M. Savart’s experiments on the vibrations of flat glass rulers are highly interesting. Let a lamina of glass 27^{in}·56 long, 0·59 of an inch broad, and 0·06 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 produced 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 interior surface of the tube are perfectly 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.