366 DR. W. M. HICKS : A CRITICAL STUDY OF SPECTRAL SERIES. 



existence of the supposed cause of the abnormal D triplet separations. The value 

 of S given by both the S,(l) has been seen to be 249'6 with A', = 4243 '2, 

 A 2 = 4780U The maximum observation errors will be taken as '03 A and the 

 actual O-C error be written -'OSp. The mantissas for the various D, lines are then 



1. 20976 890749 -30'82+4p, 



2. 20875 887648 -30'66+4p, 3101 16+4 (p,-p a ) = 12^-19-... 



3. 20871 887520-30'66+4p, 3229 - 16+4 (j^-jo,) = 13J-16-... 



4. 20842 886640-30'61+4p, 4109 - '21^+4 (p,-p^ = 16^-9-... 



5. [20763] 884207-30'50+4p, 6542 - '32f+4(p 1 -p B ) = 26i<$-10-... 



6. 20669 881350-30'36+4p, 9399 - '46^+4 (p^pt) = 37f<5-23-... 



7. 19928 859253-29-30+3p, 31496-l'52+4 (p^-p,) = 12^-16-... 



8. 19116 835908-28'2l+3p, 54841 -2'61+4 (p^-p^ = 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 is small. Further, 

 as <5 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%S. Since 16|x8 = 132 and 26^x5 == 131'25, these separations are 

 in the normal triplet satellite separation ratio. Moreover, the mantissa of the extreme 

 satellite 884207 = 189x4678'3 = 189A a 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 n , although near it. The mantissa of (8), however, is 

 835908 = 197x4243'! = 197. A' 2 within our present approximation to 8, 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 ( o ). Now y t on D ( o ) 

 produces a change of 4'42?/ and consequent changes in the mantissse as follows: 

 135'5l2/in (2), (3), 134'18</ in (6), 1247s/ in (8). As 124'80 = 2S t it follows that 

 the test for (8) is unaltered and those for 2, 3, 6 become 



-1071y-19-... = 0; -10710-16-... = 0; -9'38y-16-... = ; 



whereas in (8) the corresponding condition is not changed, but the mantissa becomes 

 835924 + 2^ = 197 (42431 + '63/). 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 



