SJCCT. XVII. VIBRATION OP LAMINJE. 14J 



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 33 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. 182). 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 contraiy direction ; that is, on one side it is 

 a right-handed screw, on the other a left (N. 183). The 

 nodal lines in the interior surface of the tubes are per- 

 fectly similar to those in the exterior, but they occupy 

 intermediate positions. If a small ivory ball be put 

 within the tube, it will follow these nodal lines when 

 the tube is made to revolve on its axis. 



AH solids which ring when struck, such as bells, 

 drinking glasses, gongs, &c., have their shape momen- 

 tarily and forcibly changed by the blow, and from their 



