Vibrations of Elastic Plates.—All elastic solid bodies, when put into a state of vi bration, may be conceived, in reference to the internal motions of their mole cules, as spontaneously separating them selves into parts, each of which vibrates independently of the others, and in such a manner that the molecules of one part are at every instant moving in a direction opposite to that of the molecules of the adjacent part. It follows that the points of separation between two parts partici pate neither in the motion of the one nor of the other, and consequently remain at rest. In the case of thin elastic plates, the continuity of these points forms lines of repose, or nodal lines, the forms and positions of which are detected by placing the vibrating plate in a horizontal posi tion, and strewing a small quantity of fine sand over its upper surface. Phis ingenious mode of determining the nodal lines was pointed out by Galileo in his Dialogues, and was practised by Chladni (Traite d'Aroustique) and more recently by Savart in his numerous experiments on this subject,.
These fines assume a great variety of forms, depending on the figure of the plate, the position of the point or points at which it is fixed, and the rapidity and direction of the motion by which the vi bration is communicated to it. Circular plates afford numerous different systems of nodal lines. When the plate is fixed at its centre between two knobs or points held fist by a vice, two nodal lines are in general produced, crossing each other at the centre. By applying the finger to the plate at a suitable point, so as to interrupt the vibration three of those lines may be formed. Disks of metal fur nish a number of nodal lines, the circle into numerous sectors. In cer tain circumstances these straight nodal lines are intersected by a greater or small er number of concentric circular lines; the circular lines may also exist by them selves ; and sometimes the nodal lines assume the form of the branches of a hyperbola.