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



the above there are lines (In) 26014-23 and (3w) 25295-58 respectively 1232-39 below S 2 and 1232-66 

 above 24062-92. Now 1231 14 + -30rfA 2 is the calculated value of a link e' constituted in the same way 

 as e, but with A 2 in place of Aj. 



8(3). 



(2) 39063 1879-80 



(2n) 33791 2x3182-598, [S 2 ] 3180 (1)44123 



(3) 39000 1942-56 



The line 40926 entered under S 2 is 769-80 ahead of Si. The a link is 768 -98, so that it may be 

 Si (3) + a. It is also numerically exactly the displaced line S 2 (3) ( - 98), also (8) S 2 (3), but see below. 

 Note that there is a rather abnormal + link with the normal value of S 2 . The calculated value of S 3 is 

 41252-26 and is close on the limit of the region observed by BALY. Again with this, e' links are in 

 evidence, viz., (2)42483-95 and (1)40023-21 respectively 1231-69 ahead and 1229-05 behind [S 8 ], 

 whilst the former has v links from it, viz., 1942 '92 and - 1942 '97. They are however not entered on 

 the diagram, since only e, u, v links are there shown. 



In the foregoing three orders the links are found in evidence. In the succeeding orders they are used 

 as sounders. 



8(4). 



(1) 41919 3178-11 Si (1) 42686 3185 '84 (38,) S a (3) 43000 3183-04(2Si)S 3 



1943-10 

 (1) 39976 (1) 43987 1884-63 



The links here are unsatisfactory as well as the lines given for S 2 3 . Numerically the second and third 

 lines are respectively (3<5i)S 2 and (281)83. They may really be displacements on the sequence terms, but 

 if so the order is too high to make any certain decision. Taking Si as correct, the normal value for 82 

 and S s would be 45884-31 and 46193-51. The former has links 1881'66 back to (1) 44002-65 with a 

 furthers, 1942-72, back to (3) 42059-93. No direct link is found for normal S 8 . Its -e link should 

 produce a line at 43010-16. This is very close to the mean of the 43000 shown in the table and a line 

 (4) 43019-17, i.e., 43009-87. In other words, these two lines are (e)(28 1 )S 8 and ()(-2Si)S 3 , indicating 

 that the normal S 3 line has been split into two by displacements 28i on the limit (or + equal displace- 

 ments in sequent). Both linked lines are seen, but only one of the lines themselves, which is possibly 

 due to the fact that they are close on the limits of the observed region. We shall find indisputable 

 evidence of such displaced parallel series as a general phenomenon. 



8(5). 



(1) 42293 



1884-65 



(2) 44237 3181-73 [Si] 



1944-48 



(3) 42352 



The separation - e is given on the value calculated from the formula. In m = 4 the observed is 2 6 

 larger than the calculated, pointing to too small a value for the limit, which is quite possible as the limit 

 determined from lines involving S(l) = -P(l) is never found correctly. An increase of this order 

 makes the - e link in Si (5) normal. It gives the line in the table with dA. = - -08. 



