204 M. Savart on the Modes of 



tion of their length. All the results which I have mentioned 

 are equally produced in whatever way the needles are placed. 

 Each experiment was repeated several times with the same re- 

 sult. It is scarcely necessary to add, that, before exposing any 

 needle to the solar action, I carefully examined whether or 

 not it was magnetic, and the experiments were made only 

 with needles which had no magnetism. 



Art. V. — On the Modes of Division of Vibrating Bodies.* 

 By M. Felix Savart. With a Plate. 



It has been hitherto supposed that all sounding bodies are 

 capable of dividing themselves into vibrating parts, the num- 

 ber of which goes on increasing according to a certain law, 

 so that each body can only produce a determinate series of 

 sounds, which become more acute in proportion to the vibrat- 

 ing parts. On the other hand, I have established it as a fact, 

 that when two or more bodies are in contact, and the one set 

 into vibration by the other, they will arrange themselves so as 

 to execute the same number of vibrations; from which it follows, 

 that it is not true that bodies are susceptible only of a deter- 

 minate number of modes of division, between which there are 

 no intermediate ones, but that, on the contrary, they may pro- 

 duce such vibrations, which gradually transform themselves 

 into others, so that they are fit to execute any number of 

 vibrations. 



This opinion is easily proved in the case of membranes 

 stretched and agitated through the air by means of a vibrating 

 body. As square membranes present modes of division simple 

 and easily perceived, and as they divide themselves nearly like 

 rigid plates of the same shape,f I shall explain the phenomena 

 presented by membranes of that form. For the sake of sim- 

 plicity I shall always suppose that we have first obtained a 

 figure composed of nodal rectilineal lines, which cut one an- 



* Translated and abridged from the Ann. de Chun. Tom. xxxii. p. S84. 



+ The only difference is, that in the rigid plates the vibrating parts near 



the free margin are always smaller than the others, while in membranes, 



all the divisions are equal. 



It 



