THE KALEIDOPHONE.

133

into an ellipse, passing into a circle, and then again through a second ellipse back to a straight line. This is due to the fact that a rod held thus in a vice vibrates not only in the direction in which it is drawn aside, but also at right. angles to this direction. The curve is due to the combination of two rectangular vibrations. I now wish to show you, that while the rod is thus swinging as a whole it may also divide into vibrating parts. By properly drawing

FIG. 53.

a violin bow across the needle I obtain this serrated circle, fig. 53, a number of small undulations being superposed upon the larger one. You moreover hear a musical tone, which you did not hear when the rod vibrated as a whole only; its oscillations, in fact, were then too slow to excite such a tone. The vibrations which produce these sinuosities, and which correspond to the first division of the rod, are executed with about 6 times the rapidity of the vibrations of the rod swinging as a whole. Again I draw the bow; the note rises in pitch, the serrations run more closely together, forming on the screen a luminous ripple more minute and, if possible, more exquisitely beautiful than the last one, fig. 54. Here we have the second division of the rod, the sinuosities of which correspond to 1713 times its rate of vibration as a whole. Thus every change in the sound of the rod is accompanied by a change of the figure upon the screen.

FIG. 54.

The rate of vibration of the rod as a whole, is to the rate corresponding to its first division, nearly as the square of 2 is

* Chladni also observed this compounding of vibrations, and executed a series of experiments, which, in their developed form, are those of the kaleidophone. The composition of vibrations will be studied at some length in a subsequent lecture.

to the square of 5, or as 4:25. From the first division onwards the rates of vibration are approximately proportional to the squares of the series of odd numbers 3, 5, 7, 9, 11, &c. Supposing the vibrations of the rod as a whole to number 36, then the vibrations corresponding to this and to its successive divisions would be expressed approximately by the following series of numbers :

36, 225, 625, 1225, 2025, &c.

In fig. 55, a, b, c, d, e, are shown the modes of division corresponding to this series of numbers. You will not fail to observe that these overtones of a vibrating rod rise far more rapidly in pitch than the harmonics of a string.

Other forms of vibration may be obtained by smartly striking the rod with the finger near its fixed end. In fact an almost infinite variety of luminous scrolls can be thus produced, the beauty of which may be inferred from the subjoined figures first obtained by Mr. Wheatstone. They may be produced by illuminating the bead with sunlight, or with the light of a lamp or candle. The scrolls, moreover, may be doubled by employing two candles instead of one. Two spots of light then appear, each of which describes its own luminous line when the knitting needle is set in vibration.

In a subsequent lecture we shall

TRANSVERSE VIBRATIONS OF RODS FREE AT BOTH ENDS. 135

become acquainted with Mr. Wheatstone's application of his method to the study of rectangular vibrations.

From a rod or bar fixed at one end, we will now pass to rods or bars free at both ends; for such an arrangement has also been employed in music. By a method afterwards to be described, Chladni, the father of modern acoustics, determined experimentally the modes of vibration possible to such bars. The simplest mode of division here possible occurs when the rod is divided by two nodes

*

into three vibrating parts. This mode is easily illustrated by this flexible box ruler, six feet long. Holding it at about twelve inches from its two ends between the forefinger and thumb of each hand, and shaking it, or causing its centre to be struck, it vibrates, the middle segment forming a shadowy spindle, and the two ends forming fans. The shadow of the ruler on the screen renders the mode of vibration still more evident. In this case the distance of each node from the end of the ruler is about one-fourth of the distance between the two nodes. In its second mode of vibration the rod or ruler is divided into four vibrating parts by three nodes. In fig. 57, 1 and 2, these respective modes

of division are shown. Looking at the edge of the bar 1, the dotted lines a a', b b' show the manner in which the segments bend up and down when the first division occurs, while c c', d d' show the mode of vibration corresponding to the second division. The deepest tone of a rod free at both ends is higher than the deepest tone of a rod fixed at one end in the proportion of 4:25. Beginning with the first two nodes, the rates of vibration of the free bar rise in the following proportion :

Number of nodes

Numbers to the squares of which the

2, 3, 4, 5, 6, 7.

pitch is approximately proportional 3, 5, 7, 9, 11, 13.
S

Here also we have a similarly rapid rise of pitch to that noticed in the last two cases.

For musical purposes the first division only of a free

rod has been employed. When bars of wood of different lengths, widths, and depths, are strung along a cord which passes through the nodes we have the claque-bois of the French, an instrument now before you, AB, fig. 58. Supporting the cord at one end by a hook k, and holding it at the other in my left hand, I run the hammer h along the series of bars, and produce this agreeable succession of musical tones. Instead of using the cord, the bars may rest at their nodes on cylinders of twisted straw; hence the name strawfiddle sometimes applied to this instrument. Chladni

informs us that it is introduced as a play of bells (Glockenspiel) into Mozart's opera of the Zauberflöte. If, instead of bars of wood, we employ strips of glass, we have the glass harmonica.

From the vibrations of a bar free at both ends, it is easy to pass to the vibrations of a tuning-fork, as analysed by Chladni. Supposing aa, fig. 59, to represent a straight steel bar, with the nodal points corresponding to its first mode of division marked by the transverse dots. Let the bar be bent to the form bb; the two nodal points still remain, but they have approached nearer to each other. The tone