VIBRATION OF BODIES IN GENERAL. 3G1 



the hypothesis, that elastic bodies are composed of 

 separate particles held together by the attractive 

 forces which they exert upon each other, and dis- 

 tended by the repulsive force of heat. M. Cauchy 10 

 has also calculated the transverse, longitudinal, and 

 rotatory vibrations of elastic rods, and has obtained 

 results agreeing closely with experiment through a 

 considerable list of comparisons. The combined 

 authority of two profound analysts, as MM. Poisson 

 and Cauchy are, leads us to believe that, for the 

 simpler cases of the vibrations of elastic bodies, 

 Mathematics has executed her task ; but most of the 

 more complex cases remain as yet unsubdued. 



The two brothers, Ernest and William Weber, 

 made many curious observations on undulations, 

 which are contained in their Wellenlehre, (Doctrine 

 of Waves,) published at Leipsig in 1825. They 

 were led to suppose, (as Young had suggested at an 

 earlier period,) that Chladni's figures of nodal lines 

 in plates were to be accounted for by the super- 

 position of undulations 11 . Mr. Wheatstone 12 has 

 undertaken to account for Chladni's figures of 

 vibrating square plates by this superposition of two 

 or more simple and obviously allowable modes of 

 nodal division, which have the same time of vibra- 

 tion. He assumes, for this purpose, certain "pri- 

 mary figures," containing only parallel nodal lines ; 

 and by combining these, first in twos, and then in 



Exercises dc Malhemalique, iii. and iv. 

 11 Wdlenlehre, p. 474. " Phil Trans. 1833, p. 593. 



