SECT, xvn.] VIBRATION OF PLATES. 161 



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 ac- 

 cumulate 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 neutralize 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 direc- 

 tion 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. Some- 

 times 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 ex- 

 cursions on one side of the plate, while the other two make 

 their vibrations on the other side of it. This mode of vibra- 

 tion produces the lowest tone of the plate (N. 178). 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. 



