C. GENERAL PHYSICS. 135 



portant results, both in our knowledge of the laws of elasticity 

 and in their application to acoustics, has been made by Mer- 

 cadier, on the movement of an elastic thread, of which one ex- 

 tremity is animated by a vibratory movement. M. Mercadier 

 had been led to this study in the construction of an electric 

 diapason, to which he had attached a metallic thread, in order 

 to reduce its vibrations. The diapason is, independently of 

 the thread, considered here only as a sounding body of spe- 

 cial form, animated by a known vibratory movement. His 

 researches affirm, in great part, the laws indicated by M. 

 Gripon, and have also furnished still newer results. Merca- 

 dier distinguishes two cases that occur; first, that in which 

 the vibrating thread follows at its extremity vibrations ex- 

 actly parallel to those of the diapason. This he calls its 

 normal state. In the other case, the extremity of the thread 

 vibrates in a more eomplicated manner, and, sometimes, even 

 in twisting vibrations. These complicated effects take place 

 especially when the end is very fine; but in all cases this 

 state of vibration, which he calls the abnormal state, is char- 

 acterized by a diminution of the amplitude and intensity of 

 the movement of the diapason itself, a remarkable diminu- 

 tion, which can even proceed so far as to completely ex- 

 tinguish those vibrations. He is able alwavs to control the 

 passage from a normal to an abnormal state of vibration. 

 Among the numerous laws that he has published concerning 

 these states of vibration, we may cite the following: 



In the normal state the thread presents a series of nodes 

 and vibrating segments, whose relations to each other, as re- 

 gards length and position, he has determined for a number 

 of metals, especially for iron, copper, platinum, and aluminum. 

 Whatever may be its length, if the thread vibrate regularly 

 or normally, it also vibrates synchronously with the diapason. 

 These vibrations are recorded very clearly upon a revolving 

 cylinder, and can be easily counted. For different diapasons 

 and the same thread, the normal distances of the nodes are 

 in the inverse ratio of the square roots of the number of vi- 

 brations of the diapason. If we make the amplitude of the 

 diapason to vary, the form of the vibration of the thread 

 does not change, except with regard to the positions of the 

 three or four first nodes, counting from the point of attach- 

 ment to the diapason; the nodes removing from it or ap- 



