36G 
DR. W. M. HICKS : A CRITICAL STUDY OF SPECTRAL SERIES. 
existence of the supposed cause of the ahiionnal D triplet separations. The value 
of S given Ijy both the 83 ( 1 ) has been seen to be 249'6 with Ah = 4243'2, 
Ag = 478O'O. The maximum observation errors will be taken as ‘03 A and the 
actual O —C error he written —'OSp. The mantissae for the various Dj lines are then 
1. 20976 890749-30-82^+4p, 
2. 20875 887648-30-66^+4jo, 
3. 20871 887520-30-66f+4p, 
4. 20842 886640-30-61^+4^, 
5. [20763] 884207-30-50^+4p, 
6 . 20669 881350-30-36^+4j9, 
7. 19928 859253-29-30^+3p, 
8 . 19116 835908-28-21^+3^, 
3101 — '16^+4 (pi—ps) ^ 
3229 — -16^+4 
4109 - -21^+4 {pi-^ 4 ) 
6542 - ■32i+4:{p,-p,) 
9399 - -46^+4 
31496 - 1 - 52 ^+ 4 (^ 1 -^ 7 ) 
54841-2-61t^+4(pi-j08) 
12p-19-. 
13^-16-.. 
16|-^-9-.. 
26 i^- 10 -, 
37|^-23-, 
126i(5-16- 
219f^-8-6- 
The test requires that the expressions to the right of the first term in the last 
column should vanish. The effect of any possible value of f is small. Further, 
as ^ is probably known within ±‘2, it is only in the two lines, 7 , 8 , that it can be 
effective towards satisfying these conditions. It is clear then that the conditions can 
be satisfied within possible observation errors by Nos. 4, 5, 7, 8 , and not by Nos. 2 , 
3, 6 , nor by 8 , if S requires diminution by as much as '1. 
Considering 1 , 4, 5, it may be noticed that the separations of 4, 5 from 1 are due 
to 16|-(5 and 26|-(i. Since 16|-x8 = 132 and 26^x5 = 13r25, these separations are 
in the normal triplet satellite separation ratio. Moreover, the mantissa of the extreme 
satellite 884207 = 189x 4678-3 = I 89 A 3 within our present degree of approximation 
to S. This again satisfies the normal rule. It is clear, therefore, that these three 
lines form a normal triplet D (l) set. As to Nos. 7, 8, the ratio of separations is not 
that of two satellites to 20976 as D„, although near it. The mantissa of (8), however, is 
835908 = 197 X 4243-1 = 197. Ah within our present approximation to S, and suggests 
that it is the extreme satellite of another group. Returning to the other lines it 
remains to see if they satisfy a test with a displaced D(oo). Now yS^ on D(oo) 
produces a change of—4-42^ and consequent changes in the mantissse as follows; 
135 - 51 ^ in ( 2 ), ( 3 ), 134 - 18 ^ in (6), 124-7^ in (8). As 124-80 = 2^i it follows that 
the test for (8) is unaltered and those for 2, 3, 6 become 
- 10 - 71 ^- 19 -..^. = 0 ; -10-71?/-16-... = 0 ; -9-38?/-16-... = 0 ; 
whereas in (8) the corresponding condition is not changed, but the mantissa becomes 
835924+ 2yfk = 197 (4243-1 +-63/y). In this case a displacement of.one oun in the 
limit produces the same effect as that of two ouns in the sequent. The test for the 
others is very closely satisfied by y = —2, or the supposition that they belong to a 
