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.
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.