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 m 

 is too large to definitely settle the sequence displacements if in them. They would be close to 188, for 

 the first and + 148, for the third. But if the connection is real a better explanation might be modification 

 of the links, + 8, on e.u give the exact numerical agreement for the two D 33 lines, and e(& l ), w(28,) 

 would give 5 86 where 6 is observed. 



m = 5. 33322 has separations 1782 '14 (4), 811 '06 (4), the sum being normal. 



m = 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 le.v linked lines 

 differ by 3 41 and 3 05 from the calculated, but are correct if the links u = u ( - 28,) and v = v ( - 28,) 

 are taken. They are inserted since the corresponding normal links occur in other lines and the amounts 

 are exact. 



m = 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,). 



m = 9. There is no observed 2 linked line, but it seems to have split up into two, thus 



(< 1)25293 -16 1778-20 (4)37071-30 



95-65 

 (<1) 25298-14 



The two observed lines are numerically D,, (9) ( A a ). 



m = 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 o/(28,)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 ( oc) because it does not pass 

 the multiple test. It serves better for ( - 28,) D, but would require at least an observation error 

 </X = - 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., -28, for + 28, on limit, and + 28, for -28, on limit, 

 i.e., interchange of 28, 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. 



m = 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 

 corresponding to m = 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 u + 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 - & l and + 8, in the third. The line 32304 however shows - 28,. 



m = 7. Modified links e ( - 8,) 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. 



m = 10, 11. Similarly the modified e makes exact agreement, and they enter in a corresponding way 

 and in both series. 



3 I 2 



