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LXXXIV. Radiation from an Electric Source, and Line 

 Spectra. (Third Paper.) By L. Silberstein, Ph.D., 

 Lecturer in Natural Philosophy at the University of Rome* . 



[Plate XVIII.] 



Contents. 



Large Permittivity and Atomic Dimensions of Source. 

 Generalities on Distribution of Spectral Lines. 

 Typical Form of Atomic Dispersion. 

 The Simplest Typical Dispersion, and the Balmer Law. 

 The Diffuse Series of Hydrogen and the Principal Series of 

 Sodium and Lithium. 



Large Permittivity and Atomic Dimensions of Source. 



TO see the justification of contemplating large permit- 

 tivities at all, and enormous ones especially, start from 

 the simplest case of unit permittivity. The radiation curve 

 for this case is drawn in the upper part of fig. 1 (PL XVIII.), 

 with A and J as abscissse and ordinates ; \ 1? X 2 , &c. are the 

 positions of maxima in the first and subsequent branches, 

 and j/ 1? v 2 , &c. are the successive zeros of J corresponding 

 to the critical frequencies of the source, as in the Second 

 Paper f. The dotted ordinates, within the first branch* have 

 the length of one half of the corresponding maximum ordinate, 

 so that their distance apart gives a certain kind of measure of 

 " breadth," as recently proposed by some authors for proper 

 line spectra. Thus, the " breadth " in the case of the first 

 branch would be, roughly, 1*8 a, and for the second branch, 

 a little more than J a> &c, a being the radius of the spherical 

 source. But it will be enough to fix our attention upon the 

 first branch. The above " breadth " being (for small K) a 

 rather coarse concept, it may be well to quote here also the 

 numbers for \ ± and y lm To four decimal figures I find 

 Xj/a = 2*2907, v 1 /a = l'3$83, so that the distance from zero 

 to maximum-radiation is 



\ l -v 1 = 'S924,a. (K=l) 



Jumping over intermediate values, pass at once to the case 

 K = 100, i.e. u = 10w, to which the lower part of fig. 1 

 corresponds. In order to obtain a just comparison the 

 radius a is now taken equal to one-tenth of the previous 



* Communicated "by the Author. 



t Phil. Mag. vol. xxx. pp. 163-178 (1915). 



