Division of Vibrating Bodies. 207 



d'Acoustique, we see distortions which are given by sounds more 

 acute by a semitone, and by a tone, and even a tierce minor than 

 their primitive type. Besides, in the case of modes of division 

 of rectangular plates, whose sides are in different proportions, 

 M. Chladni observes, that it is possible, in a great number of 

 cases, to pass from one mode of division to another, which 

 gives a sound a little different by successive transformations of 

 the nodal lines, occasioned by slight changes in the position of 

 the parts, which are rendered immoveable ; facts which confirm 

 perfectly what I have here advanced, and of which M. Chladni 

 relates several remarkable examples. 



Not only are the transformations possible, when two sounds 

 differ very little, but they are so in certain cases, when they 

 differ by a tone and even more. A rectangular plate of glass, 

 for example, 10 inches long, 2J wide, and half a line thick, 

 may pass gradually from the mode of division of No. I. Fig. 

 16, which gives the sound ut 4, to No. 4 of the same figure 

 which gives the sound re 4. We might adduce several other 

 facts of the same kind, so that it cannot be doubted, that in 

 rigid plates, we cannot produce gradual transformations be- 

 tween two modes of division which give sounds sufficiently re- 

 mote from one another. It is not that these transformations 

 do not exist ; but it is from the method of agitation which we 

 employ that they become impossible in the greater number of 

 cases. But we cannot produce any of these transformations 

 in rigid plates, of which we are led by analogy to admit the 

 existence. As the modes of division of square membranes 

 differ very little from those of plates of the same form, 

 we may remark, in comparing them, that all the distortions 

 observed by Chladni in square plates, have analogies in the 

 intermediate modes of division presented by membranes, while 

 they pass insensibly from a figure composed of right lines, 

 to another figure of the same kind. We may then maintain, 

 without the risk of error, that rigid plates are in the same pre- 

 dicament as membranes, and that they are capable of produ- 

 cing an infinity of modes of motion connected with one another, 

 and transform themselves gradually, a result which, as I have 

 shown in my Mimoire sur les Instrumens a Cordes, ought 

 to take place. 



