ACOUSTICS.

(Resumed from page 341 and concluded.) Vibration of Springs and Discs.-A glass or metallic rod, when struck at one end, or rubbed in the direction of its length with a wet finger, vibrates longitudinally, like a column of air, by the alternate condensation and expansion of its constituent particles, producing a clear and beautiful musical note of a high pitch, on account of the rapidity with which these substances transmits sound. Rods, surfaces, and, in general, all undulating bodies, resolve themselves into nodes. But, in surfaces, the parts which remain at rest during their vibrations are lines, which are curved or plane according to the substance, its form, and the mode of vibration. If a little fine dry sand be strewed over the surface of a plate of glass or metal, and if undulations be excited by drawing the bow of a violin across its edge, it will emit a musical sound, and the sand will immediately arrange itself in the nodal lines, where alone it will accumulate and remain at rest, because the segments of the surface on each side will be in different states of vibration, the one being elevated while the other is depressed, and as these two motions meet in the nodal lines, they neutralise one another. These lines vary in form and position with the part where the bow is drawn across, and the point by which the plate is held. The motion of the sand shows in what direction the vibrations take place. If they be perpendicular to the surface, the sand will be violently tossed up and down, till it finds the points of rest. If they be tangential, the sand will only creep along the surface to the nodal lines. Sometimes the undulations are oblique, or compounded of both the preceding. If a bow be drawn across one of the angles of a square plate of glass or metal held firmly by the centre, the sand will arrange itself in two straight lines parallel to the sides of the plate, and crossing in the centre, so as to divide it into four equal squares, whose motions will be contrary to each other. Two of the diagonal squares will make their excursions on one side of the plate, while the other two make their vibrations on the other side of it. This mode of vibration produces the lowest tone of the plates.

If the plate be still held by the centre, and the bow applied to the middle of one of the sides, the vibrations will be more rapid, and the tone will be a fifth higher than in the preceding case; now the sand will arrange itself from corner to corner, and will divide the plate into four equal triangles, each pair of which will make their excursions on opposite sides of the plate. The nodal lines and pitch vary not only with the point where the bow is applied but with the point by which the plate is held, which being at rest, necessarily determines the direction of one of the quiescent lines. The forms assumed by the sand in square plates are very numerous, corresponding to all the various modes of vigration.

The lines in circular plates are ever more remarkable for their symmetry, and upon them the forms assumed by the sand may be classed in three systems. The first is the diametrical system, in which the figures consist of diameters dividing the circumference of the plate into equal parts, each of which is in a different state of vibration from those adjacent. Two diameters, for example, crossing at right angles, divide the circumference into four equal parts; three diameters divide it into six equal parts; four divide it into eight, and so on. (fig. 2.) In a metallic plate, these divisions may amount to thirty-six or forty. The next is the concentric system, where the sand arranges itself in circles, having the same centre with the plate; (fig. 3,) and the third is the compound system, where the figures assumed by the sand are compounded of the other two, producing very complicated and beautiful forms, (fig. 4.)

Galileo seems to have been the first to notice the points of rest and motion in the sounding board of a musical instrument; but to Chladni is due the whole discovery of the symmetrical forms of the nodal lines in vibrating plates. Our principal cut of the present Number contains a few of Chladni's figures. The white lines are the forms assumed by the sand, from different nodes of vibration, corresponding to musical notes of different degrees of pitch.

Professor Wheatstone has shown, in a paper read before the Royal Society, in 1833, that all Chladni's figures, and indeed all the nodal figures of vibrating surfaces, result from very simple modes of vibration, oscillating isochronously, and superposed upon each other; the resulting figure varying with the component modes of vibration, the number of the superpositions, and the angles at which they are superposed. For example, if a square plate be vibrating so as to make the sand arrange itself in straight lines parallel to one side of the plate, and if, in addition to this, such vibrations be excited as would have caused the sand to form in lines perpendicular to the first had the plate been at rest, the combined vibrations will make the sand form in lines from corner to corner.

M. Savarts experiments on the vibrations of flat glass rulers are highly interesting. Let a lamina of glass 27 in. 56 long, 0.59 of an inch broad, and 0.06 of an inch in thickness, be held by the edges in the middle with its flat surface horizontal. If this surface be strewed with sand, and set in longitudinal vibration by rubbing its under surface with a wet cloth, the sand on the upper surface will arrange itself in lines parallel to the ends of the lamina, always in one or other of two systems. The long cross lines of fig. 6, show the two systems of nodal lines given by M. Savart's laminæ.

Fig. 6.

Fig. 7.

Although the same one of the two systems will always be produced by the same plate of glass, yet

among different plates of the preceding dimensions, even though cut from the same sheet side by side, one will invariably exhibit one system, and the other the other, without any visible reason for the difference. Now if the positions of these quiescent lines be marked on the upper surface, and if the plate be turned so that the lower surface becomes the upper one, the sand being strewed and vibrations excited as before, the nodal lines will still be parallel to the ends of the lamina, but their positions will be intermediate between those of the upper surface (fig. 7.) Thus it appears that all the motions of one half of the thickness of the lamina, or ruler, are exactly contrary to those of If the the corresponding points of the other half. thickness of the lamina be increased, the other dimensions remaining the same the sound will not vary, but the number of nodal lines will be less. When the breadth of the lamina exceeds the 0.6 of an inch, the nodal lines become curved, and are different on the two surfaces. A great variety of forms are produced by increasing the breadth and changing the form of the surface; but in all, it appears that the motions in one half of the thickness are opposed to those in the other half.

M. Savart also found, by placing small paper rings round a cylindrical tube or rod, so as to rest upon it at one point only, that when the tube or rod is continually turned on its axis in the same direction, the rings slide along during the vibrations, till they come to a quiescent point, where they rest. (fig. 8.) By thus tracing these nodal lines he discovered that they twist in a spiral or corkscrew round rods and cylinders, making one or more turns according to the length; but at certain points, varying in number according to the mode of vibration of the rod, the screw stops, and recommences on the other side, though it is turned in a contrary direction; that is, on one side it is a right-handed screw, on the other a left. The nodal lines in the interior surface of the tube are perfectly similar to those in the exterior, but they occupy intermediate positions. If a small ivory ball be put within the tube, it will follow those nodal lines when the tube is made to revolve on its axis.

Fig. 8 gives the nodal lines on a cylinder, with the paper rings that mark the quiescent points.

In consequence of the facility with which the air communicates undulations, all the phenomena of vibrating plates may be exhibited by sand strewed on paper or parchment, stretched over a harmonica glass, or large bell-shaped tumbler. In order to give due tension to the paper or vellum, it must be wetted, stretched over the glass, gummed round the edges, allowed to dry, and varnished over to prevent changes in its tension from the humidity of the atmosphere. If a circular disc of glass be held concentrically over this apparatus, with its plane parallel to the surface of the paper, and set in vibration by drawing a bow across its edge, so as to make sand on its surface take any of Chladni's figures, the sand on the paper will assume the very same form, in consequence of the vibrations of the disc being communicated to the paper by the air. When the disc is removed slowly in a horizontal direction, the forms on the paper will correspond with those on the disc, till the distance is too great for the air to convey the vibrations. If the disc while vibrating be gradually more and more inclined to the horizon, the figures on the paper will vary by degrees; and when the vibrating disc is perpendicular to the horizon, the sand on the paper will

a

form into straight lines parallel to the surface of the disc, by creeping along it instead of dancing up and down. If the disc be made to turn round its vertical diameter while vibrating, the nodal lines on the paper will revolve, and exactly follow the motion of the disc. It appears from this experiment that the motion of the ærial molecules in every part of a spherical wave, propagated from vibrating body as a centre, are parallel to each other, and not divergent like the radii of a circle. When a slow air is played on a flute near this apparatus, each note calls up a particular form in the sand, which the next note effaces to establish its own. The motion of the sand will even detect sounds that are inaudible. By the vibrations of sand on a drum-head the beseiged have discovered the direction in which a counter-mine was working. M. Savart, who made these beautiful experiments, employed this apparatus to discover nodal lines in masses of air. He found that the air of a room, when thrown into undulations by the continued sound of an organ-pipe, or by any other means, divides itself into masses separated by nodal curves of double curvature, such as spirals, on each side of which the air is in opposite states of vibration. He even traced these quiescent lines going out at an open window, and for a considerable distance in the open air. The sand is violently agitated where the undulations of the air are greatest, and remains at rest in the nodal lines. M. Savart observed, that when he moved his head away from a quiescent line towards the right, the sound appeared to come from the right, and when he moved it towards the left, the sound seemed to come from the left, because the molecules of air are in different states of motion on each side of the quiescent line,

INTERNAL STRUCTURE OF PLANTS. ALL vegetable substances consist of fluids and solids some of which are the food upon which plants subsist and the matters which they secrete. The others serve either to contain or convey the rest forward. This will be rendered plainer by treating

of the more solid parts first: these consist of membranes, cells, and fibres. They are all represented in a common leaf, which, as is well-known to all, consists of an outer skin or membrane; next of a pulpy portion or cellular tissue; and within these of a mass of woody vessels or fibres. All these may be compared to skin, flesh, and bones, while throughout the whole, as in the animal body, are veins, vessels, and pores, through which a circulation of fluids is carried on, and in which certain chemical changes conducive to the life, growth, and health of the individual are continually taking place.

Membranes and their pores.-A thin skin covers every part of the vegetable organs, except the stigma. This increases with their growth, and is destroyed only by disease, injury, or the natural decay of the part which it covers. The membrane is intended for various purposes. First, as a defence and protection against atmospheric changes; and, secondly, as it exists in the colored parts of a plant, particularly in the leaves; as an instrument through which the vegetable breathing is carried on, and where various juices of plants are subjected to such an influence of light and warmth as to produce the chemical changes necessary for vegetable life. It is this organ also which enables the plant to benefit by absorbing moisture and gasses from the atmosphere, and throwing off such as are useless or redundant-this it does by means of pores, called

stomata, which are more or less abundant over its general surface.

To show the nature of the cuticular membrane, we have only to tear off a part of the covering of a leaf, and submit it to a moderate microscope. That which to the naked eye appears a fine, transparent, and even skin,* now that it is magnified; will be seen composed of meshes like net-work, of different shapes, according to the plant from which it may have been torn. It is also scattered over with various pores, which are the stomata formerly spoke of, while the net-work appearance arises from different vessels passing across the membrane in various, but certain directions.

The following shows several varieties of membranous structure :

2

1

3

4 1. Cuticle of the Spiderwort. 2. Ditto of the Indian Corn. 3. Ditto of the upper surface of the Hoya Carnosa. 4. Ditto of one of the Violets.

The size of the meshes of cuticles is extremely varied in different plants, always larger than the cells within, yet so minute that more than 50,000 are sometimes found within the space of a square inch. The stomata also are somewhat different in form and size, but vary still more in their abundance. On leaves always covered with water none are discoverable, floating leaves have them only on their upper surface, and leaves wholly aerial have generally very many less upon their upper side than on their lower one, as appears from the following table :

Number of pores upon various leaves on a square

inch.

Alisma plantago..

Cobea scandens.

12,000 none

18,000

Clove Pink

Common Mezereon

Hydrangea quercifolia..

none

Common House-leek

38,500 . 77,000 4,000 16,000 6,000 . 16,710 40,000 4,000 400

shower of rain occurs after long drought, we must have witnessed that many plants revive long before the moisture can have arrived at their roots, and some much more rapidly than others-the only absorbents acting in this case being the stomata upon the cuticle.

Pulp or cellular tissue.-This consists of a number of bags, filled with air or more usually with various juices, composing the whole substance of most of the cryptogamic plants, (therefore called cellular,) and all the softer parts of flowering vegetables, such as the pulp of fruit, the fleshy part of leaves, and the pith which fills the stem. To examine the cellular structure, we have only to cut a cross section of any common pulpy stem, and to view it in a drop of water under the microscope-it will be found to consist of variously-shaped cavities. If the stem be very loose and young, it will most often consist of circular spaces, (1,) with a cavity between each. If these be subject to a slight pressure, as they will be in a future growth of the plant, they will become twelve-sided, the intervening spaces having become smaller : and finally, by the pressure of each upon the others, they will become hexagonal, the angular spaces, in the first instance so conspicuous, being wholly filled up, (2.) This appears to be the real cause of the different shapes observable in the above forms, of which the hexagon, more or less regular, is that most commonly met with. A vertical section of a stem shows the cells to be mostly longer than their breadth, like cylinders or many-sided prisms, (3.) When the cellular tissue runs between the harder parts of plants, such as that which exists in the medullary rays of wood, it becomes pressed into nearly flat tubes, (4.) Cotton is cellular tissue in a dried state. been stated, that the cellular integuments are filled with air or various juices. These are chiefly water, occasionally flavored with various products, such as bitters, acids, &c. Sometimes the water is absent, and oils, gums, resins, starch, sugar, essences, mucilage, &c., takes its place in certain, if not all of the cells-mostly in those of the bark and leaves. 3 4

The difference of numbers seen in the above will be found to agree exactly with the rapidity with which the leaves wither after being gathered, and revive again when wetted. Thus we know how long a branch of misletoe will remain without its leaves drying up, while those of the Water Lily and the Hydrangea fade almost immediately. Also when a

There are in reality two membranes covering the fleshy part of a leaf the outer one, called EPIDERMIS, is so exceedingly fine as to be scarcely ever visible even with the best microscopes. It resembles more the pellicle of a soap bladder than any thing else that described above as the cuticular membrane is to be considered the true cutis, or real skin.

WOODY FIBRES.

Distinguished from the above are the hard and tough fibres, which forms the woody parts of plants, called therefore woody tissue. In many plants it does not exist they are therefore brittle, and when dead rot away in a short time. Where the woody tissue exist, in proportion to its quantity, so the plants are durable and strong-thus in the Hemp and the Flax, the fibres possess considerable strength add durability. In shape fibres of this kind vary but little, being long cylinders tapering towards either end-they are extremely fine, generally_not one-fiftieth of the diameter of a human hair. They are always found in bundles of a considerable number united together, and every thread of Flax, however minute, is not a single fibre, but a bundle of numerous fibres interlacing each other.

The collection of various such bundles forms not only the wood of trees, but the hard coats and