[Illustration:  Fig. 168.—­Simple Rectilinear Harmonograph.]

The bob, or weight, of a pendulum can be clamped at any point on its rod, so that the rate or “period” of swing may be adjusted or altered.  The nearer the weight is brought to the point of suspension, the oftener will the pendulum swing to and fro in a given time—­usually taken as one minute.  From this it is obvious that the rates of swing of the two pendulums can be adjusted relatively to one another.  If they are exactly equal, they are said to be in unison, and under these conditions the instrument would trace figures varying in outline between the extremes of a straight line on the one hand and a circle on the other.  A straight line would result if both pendulums were released at the same time, a circle,[1] if one were released when the other had half finished a swing, and the intermediate ellipses would be produced by various alterations of “phase,” or time of the commencement of the swing of one pendulum relatively to the commencement of the swing of the other.

[Footnote 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.