The first rod is cylindrical, about 1-10th of an inch in diameter, and is surmounted by a spherical bead* which concentrates and reflects the light which falls upon it. The second is a similar rod, upon the upper extremity of which is placed a plate moving on a joint, so that its plane may be rendered either horizontal, oblique, or perpendicular; this plate is adapted to the reception of the objects, which consist of beads differently coloured and arranged on pieces of black card in symmetrical forms. The third is a four-sided prismatic rod, and a similar plate is attached to its extremity for the reception of the same objects. Another rod is fixed at the centre of the board; this is bent to a right angle, and is furnished with a bead similarly to the firstmentioned rod. A small nut and screw is fixed to the board near the lower end of the first rod, in order by pressing upon it to render occasionally its rigidity unequal. A hammer, softened by a leather covering, is employed to strike the rods; and a violin-bow is necessary to produce some varieties of effect.

I shall now proceed to describe the different appearances which the rods present when in action, and to give directions for the production of the different effects, following the order in which the rods have been previously mentioned.

curately observed. According to the different ways by which the wire is put in motion, the form of this path is no less diversified and amusing than the multifarious forms of the quiescent lines of vibrating plates discovered by Professor Chladni; and it is, indeed, in one respect even more interesting, as it appears to be more within the reach of mathematical calculation to determine it."

The extremely limited extent of the excursions of a vibrating chord prevents its motions from being distinctly observed by the naked eye, but as the rods employed in the present experiments can extend their excursions to nearly two inches, and as the means employed greatly increase the intensity of the light, the phenomena are exhibited in a far more evident manner.

*The only beads well adapted for this purpose are made of extremely thin glass silvered on the interior surface, and about one-sixth of an inch in diameter; they are to be obtained at the shops under the name of steel beads. The protuberances at the apertures must be removed or blackened, otherwise the reflections from them will render the images confused. To produce the coloured tracks, these beads must be coated with transparent colours, such as are ordinarily used for painting on glass; the light will then be reflected through the coloured surface; but in beads made of coloured glass, the reflection being made from the external surface, shows only white light. The bead is cemented into a small brass cup screwed to the top of the wire.

No. 1. On causing the entire rod to vibrate, so that its lowest sound be produced *, as it is seldom that the motions of a cylindrical rod can be confined to a plane, the vibrations will almost always be combined with a circular motion. When the pressure on the fixed end is exerted on two opposite points, and the rod put in motion in the direction of the pressure, the following progression in the changes of form will be distinctly observed: the track will commence as a line, and almost immediately open into an ellipse, the lesser axis of which will gradually extend as the larger axis diminishes, until it becomes a circle; what was before the lesser will then become the larger axis, and thus the motions will alternate until, from their

*The most simple mode of vibration of a rod vibrating transversely, when one of its extremities is fixed and the other is free, is that in which the entire rod makes its vibrations alternately on each side of the axis, which is nowhere intersected by the curve, but only touched at the fixed end. This gives the gravest sound which can be produced from the rod. In the other modes of vibration, the axis is intersected by the curve 1, 2, 3, or more times. The best means to command the production of these sounds is to touch a node of vibration lightly with the finger, and to put a vibrating part in motion by a violin-bow. In the second sound, the number of vibrations is to that of the first, as 5:22, or as 25:4; the difference of the sounds is, therefore, two octaves and an augmented fifth. Separating the first sound from the series, the number of the vibrations of all the others will be to one another as the squares of the numbers 3, 5, 7, 9, &c.; the third, in which there are three nodes, will therefore exceed the second by an octave and an augmented fourth; in the fourth, the acuteness will be augmented by nearly an octave; in the fifth, by nearly a major sixth, &c. To reduce to the same pitch all the proportions of the sounds which such a rod is capable of producing, I shall regard the sound corresponding with the most simple motion as the C one octave lower than the lowest of the piano-forte; the proportions of the sounds will then be

The possible series of sounds, regarding the fundamental as unity, will therefore be-1, 61, 1711, 34, 561, &c.; or expressed in integral numbers-36, 225, 625, 1225, 2025, &c.-CHLADNI, Traité d'Acoustique, p. 91.

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decreasing magnitudes, they cease to be visible. In the case just described the ellipses make a right angle with each other; but by altering the direction of the motion, so as to render it oblique to the direction of the pressure, they may be made to intersect under any required angle, and when this angle = 0 the motion will be merely vibratory.

Every single sound formed by the subdivisions of the rod will present similar appearances, but the excursions will be smaller as the sound is higher, or, which is the same thing, as the number of the vibrations increases.

In the most simple case of the co-existence of two sounds, shown by putting the entire rod in motion, and producing also a higher sound by the friction of a bow; the original figure will

appear waved or indented, and as unity is to the number of indentations, so will the number of vibrations in the lower sound be to the number in the higher sound. On varying the mode of excitation, by striking the rod in different parts and with different forces, very complicated and beautiful curvilinear forms may be obtained: some of these are represented by the opposite figures.

Placing the hand on the lower part of the rod, below the place at which it is excited, the excursions of the motions will rapidly decrease and exhibit spiral figures.

To obtain the figures with brilliancy and distinctness, a single light only should be employed, as that of the sun, a lamp, or a candle; rays of light proceeding from several points, as from a number of candles, or from the reflection of the clouds, occasion the track to be broad and indistinct; but double lights may be employed with effect, provided they be of equal intensity and symmetrically placed; each bead will then describe two similar figures. The appearances, in a bright sunshine, are remarkably vivid and brilliant.

No. 2. Although very beautiful and varied forms may be produced from the motion of a single point, yet the compound figures which are presented by objects, formed by a number of points, offer appearances still more pleasing to the eye.

An object being placed horizontally on the plate, and the rod being put in motion, the mutual intersections of the points, each describing a similar figure, present to the eye complicated, yet symmetrical figures, resembling elegant specimens of engineturning.

When the plate is horizontal, the figures are all in one plane, but if it be inclined or perpendicular, the curves being then made in parallel planes, gives the idea of a solid figure, and in some cases the appearances are particularly striking.

Complementary colours alone should be employed in the objects; for these harmonising together, give greater pleasure to the eye than an injudicious combination of discordant tints: the intensities should be occasionally varied, and colourless light intermingled with the different shades.

No. 3. When this prismatic rod is put in motion, in the direction of either of its sides, the points move only rectilineally, but when the motion is applied in an oblique direction, a variety of compound curves is shown: this rod is principally employed to exhibit the optical phenomena, which will be afterwards mentioned.

No. 4. When a rod is straight, the curve produced by any point describing its motion, is always in the same plane; but in a rod bent to any angle, the two parts moving most frequently in different directions, curves are produced whose parts do not lie in the same plane. A few trials will soon indicate the best way of applying the motion, so as to cause the two parts to vibrate in different directions.

Before the conclusion of this subject, I will avail myself of the opportunity of observing, that the application of this mode of experimenting may be extended to the delineation of every description of curvilinear and angular motion, when the amplitudes of the tracks are not too great; and by this means, it is not improbable that the experimental knowledge of many interesting principles in science may be facilitated.

On the Duplication and Multiplication of Objects.

When dark objects are substituted for luminous ones, their tracks become nearly invisible, and from the longer duration of the visual impression at the limits of vibration, the images are multiplied in proportion to the number of points at which they are retarded. Place horizontally on the rod No. 2, a word printed or written on a piece of card; in the lowest mode of vibration, at the opposite limits of the excursions, two legible images of the word will be distinctly seen, and but an indistinct shade, occasioned by the tracks of the letters, will appear in the intermediate space: the vibratory motion is imperceptible to the eye; the images will, therefore, appear stationary in this respect, but the diminution of the excursions will cause them to approximate very slowly and gradually towards the centre: this diminution operates so gradually, as to allow the images to superpose each other completely at each recurring vibration, without producing any intermingling or confusion.

On placing the object perpendicularly, the two images will