1916] on The Spectra of Hydrogen and Helium 647 



grating, and it is believed that an accuracy approaching one- 

 thousandth of an A.U. was attained in the measures. The new 

 value for the '• Rvdberg constant," when expressed on the Inter- 

 national scale, is 109,679 '22, but this is not final, as it was not 

 possible to take account of the fact that Ha and H^ are very close 

 doublets, which could not be separately measured with the instruments 

 available. 



Balmer's discovery of the law connecting the lines of hydrogen 

 soon led to the recognition of numerous somewhat similar series'' in 

 the spectra of other elements, chiefly through the labours of Kavser 

 and Runge, and of Rydberg. In place of the simple series shown 

 by hydrogen, however, it was found that other spectra usually 

 included several series superposed, so that in many cases the 

 regularity in the arrangement of the lines was only disclosed after 

 patient investigation. Lithium provides one of the simplest 

 examples, and in Fig. 2 we may observe how the seemingly irregular 

 spectrum has been resolved into several series, each of which bears a 



LITHIUM 



Fig. 2. — Series Lines of Lithium. 



general resemblance to the hydrogen series. Usually there are three 

 chief series, designated, in order of brightness, the Principal, Diffuse, 

 and Sharp series. There are also certain sut3sidiary series, of which 

 the one called the Fundamental series is perhaps the most important. 

 The Balmer formula is not applicable to any other series without 

 modification, and Rydberg adopted the general formula 



(m + fjiY 



where A is the limit of the series, N the number 109,675 derived 

 from hydrogen, and /x. usually a fraction. This formula is only 

 approximate, but it was sufficiently exact for the discovery of 

 important relations between different series occurring in the same 

 spectrum. Thus, the limits of the Sharp and Diffuse series are 

 identical, and differ from the limit of the Principal series by an 

 amount equal to the wave-number of the first Principal line. 

 Similarly, the limit of the Fundamental series differs from that of 

 the Diffuse series by an amount equal to the wave-number of the 



