DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
369 
or say, <18491, or A >5408. This region is examined for the separations in qiiestion 
and lists made. It is then found that some depend on the same first line, in which 
case, they clearly refer to F or related lines. Several sets are found connected by 
one of the ordinary links, which excludes at least one of them as a direct F line. It 
is now easy to select a few sets from the lists which seem suitable for the Fj line. 
This with the given FjCc gives ./’(2), and then Rydberg’s tables give a rough 
approximation to F (3). It is then only necessary to examine the lines near these for 
the separations, in order to find the actual F^ (3). The result of this examination is 
to show that for the first three orders m — 2, 3, 4, the only sets which exist without 
displacements in any correspond to the separation 301, with Fj lines (l) 17321'51, 
(iw) 23353‘84, (3) 26057’20. The formula calculated from these gives as the limit 
30678’64. This is only ‘29 less than dn and is thus in very satisfactory agreement 
with the rule. Using the value of as found from the D series with D(co) 
= 51655'56 + ^' the actual formula is given by 
n 
30678-93 + f'-N/^m+-877406-577'8^'- 
• 023916 - 363 - 3 ^ 1 ^ 
m J 
In this if D ( oo) = S (co), ^' = 4‘27, but if D ( oo) = (— <^i) S ( oo), = f+’15. 
The mantissa of the first line Fj (2) is 
865448-107-26^+I6p - 185 (4678-l--580^'+'034^) = I 85 A 2 * 
within error limits. The lines have been selected as showing the given separations. 
Quite independently they give a formula with the proper limit and with the first 
sequence mantissa a multiple of A2. The evidence therefore for the correctness of the 
allocation is incontrovertible. 
In the consideration of the notation for the various parallel F series it will be 
necessary to determine what is to be understood by the normal separations. If the 
latter are to be decided directly from the Dn (1) lines, the separations must be those 
given above. But a glance at the table of F lines will show that there is a consider¬ 
able variation from these, and indeed from one another—due as we have seen to the 
great variability in the oun displacements. Especially is this noticeable in the 
separations given by the Di(l) satellites as 213'38 and 307 27. In place of these we 
find values about 2, 4 or 6 less, corresponding to 1, 2 and 3 oun displacements. The 
separation 301 is the most frequent displacement from 307 27. Now alters the 
separation by 2’03, and therefore 3<^i alters 307'27 to 301'18. That these deviations 
from normal values correspond to real F separations can be seen by their frequent 
repetition in connection with F lines. See for instance the maps for F, especially 
F (5), in Plate 4. 
* I 85 A 2 = 204A'2 + 38i. 
3 E 2 
