DR. W. M. HICKS; A CRITICAL STUDY OF SPECTRAL SERIES. 
403 
( 1 ) 19602-66 
1774-45 
(3n) 21377-11 821-04 
(2) 22198-15 
0 
[19623-05] 
18^ 
1777-90 
(2)21400-95 809-53 
(2)22210-48 
(1) 1998972 
29f^ 
(1)20581-64 
1780-27 
(6n) 21769-99 
in which it may be noticed that in the first the sum of the separations is the same as 
178019 + 8I5'30, i.e., the modified + and in the second 809'53 = 8I5’20-5'07 
whilst a displacement on the sequent produces a change of 5'14. With the limit 
51025‘29 + ^ the mantissm of the d sequents are— d\ = '05p~ 
19602, 868240-2973^+6p = 79 x I0998-2-618 + 6j^-2973f 
19623, 868846-2975^^+6^ = 79 x 10998-2-12 + 6y-2975fe^ 
19989, 879853-30-29^+6p = 80x 10998-2-3 + 6j[)-30-29£ 
20581, 898040-31-17^+6‘5p = 80x 10998’2+ 18184+ 6-5jo-31-17^ 
in which p lies between +1 and p' depends on error of extrapolated line, and may be 
>1. Writing as before 10998‘2 = A.j—x these become respectively 
79A2-^-7 + 6j9-79;r-2973£ 
79 A 2 -12 + 6y-79a:-2975^ 
80A, -3+ 6p-80a;-30-29^ 
80A2+29f(l + 7 + 6-5j9-80a:-3ri7^ 
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 8a; = —3^. 
As a further test of the reality of the extrapolated line 19623 linked lines may be 
sought for. There is none for +c, but lines are found close for u, v, e±v, viz., 
(6)23754-27 1778-40 (3) with w-2-1 19623-19 
(<lw) 24053-37 „ 'y + 2-1 19623-16 
(2)24509-92 „ e-v 19623-82 
(2)3136271 „ e + v 19620-66 
Taking 19623 as D^g, the satellite differences are 29f(i and 18(^. Since 18x 5 = 90 
and 29f X 3 = 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 
