156 DYNAMICAL THEORY OF SOUND 



Of these the only one which has any relation to the nominal 

 pitch (d"} of the bell is the fifth in order, and this is out by an 

 octave. A mistake of an octave in judging pitch is not 

 uncommon, for physiological reasons, but it is surprising that 

 the presence of the lower dissonant tones should be so easily 

 disregarded. It is conceivable that the mode of striking may 

 be in some degree unfavourable to the production of the more 

 discordant elements. 



The vibrations of an elastic solid whose dimensions are all 

 of the same order of magnitude are from our present point of 

 view of subordinate interest. The only case which has been 

 worked out is that of the sphere. In the most important 

 mode one diameter extends and contracts whilst the perpen- 

 dicular diameters simultaneously contract and expand, respec- 

 tively. The frequency of this mode is, for such values of a- as 

 are commonly met with, 



(1) 



about, where a is the radius. This is the lowest of all the 

 natural frequencies. For a steel ball one centimetre in radius, 

 this makes N= 136000. 



