788 Dr. L. Silberstein on Radiation from 



the detection of its breadth would require a " resolving 

 power " exceeding 



^ = 500,000. 



Such being the state of things for K=10 4 , we should have 

 for K=10 6 to 10 7 , as required for reducing the source to 

 atomic dimensions, even considerably sharper lines, possibly 

 much sharper than the finest line yet observed. Should the 

 latter be the case, then the actually observed breadths of 

 spectral lines would have * to be accounted for by special 

 assumptions, such, for instance, as the attribution to the 

 various atoms or atomic sources of an emitting gas, of 

 slightly different radii a\, or the assumption of sources 

 slightly flattened. And since the required differences be- 

 tween the individual radii a would be exceedingly small 

 (even compared with 10~ 8 cm.), there would certainly be 

 no serious difficulty in accepting such or any equivalent 

 hypothesis. The reader will remember that in most, or all, 

 attempts to construct spectral theories, the difficulty — as 

 pointed out by Lord Rayleigh — has been in obtaining (not 

 sufficiently broad but) sufficiently sharp lines. And it is 

 certainly an advantage of the proposed theory that it 

 yields, without particular artifices, such exceedingly sharp 

 lines. 



Remembering that, in the case of line spectra in general, 

 K is, as in (31), of the order of 10 7 , let us estimate the 

 prodigality or the relative emissivity e (i. e. the fraction of 

 the average stored electromagnetic energy emitted per 

 period) of an atomic source, which in the case of such 

 spectra seems to acquire a particular physical interest. The 

 general expression of the relative emissivity is given by (26), 

 Second Paper. Since, in the present case, u = w V K 

 is moderate and w 2 = u 2 . 10~ 7 , we have, by (26), 



4tt uY(u) 



6 ~VK^W (32) 



The value of K being enormous, we know that the values of 

 the variable u, or wave-length X = Xj, for which the radia- 

 tion J attains a maximum, are but slightly different from 

 the values of u, or wave-length A,=v z -, for which J = ; in 

 short, that the maxima are very near the corresponding 



* Apart from the cooperation of the Doppler effect due to molecular 

 agitation. 



t Sa} r , distributed round a given value a according to the " law of 

 error." 



