206 M. Savart on the Modes of 



selves inwards. But of all the modifications which the straight 

 lines may produce, there are none which present phenomena 

 more singular than those which result from the alternate in- 

 flexions which these lines may at first take, according as they 

 present two curvatures in one direction and one in another, or 

 three in one direction and two in another. Remarkable exam- 

 ples are shown in Fig. 12 and 13. 



It follows, therefore, from these observations, not only that - 

 square membranes arc susceptible of producing all possible 

 numbers of vibrations, and that from each of these numbers 

 they divide themselves in a particular manner, but also that 

 the same number of vibrations may be given by several modes 

 of division. With regard to those membranes whose contours 

 are different, circular, triangular, &c. they present analogous, 

 though more complicated, phenomena. It is thus, for exam- 

 ple, that in a circular membrane three diametral lines may 

 pass gradually to three parallel lines, and afterwards to a single 

 diametral line, accompanied with a circular line, Fig. 14 ;— . 

 that five diametral lines may pass to five parallel lines, Fig. 15, 

 and from this to other modes of division ; for example, to two 

 circular lines divided by a single diametral line. 



The successive transformations of nodal lines are much more 

 difficult to observe on rigid plates than upon membranes, be- 

 cause, as we can only produce given modes of division by render- 

 ing immoveable several parts of the surface of these bodies, it 

 happens almost always that these parts belong to one or seve- 

 ral other systems of nodal lines, so that one often falls from a 

 sound very grave to a sound very acute, and reciprocally, with- 

 out being able to pass through intermediate ones. Neverthe- 

 less it is possible to produce general phenomena of this kind ; 

 and it is easy to see, from what we have said of the modes 

 of division of membranes, that the figures which M. Chladni 

 has designed under the name of distortions, are only modes of 

 division intermediate between different systems of rectilineal no- 

 dal lines. As this natural philosopher has only observed the 

 nearest distortions of the figures, which he regards as primitive 

 types, and as the ear is a bad judge of the number of vibra- 

 tions, he has maintained that the sound of distortions is the same 

 as that of the principal figure. In the tables of his Traite 



