an Electric Source , and Line Spectra. 799 



the number of electrical particles of the given kind contained in 

 the source, 



K=- 2 9c^ (49) 



tt am v J 



Such would be the significance of E in terms of subatomic 

 entities. If we wish, we can go a step further by assuming that 

 the mass m of the particles in question is of purely electromagnetic 

 origin. Then, supposing, for example, that the particles are spheres 

 of radius r and of homogeneous surface-charge, m=^q 2 /r, and 



tv a 



i. e. proportional to the number of particles of the y-kind contained 

 in the source (atom) and to the ratio of their dimensions to those 

 of the source. 



But it must be expressly stated that the above electronic inter- 

 pretation would hamper our progress ; for cases are known, in 

 which the lines crowd towards the infra-red (instead of towards 

 the more refrangible) end of the spectrum, so that some of the 

 coefficients b and therefore R may be negative, while all the factors 

 in (49) are essentially positive. We shall, therefore, as a rule not 

 assume this, nor any other mechanistic interpretation. 



Using the coefficient K, defined by (48), apart from any 

 subatomic interpretation, the rigorous formula (47) can be 

 written 



V = 7 ! (l+0), «=l,2,8,...co. . . (47) 



Formula (47 />) is what (47) becomes for large i's. From 

 this fact we may expect, without numerical calculation, that 

 the higher lines of the simple series represented by (47) will 

 coincide with the corresponding members of observed series 

 of the hydrogen type. How far down in the scale of i's this 

 agreement holds, can be seen only from a detailed numerical 

 comparison of (47) with spectroscopic experience. It will 

 be well, therefore, to insert here a few examples. 



1. The Diffuse Series of Hydrogen. — Let us take for <y = \ m 

 the wave-length of the convergence-point which, used in the 

 Balmer formula, gives the best representation of the experi- 

 mental series, i. e. in microns, 



7 = -3G4714. 



Let us determine the value of R = 2(A; 2 — y 2 )i f i 2 '- (try) 2 

 from the wave-length of the highest observed line H 35 , 

 measured recently by Mitchell (^strophys. Journ. 1913, 



