8. The effect in Fig. 12. where the rays form angles of 40° is produced by the very same process as that of Fig. 10, with this difference only, that the bow is drawn at a point 30" from the point in the circumfer ence that is pinched. The figures which are formed of 2, 4, 6, 8, and 10 diameters, often assume deformed shapes, in which two of the lines unite to form a curve line, which does not pass through the centre of the plate. Thus the figure with eight rays, Fig. 13. some times assumes the form shown in Fig. 14. in which there is one nodal line left, the others being united in pairs into three curves.
When the centre of the circular plate is left free, a new set of figures are formed, as shown from Fig. 15.
to 19.
9. Of these, one that gives the gravest sound, and the most simple form, is that of Fig. 15. formed of a single circular line. In order to produce this, any point through which the circular line is to pass is pinched, and the bow is drawn on the opposite side of the diameter passing through the point that is pinched; as this circular line has a determinate position, a few trials arc necessary, to find the proper distance from the centre at which the plate is to be pinched.
10. To produce Fig. 16. composed of a diameter and a circular line, we must pinch the plate nearer its edge, and apply the bow to a point 90° from that point. The sound produced is more acute than the preceding.
11. Fig. 17. is produced by pinching the plate as in the last case, and applying the bow at a point 45' from the point pinched. In proportion as the diame tral lines increase in number, the circular line ap proaches the margin of the plate.
12. Several circular nodal lines may be produced as in Fig. 18. To do this, we have only to pinch the plate in two or more places through which the lines are to pass; the two points that arc pinched being always in the same radius, and their proper distance from the centre being found by trial.
13. The distortion of Fig. 18. shown in Pig. 19. is produced by pressing a point of the circumference against a fixed obstacle, and applying the bow at a point 30° from the point of contact, the interior circle being changed into an ellipse, and the outer one bent five times into itself.
14. When a circular plate of metal is pinched as in Fig. 3. against a fixed plate e, and pressed with the fingers at c and d, the figure in Fig. 20. is produced.
15. In an elliptical plate, of which the ratio of the diameters is as 4 to 3, and held as in Fig. 2. the sand is arranged as in Fig. 21.
16. With a triangular plate, Fig. 22. the form thus represented is produced by pinching the plate at n and applying the bow at r.
17. In the rhomboidal plate, Fig. 23. the form is produced also by pinching at n and applying the bow at r.
2. On the v9couslic Figures produced by the vibration communicated through the air to elastic membranes.
The very curious experiments on this subject made by M. Savart, have been recently (1822) read to the Academy of Sciences in Paris. The following abridged account of them is copied from Dr. Brewster's Edin burgh Journal of Science, vol. ii. p. 296.
In order to perform the experiments described by M. Savart, we must stretch a thin sheet of paper, about four or five inches in diameter, over the mouth of a vessel, such as a large glass with a foot-stalk, so that the paper has an uniform degree of tension, and a ho rizontal position. A thin layer of fine and dry sand or Lycupodium powder being then scattered over the paper, a plate of glass, in a state of vibration, is brought within a few inches of the membrane. The vibrations of the glass plate are conveyed through the air to the paper membrane, and the powder on its up per surface is thrown into figures which have some times the most perfect regularity, and are often form ed with such celerity, that the eye has scarcely time to perceive the circumstances which accompany their formation.
This experiment succeeds in general, whatever be the vibrating body which we employ, though thin plates of glass or metal are the best; and it is always preferable to make the circular plate of glass vibrate in the mode in which there are concentric lines of repose. It appears from the experiments of Chladni, that, in order to obtain this kind of vibration, we must render immoveable several points in the surface of the plate, or at least two points of the circumference and one point of the surface. It is in this way, therefore, that Savart makes the experiment. Ile at first renders immoveable two diametrically opposite points of the circumference of the plate, by seizing it between the middle finger and the thumb. He then places lightly the tip of the index finger at a point, whose distance from the centre of the plate is about the fifth part of its cir cumference. The plate thus held is made to vibrate, by drawing the bow of a fiddle across its circumfer ence. By employing successively circular plates of different dimensions, and which, consequently, give different sounds, it is easy to prove, that, for every number of vibrations, the membrane affects a particu lar mode of division. When the vibrating plate is par allel to the membrane, the latter performs normal vi brations, or vibrations in a line perpendicular to its surface. The sand sometimes springs to a great height; and, by making use of an apparatus which allows us to observe what passes at both surfaces of the membrane, it is easy to see that the distribution of the nodal lines is the same. The general character of these lines is to be circular, and their number is some times very considerable. These circular lines are often cut by diametral lines, which form stars, whose num ber of points increases with the acuteness of the sound. Sometimes figures are obtained which are composed solely of these diametral lines. Perfect regularity and symmetry, howe.:er, can only be obtained by taking the greatest care that the membrane be equally thick and uniformly stretched. The first of these con ditions may be easily fulfilled by using the fines paper, particularly what is called vegetable papert which is the most homogeneous that can be employed.