DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 403 



(1)19602-66 1774-45 (3n) 2137711 821'04 (2) 2219815 



a 



[19623'05] 1777-90 (2)21400'95 809'53 (2)22210'48 



18S 

 (1)1998972 1780-27 (6)21769'99 



29f<$ 

 (1)20581-64 



m which it may be noticed that in the first the sum of the separations is the same as 

 178019 + 815-30, i.e., the modified v^ + v.,, and in the second 809'53 = 815 - 20-5'(;7 

 whilst a S 1 displacement on the sequent produces a change of 5 '14. With the limit 

 51025'29 + the mantissas of the d sequerits are d\ = '05p 



19602, 868240-2973+6p = 79x 

 19623, 868846-2975^+6^' = 79 x 

 19989, 879853-30'29^+6p = 80x 10998'2-3 + 6p-30'29 

 20581, 898040-31-17+6-5p = 80x 10998'2 



in which p lies between 1 and p' depends on error of extrapolated line, and may be 

 >1. Writing as before 10998'2 = A 2 x these become respectively 



79A 2 -l2 + 6p'-79a;-2975 

 80A 2 -3 + 6/>-80C-30'29 



The multiple rule requires that the last four terms in each expression must vanish. 

 This is clearly possible for small values of p, say <|-, and a single relation between 

 x and say 8x = 3 



As a further test of the reality of the extrapolated line 19623 linked lines may be 

 sought for. There is none for +e, but lines are found close for u, v, ev, viz., 



(6)23754-27 1778'40 (3) with u-2'1 1962319 



(<ln) 24053-37 'W + 21 1962316 



(2)24509-92 e-v 19623'82 



(2)3136271 e + v 19620'66 



Taking 19623 as D 13 , the sateUite differences are 29|<J and 18$. Since 18 x 5 = 90 

 and 29f x3 = 89"25, these separations are very closely in the ratio 5 : 3 in accordance 

 with the rule for the known triplet series in other groups. The triplet set 19602 

 appears somewhat anomalous. The middle line appears to have the modification so 



