DR. 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 

 90A 2 , as the presence of the $ suggests satellites. To get 90A 2 , requires a +S 

 displacement which decreases /(l) by 17 '02. In other words lines with wave-numbers 

 17 '02 larger for F and less for P. 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.F 2 2e.F s 



(6) 17638'55 (3) 19503'29 (l) 20333'22 



12-52 



(3) 19515'Sl 



25-53 

 (5) 17664-07 



3c.Fi 3e.F 2 3e.F 3 



[36498'90] [38363-40] (l)39193'40 



5-08 



(1) 36493-82 



17-64 17-66 



(2) 3834576 (2) 3917574 



25-45 26-31 



(3) 36473-45 (l) 38337.09 



In which permissible observation errors are dn = '7. As has been seen the 36493 

 corresponds to a S l displacement in the limit. The others to 3^, 6(5,, and $ in the 

 sequent f(l). The lines 38345, 39175 consequently have their sequent mantissa 

 exactly 90A 2 . 



Further it was found that (3n) 39683'95 is 2e.v. (-,) F, (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 90A 2 mantissa. 



If it be granted that the series is of the F type, the limit must be a (^-sequent. 

 Consequently the mantissa of 30725"30 + must be a multiple of the oun. Its 

 mantissa is 889322-3074^ = 81 (l0998-13-'38^)-10^ = 81A 9 -10<J, with great 

 exactness. Let the true value of A, be 10998 "20 + x. Then if the relation is exact 

 81o; + 3074f+57 = or = -2'63a;-'18, a; = -'38-'07. Now we know that 

 must be a small fraction, certainly < "5. Hence x must lie between "2 and 

 A 2 = 10998 "20 '20. We should, therefore, expect this value for A 2 except possibly 

 where electronic changes of atomic weight came in, as has been suggested above. If 

 then the 1864 separations depend on exact 5A 2 ^ and 2A 2 + 6^ we get as closer 

 approximations 5'6dv l = 1'40 or dvi = '25 and '80 + 13'5dv 2 = or dv. 2 = '05, in other 

 words i/i = 1864'35, i/ 2 = 829'59 when the limit is 30725. When this limit is 

 displaced by yS 1 these change by "45?/, '22y. 



