[Illustration: Fig. 176.—M. Tisley’s Harmonograph.]
By changing the relation and phases of the oscillations we obtain curves of infinitely varied aspect. M. Tisley has a collection of more than three thousand curves, which we have had occasion to glance over, in which we failed to meet with two corresponding figures. The ratio between these curves corresponds with some special class, of which the analyst may define the general characters, but which is outside our present subject. By giving the plate P a rotatory movement, we obtain spiral curves of a very curious effect, but the apparatus is more complicated. Considered from this point of view it constitutes an interesting mechanical apparatus, showing the combination of oscillations, and resolving certain questions of pure mechanics. From the point of view of acoustics it constitutes a less curious object of study. The experiments of M. Lissajons have proved that the vibrations of diapasons are oscillations similar to, though much more rapid than those of the pendulum. We can therefore with this apparatus reproduce all the experiments of M. Lissajons, with this difference, that the movements being slower are easier to study. When the ratio between the _number of vibrations_—we purposely use the term vibration instead of the term oscillation—is a whole number, we obtain figs. 177 and 178. If the ratio is not exact, we obtain fig. 179, which is rather irregular in appearance, corresponding to the distortions noticeable in M. Lissajon’s experiments. Fig. 178 has been traced in the exact ratio 2:3; fig. 177 in the ratio 1:2; and fig. 179 corresponds to the ratio 1:2 and a small fraction, which causes the irregularity of the figure.
[Illustration: Fig. 177.—Ratio 1:2. Fig. 178.—Ratio 2:3.]
[Illustration: Fig. 179.—Ratio 1:2 and a fraction.]
[Illustration: Fig. 180. Construction of the Harmonograph. Fig. 181.]
[Illustration: Fig. 182.—Method of constructing an Harmonograph.]
[Illustration: Fig. 183.—The apparatus completed.]
In considering the harmony of figs. 177 and 178,—the first of which corresponds to the octave, the second to the fifth, whilst fig. 179 corresponds to the disagreeable interval of the ninth,—one is almost tempted to put a certain faith in the fundamental law of _simple ratios_ as the basis of harmony. At first sight this appears beyond doubt, but perhaps musicians would be hardly content with the explanation. M. Tisley’s Harmonograph, it will be seen, is a rather complicated apparatus; and I will now explain how it may be constructed by means of a few pieces of wood. I endeavoured to construct as simple an apparatus as possible, and with the commonest materials, feeling that it is the best means of showing how it is possible for everybody to reproduce these charming curves of musical intervals. Also I completely excluded the employment of metals, and I constructed my apparatus entirely with pieces of wooden rulers, and old cigar boxes. I set to work in the following manner: on the two consecutive sides of a drawing board I fixed four small pieces of wood (fig. 180), side by side in twos, having at the end a small piece of tin-plate forming a groove (fig. 181). In these grooves nails are placed which support the pendulums. The piece of wood is placed on the corner of the table, so that the pendulums which oscillate in two planes at right angles, are in two planes that are sensibly parallel to the sides of the table. The pendulums are made of a thin lath, with two small pieces of wood fixed to them containing some very pointed nails, on which the pendulum oscillates. Fig. 182 gives an illustration. The pendulums have a pin fixed in vertically, which passes through a piece of wood, and by means of a hinge connects the upper ends of the two pendulums. This contrivance of the pin is very useful, and if care is taken to make the hole through the hinge in the form of a double cone, as shown in fig. 182, _c_, it makes a perfect joint, which allows the piece of wood to be freely moved.