44 HISTORY OF ACOUSTICS. 



superposition of two or more simple and obviously allowable modes 

 of nodal division, which have the same time of vibration. He assumes, 

 for this purpose, certain " primary figures," containing only parallel 

 nodal lines ; and by combining these, first in twos, and then in fours, 

 he obtains most of Chladni's observed figures, and accounts for their 

 transitions and deviations from regularity. 



The principle of the superposition of vibrations is so solidly esta- 

 blished as a mechanical truth, that we may consider an acoustical 

 problem as satisfactorily disposed of, when it is reduced to that prin- 

 ciple, as well as when it is solved by analytical mechanics : but at the 

 same time we may recollect, that the right application and limitation 

 of this law involves no small difficulty ; and in this case, as in all 

 advances in physical science, we cannot but wish to have the new 

 ground which has been gained, gone over by some other person in 

 some' other manner ; and thus secured to us as a permanent posses- 

 sion. 



Swarfs Laics. In what has preceded, the vibrations of bodies 

 have been referred to certain general classes, the separation of which 

 was suggested by observation ; for example, the transverse, longi- 

 tudinal, and rotatory vibrations of rods. The transverse vibrations, 

 in which the rod goes backwards and forwards across the line of its 

 length, were the only ones noticed by the earlier acousticians : the 

 others were principally brought into notice by Chladni. As we have 

 already seen in the preceding pages, this classification serves to express 

 important laws ; as, for instance, a law obtained by M. Poisson which 

 gives the relation of the notes produced by the transverse and longi- 

 tudinal vibrations of a rod. But this distinction was employed by M. 

 Felix Savart to express laws of a more general kind ; and then, as 

 often happens in the progress of science, by pursuing these laws to a 

 higher point of generality, the distinction again seemed to vanish. A 

 very few' words will explain these steps. 



It was long ago ^nown that vibrations may be communicated by 

 contact. The distinction of transverse and longitudinal vibrations 

 being established, Savart found that if one rod touched another perpen- 

 dicularly, the longitudinal vibrations of the first occasion transverse 

 vibrations in the second, and vice versa. This is the more remarkable, 

 since the two sets of vibrations are not equal in rapidity, and therefore 

 cannot sympathize in any obvious manner. 14 Savart found himsel. 



13 Vibrations tournanies. 14 An. Chim. 1819, torn. -xiv. p. 138. 



