208 M. Savart on the Modes of 



It cannot be doubted, that bodies, when their dimensions either 

 are equal, or approach to equality, ought to give similar results. 

 It is even to be presumed, that the variety of ways of passing 

 from one mode of motion is still greater than in these bodies ; 

 but do filiform bodies, which, like strings, are reduced to a single 

 dimension, present also transformations from one mode of divi- 

 sion to another ? This is very probable, at least we may con- 

 clude so by analogy, from what passes in plates and rectangular 

 membranes very narrow and very long. Suppose, for ex- 

 ample, that a membrane of this kind presents the mode of di- 

 vision in Fig. 17, No. 1, even if the sound becomes gradually 

 more grave, the nodes will all assume a progressive motion 

 towards B, which will increase the interval Ara, and at the 

 same time, the intervals nn r , n'n"> will increase also, and con- 

 sequently w" B will be much diminished. It would appear that 

 this part then vibrates either not at all, or very little, and that 

 n becomes, as it were, the extremity of the membrane ; at last 

 the sound always descending, n" coincides with B, and the mem- 

 brane is found divided only by two nodal lines, as in No. 2, 

 Fig. 17. This way, however, of passing from one mode of 

 division to another, seems very imperfect, and nature employs 

 many others which accompany it with great regularity, and in 

 which the continuity is constantly observed. For example, I 

 suppose that the membrane has six nodal lines, as Fig. 18, 

 No. 1. if the sound becomes more acute, these lines will incline 

 alternately and oppositely, as in No. 2, and at last their nearest 

 extremities will join in an angle, which will by degrees round 

 itself, so as to form the sinuous lines in No. 3 ; then they 

 will become straighter, and again sinuous, but in presenting an 

 inflexion, or a semi-inflexion more. In the last case, there 

 will be produced seven nodal lines parallel to the small sides 

 of the rectangle, and in the last case eight. We may conceive, 

 that this mode of transformation is applicable to every case 

 whatever in the primitive number of parallel lines. 



Rigid rods which are long, and very narrow, present phe- 

 nomena of the same kind, which are still more easily examin- 

 ed. All the transformations which they present, are gradual 

 passages from lines perpendicular to the length of the rod 

 to other systems of lines, some of which are perpendicular, 



