as well, for with a little practice it is easy to count the
beats, which are usually at the rate of five a second. By observing the
number of beats from the moment the stone is released till we see or
hear its arrival at the bottom, we determine the time occupied in the
act of falling. The square of the number of seconds (taking account of
fractional parts) multiplied by 16 gives the depth of the well or the
height of the cliff in feet, provided it be not high.