VIBRATION OF BODIES IN GENERAL. 45 



able to generalize this proposition, and to assert that in any coml.i na- 

 tion of rods, strings, and lamina?, at right angles to each other, the 

 longitudinal and transverse vibrations affect respectively the rods in 

 the one and other direction, 15 so that \vhen the horizontal rods, for 

 example, vibrate in the one way, the vertical rods vibrate in the 

 other. 



This law was thus expressed in terms of that classification of vibra- 

 tions of which we have spoken. Yet we easily see that we rnay 

 express it in a more general manner, without referring to that classifi- 

 cation, by saying, that vibrations are communicated so as always to be 

 parallel to their original direction. And by following it out in this 

 shape by means of experiment, M. Savart was led, a short time after- 

 wards, to deny that there is any essential distinction in these different 

 kinds of vibration. "We are thus led," he says 16 in 1822, "to con- 

 sider normal [transverse] vibrations as only one circumstance- in a 

 more general motion common to all bodies, analogous to tangential 

 [longitudinal and rotatory] vibrations ; that is, as produced by small 

 molecular oscillations, and differently modified according to the direc- 

 tion which it affects, relatively to the dimensions of the vibrating 

 body." 



These " inductions," as he properly calls them, are supported by a 

 great mass of ingenious experiments ; and may be considered as well 

 established, when they are limited to molecular oscillations, employing 

 this phrase in the sense in which it is understood in the above state- 

 ment ; and also when they are confined to bodies in which the play 

 of elasticity is not interrupted by parts more rigid than the rest, as 

 the sound-post of a violin. 17 And before I quit the subject, I may 

 notice a consequence which M. Savart has deduced from his views, and 

 which, at first sight, appears to overturn most of the earlier doctrines 

 respecting vibrating bodies. It was formerly held that tense strings 

 and elastic rods could vibrate only in a determinate series of modes of 

 division, with no intermediate steps. But M. Savart maintains, 18 on 

 the contrary, that they produce sounds which are gradually trans- 

 formed into one another, by indefinite intermediate degrees. The 

 reader may naturally ask, what is the solution of this apparent con- 



15 An. Chim. p. 152. 16 Ib. t. xxv. p. 33. 



1T For the suggestion of the necessity of this limitation I am indebted to Mr. 

 Willis. 

 19 An. Chim. 1826, t. xsxiL p. 384. 



