DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 
439 
from an observed line. Thus in m = 3, the observed is entered as u(3) 3897212, 
whereas the actually observed is v less. 
m. 
Calculated. 
Observed. 
dk. 
1 
-{(2) 201637 (W.) + ri + r2}.U 
# 
2 
(0) 25432-35 (W.) 
* 
3 
38972-54 
v.{3) 38972-12 (R.) 
-02 
4 
43873-80 
e.{4) 43874-02 (W.) 
--01 
5 
4618476 
see Note 
-07 
6 
47454-96 
7 
48227-14 
u.v.{l) 48227-00 (W.) 
-00 
8 
48731-22 
see Note 
N'ote .—For m = 3 the e sounder is too large, and for m = 4 the v is too small to 
act. 
The agreement is so good that the chosen low intensity lines for Sj (l) are justified. 
The low intensity may be explained by the supposition that the energy of the normal 
line has been partly transferred to other displaced ones, in the way indicated above 
for m = 3 and as shown also by higher orders. For m = 4 together with 20195 —the 
line sounded from—W. only observes (2) 201637, and R only (O) 20133’0. These 
differ successively from the first by 30 + . For m = 4 the oun displacement produces 
1 42 on the sequent and the normal 30‘5 on the limit. They are therefore possibly 
e.(^i) Si (4) and e.(2(ii) Sj (4). In m = 5 the e sounder requires 22506, not observed by 
either, but there is an isolated group, 22516'9 by both, (5) 22535'5 (W.), (3) 22540’4 
(R), of which 22535 is 30 ahead of the required line and 22540 is 35, so that the 
former is (— ^i) on the limit. The latter, however, sounds to 4621871 for ( —dj) Si(5) 
and gives Sj (5) = 46183‘25. The d\ = ’07 of the list is based on this. For m = 6 
the e requires 23776’65 with observed (O) 23760’9 (W.) and (lO) 2378375. In m = 8 
the u + v link = 2487l'8 requires 23859’5. The only observed are (2) 23841'9 (W.) 
and (4) 2387r3 (W.) or (5) 70'00 (R.), about equally displaced on either side of the 
normal line. 
Some space has been devoted to the consideration of the S series as on it depends 
the determination of the important u, v links as well as the limit for the D series. 
The latter is perhaps in general the more important as it affords with the F, the 
means of obtaining accurate determinations of the oun. In the present case, however, 
the measures have such large possible observation errors that they do not add to the 
accuracy already found in the foregoing discussion. A few points only will therefore 
be here referred to. Both the D satellites for m = 1 and the F lines for m = 2 with 
related lines form the majority of the lines in the long wave end of the spectrum 
[n < 20000). One clue as to a distinction between the two sets may be found in 
the fact that where the 5640 link occurs on a D line it links backwards, while in 
the F it links forward. Consequently where a line has a link forward it is probably 
VOL. CCXX.—A. 3 o 
