318 Mr. Challis on the Theory of the 



As this equation is exact, it follows that in all cases the body 

 acted upon will execute simultaneously two sets of vibrations, 

 one depending on its elasticity, the other on the disturbing cause. 

 For the equation may be put under the form 



^ = Q {sin (~ + e)-e''^. q sin {ht + 0-)] , 



But the latter term will quickly decrease on account of the factor 



- — 

 e " , and the oscillations will soon become isochronous, and will 



be of the same duration as those of the particles of the incident 

 waves. This may in some degree explain why the drum of the ear 

 is susceptible of the vibrations corresponding to any musical note, 

 especially as in this instance n is probably not very large compared 

 to p and m. On account of the small value of m, these oscilla- 

 tions must be excessively small, and not adequate to produce the 



phenomenon of resonances. But -jr will be much larger when 

 n is equal to, or nearly equal to — r- ; than in any other case, 



A' 



because the coefficient Q becomes great on account of the small- 

 ness of p. Tliis is just the condition which experience shews to 



2X 



be fiilfiUed when resonance takes place ; for — = the time of 

 oscillation of an aerial particle = —7= the time of oscillation of 

 the chord. In strictness the time of oscillation = — , „ , (Whe- 



^ 4 



well's Dynam. p. 206.) because the equation determining the 

 motion of the chord is 



drs (Is 



when no extraneous force acts on it. Suppose therefore -r ~ ^> 



