If, in the side of a tube containing a column of vibrating air, any aperture exist by which that air is enabled to communicate with the atmosphere, the air in that section becomes in equilibrio with the latter, and, in that section, there is consequently neither condensation nor rarefaction : this section corresponds to the middle point between two nodes in a vibrating string.
Vibrations corresponding to those which are produced in strings or rods and in columns of air may be conceived to take place in any solid bodies or in any elastic fluids whatever be the figure of their mass : in such a mass there may be several places at which the vibrations are performed in contrary directions so as to produce nodal lines ; and these, when they occur on the surface of the mass, may become sensible by means of light dust strewed over it. Some of the vibra tions are found to take place parallel to the surface, and others perpen dicular to it the former being called tangential, and the latter normal vibrations. In one case the particles of dust glide upon the surface in directions which tend alternately towards and from the nodal lines (the movements in the former direction being always more rapid than those in the other) till they come to a state of rest on those lines ; in the other case the particles alternately rise from and fall back upon the surface at the places where the latter is in a state of vibration ; and, dispersing from those places, they become quiescent in the lines of no vibration.
Galileo was the first who observed (Dialoglii delle Science Nuove) that the vibrations of elastic plates might be rendered visible by covering the plates with fine sand ; and he remarked that the sand became accumulated at the parts where the vibrating plate was in a state of rest : but this subject was extensively investigated by Dr. Chladni, of Wirtemberg, who first discovered the longitudinal vibrations of solid bodies; and, 1787, published, in a work entitled Entdeckangen fiber die Theoric des Klanges, an account of numerous experiments which he had made on the nature of the vibrations produced in plates of glass of different forms.
The plates with which such experiments may be performed should be of good window glass ; and, if square, from 4 to 8 inches on each side ; if circular, their diameters may be within the same limits : in making an experiment the plate must be held horizontally between a finger and thumb, or it may be fixed within the lips of a clamp screw or of suitable tongs, the points of contact being furnished with cork ; and when it is required to prevent any particular part of the plate from vibrating, that part, if on the edge, may be pressed against a fixed object, or, if at any part of the surface, one of the fingers of the hand rosy be pressed gently upon that tart. The plate being in a
horizontal position, it must bo covered with a layer of fine dust such as lycopodlum; and It may be put in a state of vibration by drawing a violin. ow across its edge : the dust will then arrange itself in figures which will vary with the form of the plate, the place at which the bow is applied, awl that at which the plate is held. If, for example, a square plate lati held at its centre, and the bow be applied near one of the angles, the duet will arrange itself in lines so as to divide the plate into four equal squares (No. 1). If the plate be held as before, and the bow be applied at the middle of one of the sides, the vibrations will be such as to make the dust lie in the direction of the two iago mak (No. 2). Again, if the plate be held at A (No. 3) and the bow be applied at it, the dust will assume the positions of three lines parallel to one another : and if the plate bo held at a point nearer the edge, the lines will become curves, as in No. 4.
If a circular plate, held at the centre, be pressed against a fixed object at any point on its circumference, and the bow be applied at 45' from that point, the lines will take the positions of two diameters at right angles to one another, one of them passing through the point at which the circumference touches the object. A greater number of radiating lines than four will be produced if the bow be drawn more rapidly and with less pressure against the edge of the plate than in the former case. If the centre of the circular plate be free, various curve lines will be assumed by the dust, according to the position of the point which is held ; and one of them is represented in No. 5. The figures represented in Nos. 6, 7, and 8, are selected from the great number which Chladni has obtained with glass plates of a circular, a polygonal, and a triangular form. Professor Wheatstone has calculated a large number of these acoustic figures by the principle of the super position of small motions. ( Phil. Trans.) Professor Faraday also describes (Phil. Trans., 1831) a number of interesting experiments on the subject.