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



Here there is an example of v a or of v e , v 1 appearing as links, omitting 97 '8 5 as a 

 doubtful connection. The v 2 is the exact D satellite separation. Moreover, the 

 mantissa of 17594 is 895149-110'63 differing from that of /(2) = 865448-107'26 

 by 29701 -3'37^+16'5p = 7 (4243'00 *48+2*3p) = 7A' 2 . This is a clear displace- 

 ment by 7 A',, for cannot be more than a few units and p is a fraction. It is clear, 

 therefore, that 17594 is F, (2) (7A' S ) and 17695 is F 2 (2)(7A' 2 ). The next two must 

 therefore be only the linked lines F 2 (2)(7A' 2 ) +v 6 , +i> 7 . There is a line (l) 17692'54, 

 separated by 2' 5 from 17695, which might suggest the displacement ^ in the limit. 

 But 2'5 is too large, and the line itself is really a linked line to D 12 , viz., (e) Di 2 (l). 



(2) 

 (2)1797278 135'77 (l) 18108*55; 204'97 (1)1817775; 309'42 (2n) 18282'20 



e 

 [21154-13] 102-28 (l) 21258'41 ; 1047'34 (l) 22203"47 ; 1857'50 (<l) 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 16A', + A, = 72553. The 

 line may be written F, (2) (16A' 2 + A,). Call this X,. Then remembering that S l 

 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 (-J,) X 4 exact; for 204'97 = i/ B -8 is (4J,)X B ; for 

 309"42 = i',, + 2 is ( ^,)X 6 . The others depend on + Xj. The separation 102'28 is 

 the mean of i> 2 , v ; , which depend on two d sequents differing by 2^. It may therefore be 

 written as either (<5,) rf, :! or ( S^ d l2 , we will write it X 23 + e. For 1047 "34 = v 1 1 the 

 displacement is 2<5, in the sequent, or the line is X 7 ( 2i).e. For 1857'50 = V B 2'6 

 and the line is 



(1) 19343-33 

 r 213-96 (1) 19348'SO 

 (1) 19134'54J 



822-11 L1856-62 (5) 20991'16 

 (l) 19956-65 308-13 (l) 2026478 



With 30678 + ^ the mantissa of 19134 is 216805-133'50f above that of /(2). It 

 is in the neighbourhood of 51 A'.,. The whole set of lines are re presentable as follows 

 (putting as before = 1'34) : 



19134 - (-2^,)F 1 (2)(51A / 2 -2^ 1 ) = (-2^) Y, (-2^) 

 19348 = (-2^)F 5 (2)(51A' 2 ) = (-2JJY. 



= F 5 (2)(51A' 2 ) = Y 5 



= F 8 (2)(51A' 2 ) = Y 8 



19956 = (-2^) F, (2) (51A' 2 -2^) +d = (-25,) Y, (-2^) . d 



