an Electric Source, and Line Spectra. 795 



Balmer's theoretical limit or the convergence-point o£ the 

 series. A smooth curve on which the centres of the circles 

 may be placed, is not drawn in the figure. The meaning of 

 the drawn curve (hyperbola) will be explained later on 

 (p. 801). 



Typical form of Atomic Dispersion. 



Guided partly by the aspect of curves such as that given 

 in fig. 3 (and the corresponding curve k=k(X 2 )) and partly 

 by analogy with the refractive properties of molar bodies, I 

 propose to investigate the chief consequences of assuming 

 the particular form of dispersion, 



*=*o+f^, (44) 



which, for the sake of short reference only, I shall call the 

 typical form of atomic dispersion *. Here k is the statical 

 value of k, as before, and b n y L are constants. Originally I 

 left the values of these latter constants free in relation to 7c . 

 Certain general reasons, however, along with some numerical 

 examples, have suggested the introduction of a simple relation 

 between k Q and the remaining constants. 



It is well known that in some at least of the molar 

 dispersion formula?, which (apart, from absorption bands) 

 are all of the type 



V — <y 



the constants approximately satisfy the equation 



Ko=i+s5 



and that this equation is also a consequence of every theory 

 of dispersion based on electronic assumptions. In our ease, 

 K = /r /47r 2 6r being of the order 10 G or 10 7 , unity can be 

 omitted. Let us postulate, therefore, the relation 



^=2-^ = 2/3., (45) 



1 7 t 1 



to be introduced in (-14). 



This supplementary relation, besides being familiar from 



* Some numerical applications of (44) are given in the Preliminary 

 Note, Phil. Mag. vol. xxix. 1915, p. 709. The symbols there employed 

 are thus related to the present ones: 



3 F 2 



