372 
DR. W. M. HICKS : A CRITICAL STUDY OF SPECTRAL SERIES. 
Here there is an example of 1/3 or of I'j appearing as links, omitting 97'85 as a 
donl^tfnl connection. The 1/3 is the exact D satellite separation. Moreover, the 
mantissa of 17594 is 895149 —110’63f, differing from that of/(2) = 865448 — 107'26f 
hy 29701-3-37^+16-5p = 7 (4243-00--48^+2-3p) = 7A',. This is a clear displace¬ 
ment by 7A'o, for f cannot be more than a few units and p is a fraction. It is clear, 
therefore, that 17594 is Fi(2)(7Ah) and 17695 is F 3 ( 2 )( 7 Ah). The next two must 
therefore be only the linked lines F 2 (2) ( 7 A' 2 )+ 1 ^, +i't There is a line (l) 17692'54, 
separated by 2"5 from 17695, which might suggest the displacement (ij in the limit. 
But 2 ’5 is too large, and the line itself is really a linked line to viz., (c)D,(l). 
( 2 ) 
(2) 1797278 135-77 (1) 18108-55; 204-97 (1) 1817775; 309-42 (2n) 18282-20 
e 
[21154-13] 102-28 (1) 21258-41; 1047-34 (1) 22203-47; 1857-50 (<1) 23013-63 
This is a specially interesting displaced set in that it contains all the seven 
separations, three directly depending on the line 17972 and the remainder on a line- 
linked to it by the e link. The mantissa of 17972 is 937966 — 115-6^, which is 
72518 —8-35£ above that of/( 2 ). This is very close to HA's-tA 2 = 72553. The 
line may be written F^ ( 2 ) (l 6 A' 2 -l-A 2 ). Call this Xj. Then remembering that 
produces 2-03 in the limit and -54 in the sequent, we see at once that in the others, 
for 135-77 = 13374 + 2-03 is (-dj) X^ exact; for 204-97 = ^ 5-8 is (4,!i) X 5 ; for 
309 - 42 = i'fi + 2 is ( —(5i)X(-. The others depend on e + X^ The separation 102-28 is 
the mean of 1 ^ 2 , vg which depend on two d sequents differing by 2 ^^. It may therefore be 
written as either ((^j) r/jg or ( — Si) we will write it X 2 g + e. For 1047-34 = — l the 
displacement is — 2 ^i in the sequent, or the line is X 7 ( —2(5i).e. For 1857-50 = rg— 2-6 
and the line is (S^) Xg.e. 
(3) 
( 1 ) 19343-33 
r 213-96 ( 1 ) 19348-50 
( 1 ) 19134-54J 
822-11 Li856-62 (5) 20991-16 
(1) 19956-65 308-13 (l) 20264-78 
With 30678 + ^ the mantissa of 19134 is 216805 —133-50f above that oi f(2). It 
is in the neighbourhood of 51 Ah- The whole set of lines are representable as follows 
(putting as before ^ = —1-34):— 
19134 = (-2(^0Fi(2)(51A'2-2(5i) 
19348 = (-2(ii)F5(2)(51A'2) 
19343 = F5(2)(51Ah) 
20991 = F8(2)(51A'2) 
19956 = (-2^i)Fi(2)(51A'2-2^i)+c^ 
20264 = (-2^i)F6(2)(51A'2-2^i)+c^ 
(-2J,)Y,(-2J.) 
(-2«Y, 
V 
Y, 
(-2(S,)Y, (-2i,).(i 
(-2Ji)Y,(-2^,),(i 
