DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 



391 



Both separations are about 1 6 too large and further Y l is about the same amount too small. Now 28, 

 on the sequence term produces a change of 1 40. This would indicate that with the 8 displacement 

 on the limit concomitant displacements of 28, occur in the sequence so that the observed lines are 

 (8) F, ( - 28j), (8) F 3 , (78j) F 3 (28,). The whole set again is remarkable for connection with parallel sets 

 separated by the normal i>, = 1778. 



m = 5. There are observed lines for F,. 2 , FS 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 : 



(8)F 



(28,) F 

 F 



(-38,)F 

 (-S)F 



ri863-57 (3)29540-09 830-59' 

 (1)27676-52 J 1-84 



[.1865-41 (2)29541-9.3 828'75. 

 19-63 



(5) 27696-15 

 15-51 



(1) 27711-66 

 (5) 27714-80 



1865-51 (1)29561-66 



1863-73 

 1869-68 



(3) 29575-39 

 (2) 29584-48 



829-36 



(In) 30370-68 



11-81 



(<1) 30382-49 



22 26 



(5) 30404-75 



Here 1-84 is an exact 38 displacement in the sequent. The mesh shows series inequalities with the 

 i/j + 1/,, = normal values. The two lines in question are clearly + 68, displacements on a normal line 

 (8)F 2 . On F,(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-_>, i.e., 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 7. The values of F, ( o&), F 2 ( oc) 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 (8,) 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 F, in the line (4) 29024-43, which as ( - 8,) F, gives 29019-46 for F,. It should be noted that 

 the energy of Fj 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 i> 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 (2) 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 making 

 F 3 = 35124-78 with i/ t = 831-94. 



m = 8. No line is found for the calculated 29377-00, or 77-23 if we allow the same 0-C as for 

 m = 7. The lines (3) 29368 -41 as (28j) F, and (1) 29403 -29 as ( - 58,) 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 (58,) F, and (4) 32098-20 as (-58,) F, give respectively 32Q73-76 and 73 -36 or 



VOL. COXX. A. 3 H 



