146 VIBRATING PLATES. SECT. XVII. 



of an inch broad, and O06 of an inch in thickness, be held by 

 the edges in the middle, with its flat surface horizontal. If this 

 surface be strewed with sand, and set in longitudinal vibration 

 by rubbing its under surface with a wet cloth, the sand on the 

 upper surface will arrange itself in lines parallel to the ends of 

 the lamina, always in one or other of two systems (N. 186), 

 Although the same one of the two systems will always be pro- 

 duced by the same plate of glass, yet among different plates of 

 the preceding dimensions, even though cut from the same sheet 

 side by side, one will invariably exhibit one system, and the 

 other the other, without any visible reason for the difference. 

 Now, if the positions of these quiescent lines be marked on the 

 upper surface, and if the plate be turned so that the lower surface 

 becomes the upper one, the sand being strewed, and vibrations 

 excited as before, the nodal lines will still be parallel to the ends 

 of the lamina, but their positions will be intermediate between 

 those of the upper surface (N. 187). Thus it appears that all 

 the motions of one half of the thickness of the lamina, or ruler, 

 are exactly contrary to those of the corresponding points of the 

 other half. If the thickness of the lamina be increased, the 

 other dimensions remaining the same, the sound will not vary, 

 but the number of nodal lines will be less. When the breadth 

 of the lamina exceeds the 0'6 of an inch, the nodal lines become 

 curved, and are different on the two surfaces. A great variety 

 of forms are produced by increasing the breadth and changing 

 the form of the surface ; but in all it appears that the motions 

 in one half of the thickness are opposed to those in the other 

 half. 



M. Savart also found, by placing small paper rings round a 

 cylindrical tube or rod, so as to rest upon it at one point only, 

 that, when the tube or rod is continually turned on its axis in 

 the same direction, the rings slide along during the vibrations, 

 till they come to a quiescent point, where they rest. By tracing 

 these nodal lines he discovered that they twist in a spiral or 

 corkscrew round rods and cylinders, making one or more turns 

 according to the length ; but at certain points, varying in number 

 according to the mode of vibration of the rod, the screw stops, 

 and recommences on the other side, though it is turned in a 

 contrary direction ; that is, on one side it is a right-handed 

 screw, on the other a left (N. 188). The nodal lines in the 



