378 DE. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 



improbable that the '3 difference in S could be attributed to a single observation error 

 on each of A' 2 , A 2 . As it has been shown in [III, p. 332] that the triplet separation 

 always shows a slight difference in the S from ? i/ 3 , it is probable that the same occurs 

 here also. The evidence there given goes to show that the value obtained from 

 A, + 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 mantissas depend on multiples of A 2 , viz., 19116 on 

 197A' 2 , and 20763 on 189A 2 . 



(4) The mantissa off (2) = 185A 2 . 



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 S = 249'60 + a; and 249'30+x where 

 x is certainly not greater than '3. The complete conditions are, using the displaced 

 values ( 2$i) D ( oo) for (2), (6) and omitting (3) as parallel to (2), 



249'60 + a: 249'30 + a: 



(2) -2'4+ l6-4(p 1 -p,)+ 13&E = 6'5 + ... =0, 



(4) 9'0+ 21-4(p 1 -p 4 )+ 16^ = 4 +... =0, 



(5) 10'0+ 32-4(jp,-p 5 )+ 26%x = 2'1 + ... =0, 



(6) -27 + ' 46-4(p,-p ti )+ 38fa; = -14'3 + ... -0, 



(7) 16 +1-52^-4 (p,-jo 7 ) + 126jz = -21'8 + ... =0, 



(8) 8'6 + 2-61-4(p 1 -p 8 ) + 219fz = -56 + ... + 220z = 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, <^ must be < 249 '60 and > 249 '30. The 

 first four equations, however, give no indications of amount, as the multiples of x 

 are not sufficient 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 



(7) 16 9'5 



(8) 8'610'61+219fa;=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 '6 1-4 (p t -p) =0. This last case offers some 

 difficulties which we will consider later. For a further approximation we will there- 

 fore put A 2 = 4678 + a;, A' 2 = 424r386 + '907a; which give S = 249'4933 + '053a;, and 

 D 16 = 20763-25 + dn. Then, (p. 366) 



d u = 884207-30-50^ + 30-50 dn "5 = 189{4678'343-161'+-161dn-002} 

 = 865448-107'26'+16p-5 



