DE. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
395 
the F sets depending on (30725). In case, however, of dn being small and the 
mantissa involving the term in S, we might expect still to find lines depending on the 
90As, as the presence of the S suggests satellites. To get 90As, requires a 
displacement which decreases/(l) by 17’02. In other words lines with wave-numbers 
17'02 larger for F and less for F. We do not find this completely, but the following 
sets are observed, already given in the notes to the list under m = 1. 
2e.Fi 
2e.F2 
2e.F3 
(6) 17638'55 
(3) 19503'29 
(l) 20333'22 
12-52 
(3) 19515'81 
25-53 
(5) 17664'07 
3c,Fi 
Se.Fa 
3e.F3 
[36498'90] 
[38363'40] 
(l) 39193'40 
5-08 
(1) 36493'82 
17-64 
17-66 
(2) 38345'76 
(2) 39175'74 
25-45 
26-31 
(3) 36473-45 
. (1) 38337.09 
In which permissible observation 
errors are dn = ±'7. As 
has been seen the 36493 
corresponds to a displacement 
in the limit. The others to 3^i, 6(5i, and 8 in the 
sequent /(l). The lines 38345 
, 39175 consequently have their sequent mantissa 
exactly OOAg. 
Further it was found that {3n) 39683'95 is 2e.v.{ — Sy) Fi (l). The next 
preceding line to this is (l) 39666’49 or 17'46 behind it, again showing the required 
S displacement and having the 90 As mantissa. 
If it be granted that the series is of the F type, the limit must be a d-sequent. 
Consequently the mantissa of 30725'30-l-^ must be a multiple of the oun. Its 
mantissa is 889322 —30'74^ 81 (l0998'13-'38^) —10(i] = SlAs— 10(^1 with great 
exactness. Let the true value of As be 10998'20-fic. Then if the relation is exact 
81a;-l-30'74f + 5'7 = 0 or —2'63a:—'18, x= —'38^—'07. Now we know that 
^ must be a small fraction, certainly < + '5. Hence x must lie between + '2 and 
As = 10998'20±'20. We should, therefore, expect this value for As except possibly 
where electronic changes of atomic weight came in, as has been suggested above. If 
then the 1864 separations depend on exact and 2A2-f6(5i we get as closer 
approximations 5'6di/i = 1'40 or dvi = '25 and '80-^ 13'5dj/2 = 0 or dv.^ = —'05, in other 
words = 1864'35, = 829'59 when the limit is 30725. When this limit is 
displaced by these change by '45^, '22y. 
