Seer. XVII. VIBRATION OF PLATES. 139 



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 tan- 

 gential, 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 center, the sand will ar- 

 range itself in two straight lines parallel to the sides of 

 the plate, and crossing in the center 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. 178). If the plate be still held by the center, 

 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. The nodal lines and pitch vary not only with 

 the point where the bow is applied, but with the point 

 by which the plate is held, which being at rest, neces- 

 sarily determines the direction of one of the quiescent 

 lines. The forms assumed by the sand in square 

 plates are very numerous, corresponding to all the va- 

 rious modes of vibration. The lines in circular plates 

 are even more remarkable for their symmetry, and 

 upon them the forms assumed by the sand may be 

 classed in three systems. The first is the diametrical 

 system, in which the figures consist of diameters divid- 

 ing the circumference of the plate into equal parts, 

 ench of which is in a different state of vibration from 



