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LI V. The Emission- Function of a Body emitting a 

 Line-Spectrum. By Alfred W. Porter*. 



WHATEVER the emission-function for the energy 

 radiated from such a body may be, it must satisfy 

 the following conditions : — 



i. It must vanish for all values of wave-length (A.) except 

 those which correspond to the spectral lines. 



ii. That part of the function which determines the position 

 of these lines must be independent of the temperature. 



An attempt has been made by P. G. Nutting (Astrophysical 

 Journal, Oct. 1900, and Phil. Mag. Oct. 1901) to supply 

 such a function ; and he gives a series-form each term of 

 which corresponds to a spectral maximum of infinite value. 



It has occurred to me that in the case of Hydrogen the 

 following form is preferable, inasmuch as the difficulty of 

 infinite values does not enter and, moreover, a single term is 

 sufficient to represent all the lines in the elementary line- 

 spectrum instead of a summation of 13 terms : — 



E = Fsin 2 [Ni;]|sin 2 V , 



where F is a factor to be presently examined ; 



V fln — n 



v 



Po~P 



where /? = 27418*3 ; N is any large integer, for example 1000 

 or 10,000, and p ( = oscillation-frequency) may assume any 

 value for which v is real. 



The way in which this formula is based on Balmer's formula 

 for the position of the spectral lines will be very evident ; 

 while the inarch of E as v varies may at once be pictured by 

 recalling the similar formula which occurs in connexion with 

 diffraction- gratings. 



Ewill be of quite negligible value for most values of p, but 

 suddenly mounts to the value N 2 F for the wave-length of 

 each of the lines given by Balmer's formula : it therefore 

 represents the position of the maxima to the accuracy of the 

 latter formula, viz. one part in 50,000. 



To represent the fact that the lines are not of equal 

 intensity the factor F must depend on X and T; and in the 

 absence of sufficient knowledge concerning the probable form 

 of F, I can only suggest that these enter in the same way as 

 in the expression for the radiation from an absolutely black 

 body. Thus adopting Wien's formula, the emission-function 

 will be 



E = [sin Nv/sin vj 2 p° exp. ( — cp/T). 



Similar formula) may be written down for other substances 

 * Communicated bv the Author. 



