348 
DR. W. M. HICKS : A CRITICAL STUDY OF SPECTRAL SERIES. 
the above there are lines (In) 26014‘23 and (3n) 25295'58 respectively 1232'39 below S 2 and 1232’66 
above 24062'92. Now 1231 • 14+ -.SO^Ao is the calculated value of a link e' constituted in the same way 
as e, but with A 2 in place of Aj. 
S(3). 
(2) 39063 1879-80 
( 2 n) 33791 2x 3182-59 Sj [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) (- 96), also (S)S 2 ( 3 ), but see below. 
Note that there is a rather abnormal +e 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 3 ], 
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. 
S(4). 
(1) 41919 3178-11 Si 
(1) 42686 
3185-84(38i)S.2 
(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 (38i) S 2 and (28i) S 3 . 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 S 2 
and S 3 would be 45884-31 and 46193-51. The former has links 1881-66 back to (1) 44002-65 with a 
further?), 1942-72, back to (3) 42059-93. No direct link is found for normal S 3 . 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) (2Si) S 3 and (e)(-28i)S3, indicating 
that the normal S 3 line has been split into two by displacements ± 2 Si 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. 
S(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 dX = - -08. 
