Popular Scientific Recreations in Natural Philosphy, Astronomy, Geology, Chemistry, etc., etc., etc. Gaston Tissandier

shown in fig. 174; we then slightly swing the spoon until we make it touch the edge of the table; the transmission of sound is in consequence so intense that we are ready to believe we are listening to the double diapason of an organ. This experiment explains perfectly the transmission of spoken words by means of the string of a telephone, another contrivance which any one may make for himself without any trouble whatever. Two round pieces of cardboard are fitted to two cylinders of tin-plate, as large round as a lamp-glass, and four-and-a-half inches in length. If the two rounds of cardboard are connected by a long string of sixteen to eighteen yards, we can transmit sounds from one end to the other of this long cord; the speaker pronouncing the words into the first cylinder, and the listener placing his ear against the other. It is easy to demonstrate that sound takes a certain time to pass from one point to another. When one sees in the distance a carpenter driving in a stake, we find that the sound produced by the blow of the hammer against the wood only reaches the ear a few seconds after the contact of the two objects. We see the flash at the firing of a gun, before hearing the sound of the report—of course on the condition that we are at a fairly considerable distance, as already remarked upon.

      Fig. 174.—Conductibility of sound by solid bodies.

      Fig. 175.—Musical glasses.

      We can show the production of the Gamut by cutting little pieces of wood of different sizes, which one throws on to a table; the sounds produced vary according to the size of the different pieces. The same effect may be obtained much better by means of goblets more or less filled with water; they are struck with a short rod, and emit a sound which can be modified by pouring in a greater or less quantity of water; if the performer is gifted with a musical ear, he can obtain, by a little arrangement, a perfect Gamut by means of seven glasses which each give a note (fig. 175). A piece of music may be fairly rendered in this manner, for the musical glasses frequently produce a very pure silvery sound. We will complete the elementary principles of acoustics by describing a very curious apparatus invented by M. Tisley, the Harmonograph. This instrument, which we can easily describe, is a most interesting object of study. The Harmonograph belongs to mechanics in principle, and to the science of acoustics in application. We will first examine the apparatus itself. It is composed of two pendulums, A and B (fig. 176), fixed to suspensions. Pendulum B supports a circular plate, P, on which we may place a small sheet of paper, as shown in the illustration. This paper is fixed by means of small brass clips. Pendulum A supports a horizontal bar, at the extremity of which is a glass tube, T, terminating at its lower extremity with a capillary opening; this tube is filled with aniline ink, and just rests on the sheet of paper; the support and the tube are balanced by a counterpoise on the right. The two pendulums, A and B, are weighted with round pieces of lead, which can be moved at pleasure, so that various oscillations may be obtained. The ratio between the oscillations of the two pendulums may be exactly regulated by means of pendulum A carrying a small additional weight, the height of which may be regulated by means of a screw and a small windlass. If we give to pendulum A a slight movement of oscillation, the point of tube T traces a straight line on the paper placed in P; but if we move pendulum B, the paper also is displaced, and the point of tube T will trace curves, the shape of which varies with the nature of the movement of pendulum B, the relation between the oscillations of the two pendulums, etc. If the pendulums oscillate without any friction the curve will be clear, and the point will pass indefinitely over the same track, but when the oscillations diminish, the curve also diminishes in size, still preserving its form, and tending to a point corresponding with the position of repose of the two pendulums. The result is therefore that the curves traced by the apparatus, of which we produce three specimens (figs. 177, 178, 179), are traced in a continuous stroke, commencing with the part of the greatest amplitude.

      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.

      Fig. 177.—Ratio 1:2. Fig. 178.—Ratio 2:3.

      Fig. 179.—Ratio 1:2 and a fraction.

      Fig. 180. Construction of the Harmonograph. Fig. 181.

      Fig. 182.—Method of constructing an Harmonograph.

      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.