ote 1: It should be pointed out here that the presence of friction
reduces the "amplitude," or distance through which a pendulum moves, at
every swing; so that a true circle cannot be produced by free swinging
pendulums, but only a spiral with coils very close together.]

But the interest of the harmonograph centres round the fact that the
periods of the pendulums can be tuned to one another. Thus, if A be set to
swing twice while B swings three times, an entirely new series of figures
results; and the variety is further increased by altering the respective
amplitudes of swing and phase of the pendulums.

We have now gone far enough to be able to point out why the harmonograph is
so called. In the case just mentioned the period rates of A and B are as 2:
3. Now, if the note C on the piano be struck the strings give a certain
note, because they vibrate a certain number of times per second. Strike the
G next above the C, and you get a note resulting from strings vibrating
half as many times again per second as did the C strings--that is, the
relative rates of vibration of notes C and G are the same as those of
pendulums A and B--namely, as 2 is to 3. Hence the "harmony" of the
pendulums when so adjusted is known as a "major fifth," the musical chord
produced by striking C and G simultaneously.

In like manner if A swings four times to B's five times, you get a "major
third;" if five times to B's six times, a "minor third;" and if once to B's
three times, a "perfect twelfth;" if thrice to B's five times, a "major
sixth;" if once to B's twice, an "octave;" and so on.

So far we have considered the figures obtained by two pendulums swinging in
straight lines only. They are beautiful and of infinite variety, and one
advantage attaching to this form of harmonograph is, that the same figure
can be reproduced exactly an indefinite number of times by releasing the
pendulums from the same points.

[Illustration: FIG. 169.--Goold's Twin Elliptic Pendulum Hamonograph.]

But a fresh field is opened if for the one-direction suspension of pendulum
B we substitute a gimbal, or universal joint, permitting movement in all
directions, so that the pendulum is able to describe a more or less
circular path. The figures obtained by this simple modification are the
results of compounded rectilinear and circular movements.

[Illustration: FIG. 170.--Benham's miniature Twin Elliptic Pendulum
Harmonograph.]

The reader will probably now see