Prof. Stokes on the Communication of Vibration 



mc. 



n=0. 



»=1. 



w=2. 



n=3. 



n=4. 





4 



17 



16-25 



14-879 



13-848 



20177 



a g 



2 



5 



5 



9-3125 



80 



1495-8 



<M 



1 



2 



5 



89 



3965 



300137 



CO 



0-5 



1-25 



16-25 



13302 



236191 



72086371 



=3 



0-25 



1-0625 



64062 



20878 



14837899 



18160 xlO 6 



? 



4 



1 



0-95588 



0-87523 



0-81459 



1-1869 



is 



2 



1 



1 



1-8625 



16 



299- 16 



S-i 



1 



t 



2-5 



44-5 



1982-5 



150068 



CO 



0-5 



I 



13 



1064-2 



188953 



57669097 



S 



0-25 



1 



60-294 



19650 



13965X10' 



17092 XlO 6 



ii 



When mc = go we get from the analytical expressions I n = l. 

 We see from the Table that when mc is somewhat large I n is 

 liable to be a little less than 1, and consequently the sound to 

 be a little more intense than if lateral motion had been prevented. 

 The possibility of this is explained by considering that the waves 

 of condensation spreading from those compartments of the sphere 

 which at a given moment are vibrating positively, i. e. outwards, 

 after the lapse of a half period may have spread over the neigh- 

 bouring compartments, which are now in their turn vibrating 

 positively, so that these latter compartments in their outward 

 motion work against a somewhat greater pressure than if each 

 compartment had opposite to it only the vibration of the gas 

 which it had itself occasioned ; and the same explanation applies 

 mutatis mutandis to the waves of rarefaction. However, the in- 

 crease of sound thus occasioned by the existence of lateral motion 

 is but small in any case, whereas when mc is somewhat small I w 

 increases enormously, and the sound becomes a mere nothing 

 compared with what it would have been had lateral motion been 

 prevented. 



The higher the order of the function, the greater will be 

 the number of compartments, alternately positive and negative 

 as to their mode of vibration at a given moment, into which the 

 surface of the sphere will be divided. We see from the Table 

 that for a given periodic time as well as radius the value of I n 

 becomes considerable when n is somewhat high. However, prac- 

 tically vibrations of this kind are produced when the elastic 

 sphere executes, not its principal, but one of its subordinate vi- 

 brations, the pitch corresponding to which rises with the order 

 of the vibration, so that m increases with that order. It was for 

 this reason that the Table was extended from mc — Q'5 further in 

 the direction of high pitch than low pitch, namely, to three oc- 

 taves higher and only one octave lower. 



When the sphere vibrates symmetrically about the centre, i. e. 

 so that any two opposite points of the surface are at a given 



