PROF. A. FOWLER ON SERIES LINES IN SPARK SPECTRA. 
233 
It will be seen that the lines are very closely represented by any of the formulae. 
Even the simple Rydberg equation (I.) leaves no error so great as a quarter of an 
Angstrom unit, and it would require wave-lengths of still greater accuracy to test the 
relative merits of the other formulae. In each case, however, the residuals, although 
very small, are sufficiently systematic to indicate that not one of the formulae can be 
considered exact, unless some unrecognised source of systematic error in the deter¬ 
mination of the wave-numbers may eventually be traced. In choosing between the 
different forms of equation it is accordingly necessary to be guided by experience of 
their application to other series of the same character, if they can be found. The 
result of such trials, as will presently appear, is to indicate that the Hicks 
form of equation is the one which most closely accords with the observations in 
general. 
In the absence of an exact formula, a consideration of the residuals given in Table II. 
indicates that the limits of the “ 4481 ” series may be taken as 49778'0 and 49779'0 
with very small probable error, and these values will be adopted in the subsequent 
discussion. 
§ 4. The Doublet Series of Calcium , Strontium , and Barium. 
Other series of lines apparently similar in character to the “ 4481 ” series of Mg 
were found in Lyman’s observations of narrow doublets of Ca, Sr, and Ba in the 
Schumann region,* combined with Saunder’s observations in the ordinary ultra-violet. 
While the investigation was in progress, however, a discussion of the available 
observations of these series was published by E. Lorenser,! who also found that the 
ordinary formulae could not be applied to them. Lorenser has further established 
that these series stand in the relation of Fundamental (F), or “ Bergmann,” series to 
the systems of series comprising the well-known wider doublets in the spectra of these 
elements, of which the H and K lines of calcium may be quoted as a familiar example. 
In each case the separation of the narrow doublets of the F series is identical with 
that of the first member and its satellite in the Diffuse (D) series of the wider doublets ; 
and the limits of the F are apparently identical with the variable parts of the 
expressions for these lines. 
Omitting Ba, which presents some difficulties, though generally conforming, 
Lorenser’s for mu he} are as follows, the Sharp series being indicated by S :— 
* 1 Astrophys. Jour.,’ vol. 35, p. 341 (1912). 
t ‘Dissertation,’ Tubingen (1913). 
\ Formulae of this type were first employed for the doublets of Ba by Saunders (‘Astrophys. Jour.,’ 
vol. 32, p. 164, 1910). In a later paper Saunders also indicated a connection between the limits of the 
wide and narrow doublets (‘Physical Review,’ Series 2, vol. 1, p. 332, 1913). 
2 H 
VOL. CCXIV.-A. 
