406 
DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
0 
The mean of the two first separations is 1777'90 or exact and we have an exact 
parallel inequality. The inequality is due to two successive displacements, and 
37159 is exactly extra on the calculated 37174, or 76S from the first satellite. 
The fu'st two orders of the two groups are represented in the following scheme in 
which the satellite separations are given as sequent displacements from dn ;— 
The 79Aa group. The 70Aa group. 
m = 1 . 
[19623-05] 
(2) 21400-95 
(2) 22210-48 
[16013-45] 
(1) 17791-35 
(8) 18607 
47|8 
485 
195|5 
(1) 19989-72 
(6ft) 21769-99 
[17725-39] 
(3) 19503-29 
29|S 
122f5 
(1) 20581-64 
145 (1) 20305-60 
m = 2. 
(1) 38129-37 
(1) 39907-58 
(1) 40717-94 
(1) 37159-39'1 
1 
444S 
4415 
4615 
19918 ' 
Ul) 38940-81 
(<1) 39754-48 
(In) 37166-43J 
1 
(1) 38199-58 
1975 
19815 
198|5 
31P 
(2) 37606-15 
(1) 39386-98 
(1) 38217-68 
(3) 28548-26.6.^ 
12315 
122|5 
285 
285 
(10)38366-36 
145 (1) 38285-86 
Without dealing with the whole of the material at disposal we will illustrate its 
application by considering in more detail the portion of the spectrum given on p. 382 
in which the majority of the lines undoubtedly belong to D (l) systems. It is to be 
noticed that the effectiveness of the method in the present case-depends on the facts, 
(l) that the observation errors do not exceed d\ = '05, and (2) that with m = 1 it is 
consequently possible to determine the values of the maiitissse to within 6 units in 
the sixth significant figures, whilst a displacement of one oun in the sequent produces 
a change in \ of the order 1‘2, or twenty-four times the maximum observation error. 
The limit 51025 being supposed displaced by becomes 51025'29 —10‘62^ + ^. The 
mantissse of the sequences are then calculated with this limit, and expressed in terms 
of As, <5i, X and p where As = 10998’2 -I- x, and —p is the ratio of the observation error 
to the maximum {dX = ’05). The series more fully discussed above is definitely taken 
as depending on the limit p = 0. In other words the mantissa of 19989 is exactly 80As 
which condition requires, writing q for its p, 
3-2 + 30-29f-6g + 80.x = 0, 
and gives a relation between ^ and x. The term in x in each mantissa is then 
eliminated by means of it. There can be little doubt about the allocation of 19889, 
