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



In this table under each order the first line gives the wave-length of the observed 



O 



line to the last Angstrom, its intensity, and, where necessary, the displacement or 

 linkage to be applied. The second line gives the wave-numbers of the F lines and the 

 thick type the separations from the F t line adopted. Up to m = 10 the fourth line 

 gives in the same way the wave-numbers of the P lines and the fifth the corresponding 

 wave-lengths. In the third line the numbers give the mean limit ^(F + F), but only 

 the last four significant figures are entered, the complete calculated values being given 

 at the head of the table. 



Notes to Table. m = 2. For F 3 in addition to that given there are ( - 28) (1) 38632 72.r = 43101 20, 

 (38,) (1) 38687-71.?' = 01-53, (8) (1) 38988'33.?< = 01-27, (Si) (< 1) 38973 -59.it = 01-71. 



m = 3. The linked F 2 agrees with (38j) (2) 23650- 79 = ...35-79. The linked F 4 with (38i)(l) 24077-41 

 and (-68!) (1) 24062-12 both of which give the same value ...92'30. 



m = 4. The linked F! agrees with (-eSj) (1)26048 -86 =...78-32. ForF 2 ,(28 1 )(l)26U7-89 =...38-06 

 is closer to the calculated value... 37 -95. F 4 hasalinkv = 4428-62. ForF , ( - 28j)(3)26744-54 =...54-72 

 is only -26 greater than the calculated value. Most of the observed lines of this order are one 

 or two units larger than the calculated. F 3 is also given by (38^ (< 1) 37675 -75 = 60 '66. For 

 F 4 , (-8,) (2) 35417-16 = ...22-19 gives separation correct. For F 6 (-8,)(1) 35580-98 = ...86-07 gives 

 much closer separation. 



m = 5. For F,,, (280 27498-89 =...88-03. For F.,, .35261 18 = 27947 -18 and (38 t ) 27963-59 =...48-50 

 both give better separations. F 5 shows a series inequality with - (u+ 3 -28) and u- 2 -93. For F also 

 (Sj) 28113-58 = ...08-49 and (8) 28133-98 = ...13-62. FI is a strong observed line which makes the 

 mean limit ...91 -83 too small and someof the other separations too large. ( - 28^ 33544-55 = ...54-37 or 

 (-53!) 33530-95 = ...55 '50 are better. The latter makes mean limit .. 92 '92 practically exact, and the 

 separations 58-70, 249'00, 538, 680'65 all much improved. 



m = 6. All the F are in good agreement with the calculated except for F 2 . For this 

 e.35617-10 = 28303-00, but too large. Also 28335-60, 28305-20 differ by 30-40 arid 63, gives 29-58. 

 Near F! 32727-98, 32762-39 differ by 34-41 and 78 t gives 34-37. 



- 38 t on the first or 8 on the second give 32742-71 a better line for F as it makes the limit 

 sum = 92-77 and gives better separations with F 3i4 . 5 . There are clearly two sets with probable displace- 

 ment in the / sequent. With the FI in the table would go better (-680 33232-22 = ...62-39 for F 4 

 and ( -3^ 33378-17 =...83-21 for F s . The linked F agrees with (8 L ) 33427-04 = ...21-95. 



m = 7. This presents several interesting points bearing on general theory. We may consider F 3 as 

 correctly allocated since it differs only 55 (f/A. = 06) from the value calculated from the formula, but it 

 is coincident with FI (7) of the 1864 series. Judging from the separations which are too small (except F a ) 

 the observed F a is from 1 to 2 too large. This F = 28773-67 would seem to give some insight into the 

 connection between sequent displacements and concomitant limit displacements or linkage attachments. 

 Thus this line has relations with displaced limits with the two lines 28788-83 = (-38^+ -43 and 

 28733-40 = (23) F- -99 very close, but scarcely sufficiently so to exclude the probability of small sequent 

 displacements. Further, it is linked forwards and backwards with all the three links e u.v as shown in the 

 following scheme on the left. The 24638, 32912 form with FI an exact series inequality. Now a series 

 inequality indicates that in the successive lines each is displaced from the preceding by the same amount, 

 in this case about ISSj. The whole set may then be arranged as indicated in the right-hand scheme 

 where X = 28771 80 = 28773 67 ( - k) and k denotes the displacement (1 158!). The k may be the same 

 for the different links within observation errors,* but probably not. If we take X as normal F! the other 



* To make exact it would require the following : 78 gives 1 84 ; 48, 1 05 88, 2 10 ; 98, 2 36 ; 33, 79. 



