144 YIBEATING PLATES. SECT. XVII. 



pass as many times as there are apertures in it, and a sound is 

 produced whose pitch depends on the velocity of rotation. 



A glass or metallic rod, when struck at one end, or rubbed in 

 the direction of its length with a wet finger, vibrates longitudi- 

 nally, 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 transmit sound. Eods, 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 plate (N. 183). 

 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 



