418 
DE. W. M. HICKS: A CEITICAL STUDY OF SPECTRAL SERIES. 
Ill this table under each order the first line gives the wave-length of the observed 
line to the last Angstrom, its intensity, and, where necessary, the displacement or 
linkage to be applied. The second hue gives the wave-numbers of the F lines and the 
thick type the separations from the Fj line adopted. Up to wi = 10 the fourth line 
gives in the same way the wave-numbers of the F lines and the fifth the corresponding 
wave-lengths. In the third line the numbers give the mean limit F(F-l-F), hut only 
the last four significant figures are entered, the complete calculated values being given 
at the head of the table. 
Xofes to Table.—vi = 2. For F3 in addition to that given there are ( - 28) (1) .38632 •72.r = 43101'20, 
(3Si) (1) 38687-71.?> = 01-53, (8) (1) .38988-33.?/ = 01-27, (81) (<1) 38973-59.?/ = 01-71. 
m = 3. The linked Fj agrees with (38i) (2) 23660-79 = ...35-79. The linked F4 with (38i) (1) 24077-41 
and ( — 681) (1) 24062-12 both of which give the same value ...92-30. 
rn = 4. The linked Fi agrees with (-681) (1) 26048-86 =...78-32. For F2,(28i) (1) 26147-89 =...38-06 
is closer to the calculated vahie ...37 - 95. ■ F4has alinkr = 4428-62. For Fg, (- 28i)(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. F3 is also given by (38i) (< 1) 37675-75 = 60-66. For 
F4, (- Si) (2) 35417-16 = ...22-19 gives separation correct. For Fe (-8i)(l) 35680-98 = ...86-07 gives 
much closer separation. 
??/ = 5. ForF.2,(28i) 27498-89 =...88-0-3. For F4, e..35261 -18 = 27947 -18 and (.38i) 27963-59 =...48-50 
both give better separations. F5 shows a series inequality with -{u + 3'28) and ?/-2-93. For Fg also 
(81) 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 some of the other separations too large. ( - 28i) 33644-55 = ...54-37 or 
(- 581) 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. 
??? = 6. All the F are in good agreement with the calculated except for F-2. For this 
6.35617-10 = 28303-00, but too large. Also 28335-60, 28305-20 differ by 30'40 and 684 gives 29-58. 
Near Fi 32727-98, 32762-39 differ by 34-41 and 78i gives 34-37. 
- 38i 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 F3 4 5. There are clearly two sets with probable displace¬ 
ment in the / sequent. MTth the Fi in the table would go better (-684) 33232-22 = ...62-39 for F4 
and (-84) 33378-17 = ...83-21 for F5. The linked Fg agrees with (84) 33427-04 = ...21-95. 
■m = 7. This presents several interesting points bearing on general theory. We may consider F3 as 
correctly allocated since it differs only -55 (dX = -06) from the value calculated from the formula, but it 
is coincident with F4 (7) of the 1864 series. Judging from the separations which are too small (except Fg) 
the observed F4 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 = (-.384) F-t- -43 and 
28733-40 = (28) 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 F4 an exact series inequalit}’. Now a series 
inequality indicates that in the successive lines each is displaced from the preceding by the same amount, 
in this case about I584. 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 I584). The k may be the same 
for the different links within observation errors,* but probably not. If we take X as normal F4 the other 
* To make exact it would require the following :—78givesl-84; 48,1-05; 88,2-10; 98,2-36; 38, -79. 
