362 HISTORY OF ACOUSTICS. 



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 established as a mechanical truth, that 

 we may consider an acoustical problem as satisfac- 

 torily 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 

 possession. 



Savarfs Laws. In what has preceded, the 

 vibrations of bodies have been referred to certain 

 general classes, the separation of which was sug- 

 gested by observation ; for example, the transverse, 

 longitudinal, and rotatory, vibrations of rods. The 

 transverse vibrations, in which the rod goes back- 

 wards and forwards across the line of its length, 

 were the only ones noticed by the earlier acous- 

 ticians: 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 

 13 Vibrations tournantes. 



