251 
PROF. A. FOWLER ON SERIES LINES IN SPARK SPECTRA. 
accordingly be drawn up for the “ F.P.” system, it being understood that the 
variable parts of the p, d, and s series are equally applicable to the Wide doublets. In 
each case the terms md, &c., are given as derived from the observed wave-number of 
the less refrangible components; they would be the same for the more refrangible 
components if there were no errors of observation. The wave-numbers included are 
those which have been actually observed ; others may readily be obtained from the 
limits and variable parts given. Terms depending wholly on calculation from formulae 
are enclosed in brackets, and for simplicity the satellite has been disregarded. Further 
reference to this table will be made in the discussion of Combination series. 
§ 10. Combination Lines and Series of Magnesium. 
In the discussion of series, the wave-number of a line is represented by the 
difference of two other wave-numbers, the first of which (the limit) is constant for a 
given series, and the other variable, the limit itself appearing as one of the variable 
parts in an associated series. Combination lines and series, as is well known from the 
work of Ritz and Paschen, are formed by taking differences between the variable 
parts from different series. The Fundamental series was regarded by Ritz as a special 
type of Combination series, in which the variable part, in a doublet series, is given by 
m (p x — p 2 ), or m A p, where p x and p 2 are taken from the formulae for the two com¬ 
ponents of the Principal series, or derived from the constant separation in the Diffuse 
and Sharp series. This relation, however, is only approximate, and mf will be used to 
denote the variable part in the Fundamental series. It should be recalled that if there 
are no satellites in the D series, the F series consists of single lines, and that when 
satellites are present in a doublet system, the F lines are also doublets, with a separa¬ 
tion equal to that of the satellite and chief line in the first member of the D series. 
The whole of the “ F.P.” system may be considered to consist of Combination series 
derived from the Wide doublets, or vice versa. Retaining the use of capital letters for 
the Wide, and small ones for the “ F.P.” doublets, and disregarding the satellites, we 
have the relations 
p 2 (m) = 2S— mP 2 , 
Pi i m ) = 2S— mPj. 
s x (m) = 2Pj— mS, 
s 2 (m) ---- 2P 2 —mS. 
d\ ( m ) = 2Pj—mD, 
d 2 ( m) — 2P S — mD. 
f (m) = 2D— mf or 
2 k 2 
P 2 (m) = ls—mp 2 , 
Pi (m) = 1 s—mp x . 
Sj (m) — lp 1 —ms, 
S 2 (m) - 1 p 2 —ms. 
Dj (m) = 1 p x —md, 
D 2 (m) - 1 p 2 —md. 
2D —m (Pj —P 2 ). 
