374 Beats in the Vibrations of a Revolving Bell. 



These results afford, moreover, the means of determining 

 in the case of a non-revolving bell the proportion of the whole 

 kinetic energy which is due to the longitudinal components 

 of the displacement, and thus give an indication of the extent 

 to which the vibrations differ from two-dimensional vibrations 

 on the one hand (in which the proportion is zero), and from 

 the vibrations of a circular plate on the other hand (in which 

 the proportion is unity). 



For, according to Mr. Bryan's results, the kinetic energy in 

 the case of a non-revolving bell is proportional to (X s + 1 + s 2 )p 2 , 

 in which expression the term \ s p 2 arises from the longitudinal 

 motion, and hence the proportion in question is 



\ + l + s 2 



On the other hand, when the bell is rotated the number of 

 beats per revolution is 



2s 



\ s + s 2 -l 

 \ + s 2 + l 



= n sav, 



whence we easily obtain 



X. _ n y + l)-2^-l) 



X,+ l + « s 



4* 



Using the values given above for the number of beats per 

 revolution in the case of the different modes of vibration of 

 the two glasses, we obtain from the above formula the fol- 



lowing results 



Number of Nodes, 



2s. 



Proportion of the whole kinetic energy 

 which is clue to longitudinal motion. 



1 

 Glass No. 1. Glass No. 2. 



4 

 6 



8 



•05 



•033 



•232 



•019 

 •025 

 •076 



