Radiation from an Electric Source, and Line Spectra* 785 



one, so that, for instance, v x is rigorously the same wave- 

 length as before. The scale for J is chosen in an arbitrary 

 manner, the essential thing being the distribution of maxima 

 and zeros of intensity. The breadth is so small in this case 

 that it is impossible to more than indicate it in the figure, 

 but this is sufficient for the reader to be able to form a 

 rough judgment of the "breadth" in comparison with the 

 previous case. The distance from maximum- to zero- 

 radiation is 



^-^=•01527 . a VK, (K = 100) 



i. e., remembering that 10 a is the previous a, nearly one- 

 sixtieth as large as in the previous case. The two radiation 

 curves represented in fig. 1 may suffice. 



To quote some further numerical results, I find, for 

 K = 500, X,/a \/K=l-4013, and Vl /a \/K = l-3983, so that 



Xi-n= a 0030a SK, (K = 500) 



and, what may be more interesting, the wave-length for 

 which J falls to less than -^ of J (more exactly, 



400 max. V J > 



J mai :469) is found to be \=r4008 . a VK, so that the 

 corresponding distance is only 



S\=-0005.av'K. (K=500) 



The physically observable breadth of the first band or branch 

 would therefore certainly be much smaller than {1Z\ or) 

 one-thousandth of a^K. Examples concerning much 

 larger permittivities will be given later on. 



From the above examples the reader will see that in 

 order to obtain bands sufficiently sharp to represent actual 

 line-spectra, the permittivity of the source must exceed 

 values of the order of 10 2 . This being granted, it is e;>sy 

 to show that we are compelled at once to assume much 

 greater permittivities, even apart from the ultimate physical 

 requirement of sharpness of the lines. 



In fact, imagine a number of similar spherical sources, 

 all of radius a (or nearly so), homogeneously distributed in 

 empty space. To fix the ideas, let this assemblage represent 

 a given volume of hydrogen gas. Call K the value of K * 

 for infinitely long waves, for each of the spheres, and let 

 K be the observable, macroscopic, permittivity of hydrogen, 

 under normal conditions. Then K (being at least 10 2 ) will 

 certainly be large enough to justify the application of 



* In the preceding- examples K has, of course, been assumed constant 

 only for the sake of simplicity. 



