and the Spectrum of Helium. 91 



its capacity to take account more completely of the spectra 

 of: these two elements, to which the analysis of the preceding 

 paper does not apply. 



The idea that series spectra are only an illustration of 

 Planck's law, by the energy which is radiated during the 

 passage of an atom from one state to another, is. at first sight, 

 very promising, for it takes account of the fact that all 

 frequencies in series spectra are differences of two functions 

 of whole numbers. Leaving aside, in order to avoid compli- 

 cation, the existence of double and triple lines, satellites, and 

 such series as those known by the name of Bergmann, we may 

 say that for all ordinary elements whose spectra can be put 

 into series of Rydberg's approximate type, there are three 

 important series to be explained, — the Diffuse, Sharp, and 

 Principal series, whose mutual relations are exhibited by the 

 following formulas for their frequencies, where B is Ryd berg's 

 constant, 



Diffuse, v = B {^ )2 - ( -^}, 



Sharp, v = 13 ' - — ? — -— -„ > , 



( (1 + */ {m + py ) 



nncipaJ 



- B f_i ±—\ 



\ a+p) 2 (m+*) 2 /' 



where (p, s, d) are definite constants for the elements." 



It is apparent that these series alone require, on Bohr's 

 theory, the existence of three different types of stationary 

 states, to which the constants m, $, p are individually peculiar, 

 and that the spectral series are formed during the passage of 

 the atom not between different states or configurations of the 

 same type, but between different types of states. If a helium 

 atom only contains two electrons and a comparatively very 

 inert nucleus, difficulties are at once apparent, for two 

 electrons have not the necessary amount of freedom, in 

 presence of each other, to take up three different types of 

 relative configurations. Moreover, the spectrum of helium 

 contains six such series, with six apparently independent 

 constants. The atom of helium, not only according to the 

 theory of Bohr, but in actual experiments such as those of 

 Sir J. J. Thomson, will not take up an extra electron, so that 

 the neutral atom and the atom which only retains one electron 

 are alone left to explain the entire spectrum. 



It was shown in a recent paper"', that on the present form 



* Monthly Notices of R. A. S. March 1014, 



