[Illustration: FIG. 82.]
590. We first experiment with a pendulum on a large scale. Our lecture
theatre is 32 feet high, and there is a wire suspended from the ceiling
27' long; to the end of this a ball of cast iron weighing 25 lbs. is
attached. This wire when at rest hangs vertically in the direction O C
(Fig. 82).
I draw the ball from its position of rest to A; when released, it
slowly returns to C, its original position; it then moves on the other
side to B, and back again to my hand at A. The ball—or to speak more
precisely, the centre of the ball—moves in a circle, the centre being
the point O in the ceiling from which the wire is suspended.
591. What causes the motion of the pendulum when the weight is
released? It is the force of gravity; for by moving the ball to A I
raise it a little, and therefore, when I release it gravity compels it
to return to C it being the only manner in which the mode of suspension
will allow it to fall. But when it has reached its original position
at C, why does it continue its motion?—for gravity must be acting
against the ball during the journey from C to B. The first law of
motion explains this. (Art. 485). In travelling from A to C the ball
has acquired a certain velocity, hence it has a tendency to go on, and
only by the time it has arrived at B will gravity have arrested the
velocity, and begin to make it descend.
592. You see, the ball continues moving to and fro—oscillating, as it
is called—for a long time. The fact is that it would oscillate for
ever, were it not for the resistance of the air, and for some loss of
energy at the point of suspension.
593. By the time of an oscillation is meant the time of going from A to
B, but not back again. The time of our long pendulum is nearly three
seconds.
594. With reference to the time of oscillation Galileo made a great
discovery. He found that whether the pendulum were swinging through
the arc A B, or whether it had been brought to the point A´, and was
thus describing the arc A´ B´, the time of oscillation remained nearly
the same. The arc through which the pendulum oscillates is called its
amplitude, so that we may enunciate this truth by saying that _the
time of oscillation is nearly independent of the amplitude_. The means
by which Galileo proved this would hardly be adopted in modern days.
He allowed a pendulum to perform a certain number of vibrations, say
100, through the arc A B, and he counted his pulse during the time; he
then counted the number of pulsations while the pendulum vibrated 100
times in the arc A´ B´, and he found the number of pulsations in the
two cases to be equal. Assuming, what is probably true, that Galileo’s
pulse remained uniform throughout the experiment, this result showed
that the pendulum took the same time to perform 100 vibrations, whether
it swung through the arc A B, or through the arc A´ B´. This discovery
it was which first suggested the employment of the pendulum as a means
of keeping time.
595. We shall adopt a different method to show that the time does
not depend upon the amplitude. I have here an arrangement which is
represented in Fig. 83. It consists of two pendulums A D and B C, each
12' long, and suspended from two points A B, about 1' apart, in the
same horizontal line. Each of these pendulums carries a weight of the
same size: they are in fact identical.
[Illustration: FIG. 83.]
596. I take one of the balls in each hand. If I withdraw each of them
from its position of rest through equal distances and then release
them, both balls return to my hands at the same instant. This might
have been expected from the identity of the circumstances.
597. I next withdraw the weight C in my right hand to a distance of
1', and the weight D in my left hand to a distance of 2', and release
them simultaneously. What happens? I keep my hands steadily in the same
position, and I find that the two weights return to them at the same
instant. Hence, though one of the weights moved through an amplitude
of 2' (C E) while the other moved through an amplitude of 4' (D F),
the times occupied by each in making two oscillations are identical.
If I draw the right-hand ball away 3', while I draw the left hand only
1' from their respective positions of rest, I still observe the same
result.
598. In two oscillations we can see no effect on the time produced by
the amplitude, and we are correct in saying that, when the amplitude
is only a small fraction of the length of the pendulum, its effect is
inappreciable. But if the amplitude of one pendulum were very large, we
should find that its time of oscillation is slightly greater than that
of the other, though to detect the difference would require a delicate
test. One consequence of what is here remarked will be noticed at a
later page. (Art. 655.)
599. We next inquire whether the weight which is attached to the
pendulum has any influence upon the time of vibration. Using the 12'
pendulums of Fig. 83, I place a weight of 12 lbs. on one hook and
one of 6 lbs. on the other. I withdraw one in each hand; I release
them; they return to my hand at the same moment. Whether I withdraw
the weights through long arcs or short arcs, equal or unequal, they
invariably return together, and both therefore have the same time of
vibration. With other iron weights the same law is confirmed, and hence
we learn that, besides being independent of the amplitude, the time of
vibration is also independent of the weight.
600. Finally, let us see if the _material_ of the pendulum can
influence its time of vibration. I place a ball of wood on one wire and
a ball of iron on the other; I swing them as before: the vibrations are
still performed in equal times. A ball of lead is found to swing in the
same time as a ball of brass, and both in the same time as a ball of
iron or of wood.
601. In this we may be reminded of the experiments on gravity (Art.
491), where we showed that all bodies fall to the ground in equal
times, whatever be their sizes or their materials. From both cases the
inference is drawn that the force of gravity upon different bodies is
proportional to their masses, though the bodies be made of various
substances. It was indeed by means of experiments with the pendulum
that Newton proved that gravity had this property, which is one of the
most remarkable truths in nature.