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LXXIV. Radiation from an Electric Source, and Line Spectra. 

 2 he Hydrogen Series. (Preliminary Note.) By L. Silber- 

 stein, Ph.D., Lecturer in Natural Philosophy at the 

 University of Rome *. 



LET the source, i. e. the seat of impressed electric force, 

 be a sphere, of radius a, having the permittivity K, 

 while that of the surrounding medium is unity. Then the 

 intensity of electromagnetic radiation emitted by the source 

 is, at distances great in comparison with a, 



J = /0,K), (1) 



where X is the wave-length in vacuo and / is a certain 

 function of X and K(X) which I will not write out here f. 

 For large values of K, viz. when the refractive index 

 c/v = K 1/2 is of the order 10 3 , the spectrum (1) of our 

 source consists of an infinite series of very thin and sharp 

 " lines" corresponding to the maxima of J, say J 1? J 2 , etc., 

 arranged after the descending wave-lengths X 1? X 2 , etc. ; the 

 reciprocals of the latter are the successive roots of a com- 

 paratively simple transcendental equation. The requirement 

 that these "lines," or exceedingly narrow bands, should lie 

 within the visible spectrum, reduces the source to molecular 

 dimensions %. The intensities of the successive spectrum- 

 lines are, with a high degree of approximation, proportional 

 to the square of the wave-length, i. e. 



J T : J 2 : = V : X 2 2 : (2) 



In other words, the lines, from red to violet, become fainter and 

 fainter. 



The permittivity of the source, K, may be, in the general 

 treatment of the problem, any function of X, which function 

 may be said to define the intrinsic or the atomic dispersion. 

 In accordance with the essence of the method of investi- 

 gation employed (cf. loc. cit.), I have strictly avoided any 

 attempt to enter into the mechanism of the " source," 

 which may consist of many electrons or other subatomic 

 entities. Guided by the analogy of molar lumps of matter, 

 I assume & = 47r 2 a 2 K to be, in general, of the form 



l — K 



*-+5d^ (3) 



* Communicated by the Author. 



t This function and the corresponding details of the problem are 



given in a paper communicated to the Royal Society, 22nd March, L915, 



% The case of small K, corresponding very nearly to the (normal) 



continuous spectrum, is treated in the paper quoted above. En that ease 

 a is, at all accessible temperatures, greater than 10~° cm. 



