DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
401 
In which it may be noticed that the sum of the separations is 2593'12, the normal value. The order to 
is too large to definitely settle the sequence displacements if in them. They would be close to ± 183^ for 
the first and ± 146j^ for the thii’d. But if the connection is real a better explanation might be modification 
of the links, ± on e.u give the exact numerical agreement for the two D 33 lines, and e (± 8^), u{± 23j) 
would give 5 '86 where 6 is observed. 
TO = 5. 33322 has separations 1782'14 (4), 811'06 (4), the sum being normal. 
rii = 6 . 34140 has separations 1782-92 to (2) 35923. Further, there is 30005 1780-45 (1) 31785 
813 4 ( 1 ) 32599, in which the sum of the separations is closely normal. The 2e.u and 2e.v linked lines 
differ by 3-41 and 3-05 from the calculated, but are correct if the links u = u{ - 2oj) and v = v{ - 28^) 
are taken. They are inserted since the corresponding normal links occur in other lines and the amounts 
are exact. 
TO = 7. The 2e linked 34870 has triplet separations 1784 -44 ( 3 ), 813-73 ( 3 ), also the 2e.v has 1778 14 
to intensity (<1). The e.u, e.v linked lines are inserted although their difference as they stand are so 
considerable, because they all are exact if the links involved are taken as displaced (— 8 j). 
TO = 9. There is no observed 2e linked line, but it seems to have split up into two, thus 
(<1) 25293-16 1778-20 (4) 37071-36 
95-65 
(< 1) 25298-14 
The two observed lines are numerically D^j ( 9 ) ( ± A 2 ). 
fii = 10. The 2e.u line is split up into two (< 1) 31350-91, (< 1) 31359-66, of which the former shows 
1778-79 (4), 811-75 (5). 
It should be noticed how many of the e and 2e linked lines introduce the modified triplet separations. 
Notes on Table of (±28j)D .—m = 1 . The displacements on the limits would give 20560-40 and 
20602-89. There is the already noted 20559 near the first discarded for D( 00 ) because it does not pass 
the multiple test. It serves better for (- 28-^) D, but would require at least an observation error 
= - ■ 1 which we have regarded as excessive. There are no observed lines connected by e, u, v links 
to either, nor near them. Those given in the table are, however, very clear. They make the sequence 
term displaced 28^ from that of the D series, viz., - 28j for + 2Si on limit, and +28^ for - 28i on limit, 
i.e., interchange of ± 28j for + 28^^ on limit. In the third series the e and v linked lines differ respectively 
by e + 1 - 74 and v- 1-70. They form therefore a parallel inequality, and are good evidence in spite of the 
considerable difference 1 - 7. 
TO = 2. The limit separation should give for the first series 38345-11, and it apparently exists 
although possibly it belongs to a series commencing with 20559. There is clear evidence of a set 
coiTesponding to to = 1, shown by sounding and giving a sequence displacement of - 68 ^. In the third 
series the line depending on the limit change alone would be 38387-56. This gives links 'a + 2-85 and 
V - 2 - 87 with the lines indicated or a parallel inequality. They are explained by ± 28^ displacements in 
the sequent. 
TO = 3. Here 8 ^ as a displacement in the sequent produces a separation of - 5 . The sequent displace¬ 
ment in the first series is therefore - 8 ^ and -i- 8 j in the third. The line 32304 however shows - 28-^ 
TO = 7. Modified links e ( - 8j) are introduced. This is supported by the fact that the two lines given 
differ respectively by 2-37, 2-32 from values given by normal e, whilst the modification of e by 8^ produces 
2 - 32 . The double example and exact difference give weight to the suggestion. 
TO = 10, 11. Similarly the modified e makes exact agreement, and they enter in a corresponding way 
and in both series. 
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