THE SIZE OF ATOMS. 191 



Stokes's hitherto unpublished explanation of 

 phosphorescence. 



This supposition of each molecule acting with 

 direct force only on its nearest neighbours is not 

 exactly the postulate on which Cauchy works. 

 He supposes each molecule to act on all around 

 it, according to some law of rapid decrease as the 

 distance increases ; but this must make the 

 influence of coarse-grainedness on the velocity of 

 propagation smaller than it is on the simple 

 assumption realised in the models and diagrams 

 before you, which therefore represents the extreme 

 limit of the efficacy of Cauchy's unmodified theory 

 to explain dispersion. 



Now, by looking at the little table (Table II. 

 p. 184) of calculated results, you will see that, with 

 as few as 20 molecules in the wave-length, the 

 velocity of propagation is 99! per cent, of what 

 it would be with an infinite number of molecules ; 

 hence the extreme difference of propagational 

 velocity, accountable for by Cauchy's unmodified 

 theory in its idealised extreme of mutual action 

 limited to nearest neighbours, amounts to i/2ooth. 



