378 
DR. W. M. HICKS : A CRITICAL STUDY OF SPECTR.AL SERIES. 
improbable that the '3 difference in S could be attributed to a single observation error 
on each of Ah, A 2 . As it has been shown in [III., p. 332] that the triplet separation 
always shows a slight difference in the S from 1 ^ 2 , it is probable that the same occurs 
here also. The evidence there given goes to show that the value obtained from 
Ai + A 2 is always closer to the true value. We should expect, therefore, a value 
between the two values above. 
( 2 ) The evidence obtained from the D qualification test. 
( 3 ) The D satellites whose mantissse depend on multiples of A 2 , viz., 19116 on 
197Ah, and 20763 on I 89 A 2 . 
( 4 ) The mantissa ofy (2) = 185A2. 
Before however conditions (3), (4) can be applied it is necessary to obtain if possible 
a closer approximation to S from (2). The material for discussion is that given on 
(p. 366). We shall discuss it on the two bases of d = 249‘60 +a: and 249‘30 + x where 
X is certainly not greater than "3. The complete conditions are, using the displaced 
values ( — 2 ^ 1 ) D ( 00 ) for (2), (6) and omitting (3) as parallel to (2), 
249-60 + x 249-30 + x * 
(2) 
-2*4+ '16^-4 (^ 1 -^ 2 )+ 13|-x = 
0 
- 6*5 + .. 
= 0, 
(4) 
9*0+ -21^-4 (pi-pi}+ 16ix = 
0 
4 +.. 
= 0, 
(5) 
10 *0+ *32^-4 (_pi-_p5)+ 26ix = 
0 
2*1 + .. 
= 0, 
(6) 
-2*7+ *46^-4 (pi-p6)+ 38fa: = 
0 
-14*3 + .. 
= 0, 
(7) 
16 +l'52^ — 4 (pl—p^) + 126ix = 
0 
-21*8 + .. 
= 0, 
(8) 
8*6 + 2*61^-4 (p,-ps) + 219fx = 
0 
-56 +.. 
,. +220a; = 0. 
It is quite clear that the conditions in the first column cannot be satisfied without 
assuming very large observation errors unless x is negative, nor on the right hand 
column unless x is positive. In other words, S must be < 249‘60 and > 249'30. The 
first four equations, however, give no indications of amount, as the multiples of x 
are not sufiicient to make the term in x more important than the error terms. In 
(6, 7, 8) the conditions may be written with ^ > 1. 
(6) - 27± 8-5 + 38|-a;=0 -14-3..., 
(7) 16 ± 9-5 +126^0; = 0 -21-8..., 
(8) 8-6±10-61 + 219fic = 0 -56 .... 
Nos. (6, 7) require x to be about equal and opposite in the two cases, say, S = 249‘5. 
This would make (8) give —13'5+ 2‘61^ — 4 (pi—ps) =0. This last case offers some 
difficulties which we will consider later. For a further approximation we will there¬ 
fore put A 2 = 4678+x, A '2 = 4241*386 +■907a: which give S = 249*4933 +’OSSa;, and 
Di 5 = 20763*25+ c?n. Then, (p. 366) 
d,,= 884207-30*50^' + 30*50 dn±*5 = 189{4678*343-*161^'+*161c?n±*002} 
/(2) = 865448-107*26^'+16p±*5 = 185{4678*098 - *580^'+*086jo± *002}. 
