DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. V.)! 
Both separations are about 1 ’6 too large and further F, is about the same amount too small. Now 25^ 
on the sequence term produces a change of 1-40. This would indicate that with the S displacement 
on the limit concomitant displacements of. 23^ occur in the sequence so that the observed lines are 
(S)Fi(-28j), (S)F 2 , (7Si)F3(28j). The whole set again is remarkable for connection with parallel sets 
separated by the normal jq = 1778. 
m = 5. There are observed lines for F^.o, F 3 is entered as depending on a u link. F .2 is too large by 
about one unit, but F 3 - F;^ is normal. This order affords good evidence for the existence of the displaced 
sets. Consider the following system of lines :— 
I 
ri863-57 
(3) 29540-09 
830-591 
( 8 )F 
(1) 27676-52 J 
1 
1-84 
\ (In) .30370-68 
1 
ll865-41 
(2) 29541-93 
828-75 J 
1 
19-63 
11-81 
(280 F 
(<1) 30382-49 
F 
(5) 27696-15 
1865-51 
(1) 29561-66 
15-51 
22-26 
(- 3S0 F 
( 1 ) 27711-66 
1863-73 
(3) 29575-39 
829-36 
(5) 30404-75 
(- 8 )F 
(5) 27714-80 
1869-68 
(2) 29584-48 
Here 1 84 is an exact 38 displacement in the sequent. The mesh shows series inequalities with the 
'4 T ''2 ~ normal values. The two lines in question are clearly ± 6 Sj disjjlacements on a normal line 
( 8 )F 2 . On Fi(oo), 8 gives 19-88, and 38^ 14-91; on F 3 , 28^ gives 11-30 and 8 22-60. These show 
how closely all the conditions of the allocations are satisfied. Further, it shows how 29561 has its excess 
value and that the normal sequent should be the same as in ( 8 ) F 2 , ie., 9 less, thus making its separation 
with F = 1864-61. The same sequent change is shown by F 2 . Both give it as ( 68 ^)/. 
m = 6 . Again with an even order the F lines do not appear, but there are apparent also a congery of 
displaced lines analogous to that in F (5). The lines given in the list give wave-numbers 28498-61, 
30362-74, 31191-93. On the contrary, F lines are observed although F 3 has probably been displaced. 
These also show evidence of displaced sets, e.g., (In) 32972-50 1864-28 (< 1 ) 34836-78 is 20-53 ahead 
of F^, and 8 on the limit gives 19-88. 
m = 1. The values of F;^ ( go), F 2 ( oo) as deduced from the means are clearly too small. F;^ (7) is very 
close to the calculated value, so that if any error has been made it is probably due to the F which should 
be about 1-8 larger, and suggests a close doublet, i.e. a small sequence displacement as in the preceding 
sets. As supporting this there is a line ( 1 ) 32426 -15 which as (Sj) F^ would give 32431 -12 making with 
F;^ the limit 30725 - 22. This corresponds clearly to the normal value. A similar displacement is also 
found in Fi in the line (4) 29024 - 43, which as (- 8^) F^ gives 29019 - 46 for F^. It should be noted that 
the energy of F^^ has passed chiefly to the displaced line, whilst in F 2 most of its energy remains with it 
and a fraction passes to the displaced line. This probably means that only a small number of the normal 
F 2 configurations are broken up, whilst most of the F^ are. F 3 as ( 5 ) 31717-13 gives V 2 too large. This 
line and (4) 31705-47 are separated by 11-66 or a 28^ displacement, so that there is a concomitant 
sequence displacement. A similar effect is shown in F 3 with two lines {2n) 35119-14, (2) 35126-05. 
The lines entered appear correct for they give the normal limit, but their half difference shows a displace¬ 
ment in the/(7) sequent. The normal line would appear to be given by ( -28^) F 3 = 35136-05 makino- 
F 3 = .35124-78 with ..j = 831-94. ^ 
ra = 8 . No line is found for the calculated 29377-00, or 77-23 if we allow the same 0 - C as for 
rn — t. The lines (3) 29368-41 as (2Sj) Fj and ( 1 ) 29403-29 as (-58j)F give respectively 29378-34 and 
78 45, which are larger than should be expected. The calculated value has been taken as correct. Also 
the lines (1) 32048-92 as (58j)Fj and (4) 32098-20 as (- 58j) Fj give respectively 32073-76 and 73-36 or 
VOL. CCXX.—A. 3 H 
