an Electric Source, and Line Spectra, 801 



"simple series'" (47) represents fairly well the higher 

 members of the observed diffused series of hydrogen from 

 H 35 down to H ]4 = H^, with a difference not much exceeding 

 JA.U., and generally much smaller. For the remaining lines, 

 H 13 to H 1 = H^, the differences A\ mount up with increasing 

 rapidity. Thus the said approximation holds at least for 

 twenty or twenty-two members of the series. This is shown 

 also in fig. 3 (PL XVIII.) where the continuous curve 

 is drawn according to (47), i. e. represents the equilateral 

 hyperbola 



w 2 (\' 2 -7 2 ) = 7rVW2, 



the value of R being as in (50). 



2. The Principal Series of Sodium. — This is, owing to the 

 admirable work of R. W. Wood *, the most extended and 

 most complete series hitherto observed. It is well-known 

 that this series, similarly to those of lithium, potassium, &c, 

 is more closely represented by formulae of the Moggendorff- 

 Hicks type f (involving four constants) than by the original 

 Balmer formula. In view of this fact and by what has been 

 remarked above, one could expect that the asymptotic agree- 

 ment with experience of our " simple series " (47) will 

 extend in the present case further down in the scale oE i's 

 than in the preceding case of hydrogen. A detailed calcu- 

 lation has fully corroborated this vague expectation. 



Prof. Wood estimates the convergence-point of his beautiful 

 series to be at about 7 = 0*2411//,, which would give 

 ty' i = -05812921. After some preliminary trials I have found 

 most suitable for the majority of lines the slightly greater 

 value, 7 2 = '05818 14. By doing justice to several members 

 of the observed series at the same time, the corresponding- 

 value of 7r 2 7 2 R/2 comes out as 2' 705044. With these figures, 

 formula (47) becomes 



Ar = -0581814+ 2 — °^. . . (47, Na) 



The second column of Table VII. contains the wave-lengths 

 calculated according to this formula, and the third column 

 the wave-lengths (means of doublets, whose components 

 down to i = 4 are exceedingly close to one another) measured 

 by Wood in the absorption spectrum of sodium vapour. The 

 fourth column contains the differences, X ca ic. — ^obs. hi A.U. 



* Phil. Mag. vol. xvi. 1908; Physik. Zeitschrift, vol. x. 1909, pp. 88- 

 90, and p. 913, where some errata in the figures are amended. 



1" Cf. Dr. W. Marshall Watts's paper in Phil. Mag., vol. xxix. 1915, 

 p. 775. 



