DE. W. M. HICKS: A CEITICAL STUDY OF SPECTEAL SEEIES. 
433 
The material at disposal then goes to show that the S separations are near 5371, 
2649 for some definite limit and 5374, 2652 for another whose limit mantissa is one 
oim less. 
Arguing from analogy with the successive spectra of A, Kr, X we should expect to 
find in the observed region only lines corresponding to D (l) and S (2). The D (2) 
lines would be considerably shorter than the last observed line n = 33259. The S (l) 
would be in reversed order with Sj (l) near -42100 or 83 ( 1 ) near -34000, the first 
absorbed by the glass apparatus used. We should expect D (l) lines up to the 
longest observed (n = 14166) with Dii(l) lines down to at least n = 21000, and 
showing the same kind of modified separations as in previous cases, and taken 
account of above. Si (2) should be about 25600 with 8^(2) about 31270, just on the 
observed boundary and S 3 ( 2 ) quite beyond about 33900. This absence of 8 sepa¬ 
rations is the reason why it was so difficult above to obtain accurate values of j/j, v.^ for 
a definite limit. By themselves therefore the material is hopelessly inadequate to 
determine the 8 ( 00 ) limit, the values of Aj, Ag, or of the various links. We have 
only five possible—or three probable—choices for ^ to 5 significant figures, and also the 
value of one d(l) sequent correct to a few decimals, with estimates of the F and 8 
triplet separations. The only method of attack then seems to be an indirect one, to 
tabulate the sets of lines giving the triplet separations, to try to distinguish between 
those related to D and 8 systems, to obtain as close a value as possilfie of the v^, to 
determine some of the satellite separations, and from these last to attempt to find the 
corresponding F series with the same constant separations. These F series ought in 
each set to consist of several orders (m) at least, .as the F ( 00 ) all lie in the observed 
although badly observed region. The observed separations and the values of v.j 
combined with the approximate value of the oun may enable a determination of the 
important constants 8 ( 00 ), A^, A 2 to be arrived at. 
We shall take then 5371+d:^i + and a set about 3 larger for the values of 
V 2 , the two sets belonging to two limits, relatively displaced hy an oun, and both 
giving the same values of Aj, A^. In the above the di>i, dv 2 will probably not be 
greater numerically than 1 . The calculations will be made with the 5371 set and the 
conditions applied dv^= + 1 , &c., and dv-^ = a:± 1 , dv 2 = y±l where x, y are the changes 
produced by the oun displacement. We start the first approximation by taking 
8 ( co) = 50500 + ^ where ^ may amount to several hundreds and in which x, y are of 
the order 47, 2 ‘ 2 . The denominators of the 81 , 82 , 83 limits with their differences 
calculated from these are 
r473697-14'591^ 
1-401073-12-538 {i+dv^) 
r368995-ir699 {i^dv^ + dv2) 
72624-2-053^-t 12-54 dv, 
32076--839 {i+dp,) + ll-70 dv2 
3 N 2 
