656. We have learned to regard the elliptic motion in the conical
pendulum as compounded of two vibrations. The importance of the
composition of vibrations justifies us in examining this subject
experimentally in another way. The apparatus which we shall employ is
represented in Fig. 95.
A is a ball of cast iron weighing 25 lbs., suspended from the tripod by
a cord: this ball itself forms the support of another pendulum, B. The
second pendulum is very light, being merely a globe of glass filled
with sand. Through a hole at the bottom of the glass the sand runs out
upon a drawing-board placed underneath to receive it.
[Illustration: FIG. 95.]
Thus the little stream of sand depicts its own journey upon the
drawing-board, and the curves traced out thus indicate the path in
which the bob of the second pendulum has moved.
[Illustration: FIG. 96.]
657. If the lengths of the two pendulums be equal, and their vibrations
be in different planes, the curve described is an ellipse, passing
at one extreme into a circle, and at the other into a straight line.
This is what we might have expected, for the two vibrations are each
performed in the same time, and therefore the case is analogous to that
of the conical pendulum of Art. 648.
658. But the curve is of a very different character when the cords
are unequal. Let us study in particular the case in which the second
pendulum is only one-fourth the length of the cord supporting the
iron ball. This is the experiment represented in Fig. 95. The form of
the path delineated by the sand is shown in Fig. 96. The arrowheads
placed upon the curve show the direction in which it is traced. Let us
suppose that the formation of the figure commences at A; it then goes
on to B, to O, to C, to D, and back to A: this shows us that the bob
of the lower pendulum must have performed two vibrations up and down,
while that of the upper has made one right and left. The motion is thus
compounded of two vibrations at right angles, and the time of one is
half that of the other.
The time of vibration is proportional to the square root of the
length; and, since the lower pendulum is one-fourth the length of the
upper, its time of vibration is one-half that of the upper. In this
experiment, therefore, we have a confirmation of the law of Art 605.
LECTURE XX.
_THE MECHANICAL PRINCIPLES OF A CLOCK._
Introduction.—The Compensating Pendulum.—The
Escapement.—The Train of Wheels.—The Hands.—The
Striking Parts.