436 
DE. W. M. HICKS: A CKITICAL STUDY OF SPECTRAL SERIES. 
The limit 50403 and S — 1787’01 require the smallest changes and seems prefer- 
al)le, although limit 50410 and ^ = 1786 is perhaps possible. Both 1787’87 and 
1785'26 would appear excluded. The numerical work to follow will he based on the 
limit 50403, v, = 53707+ dp„ v., = 264:97+dv,, S ( oo) = 50403-00+ f. These make 
A 1= 72820, A2 = 32166. 
With these more exact values of S(cxd) and it is now possible to obtain the 
important constants, the ^-links. They are found to be 
a = 4630-72-4-lla:+-010^+-74^1/1 c = 6277-21-6-16a;-'020^+r347dri 
h = 5370-70-5-01* d = 7 399'60-7'67x--04:6i-\-V322dv, 
e = 23678-42-22-96*--056^+4-912dj.i 
where the terms in * denotes the changes for a displacement of xdj in S (oo). 
To determine the v links requires a knowledge of Sj (l). It is impossible to obtain 
really definite information on this point from direct observations. In default of this 
the following considerations will give some indications, and will serve to illustrate how 
the laws of relationship already determined can give clues indirectly. In the cases of 
A, Kr, X the lines for Si(l) are respectively —42642, —42469, —42153. The corre¬ 
sponding line for RaEm should therefore be looked for about —41800, with 5 ( 1 ) = 
P(go) about 50403 + 41800, or, say 92200. The e link unfortunately is too large to 
test for the lines for it would reach back to lines about 11103 2649*5 12751*5 
5370*7 ] 8122-2, of which the last only would be in the observed region. Con¬ 
sequently no evidence can be obtained with reference to it from the i/g separations. 
There is a strong line at (8) 17909*9. It would give Si(l) = 41586, smaller than 
seems likely. Also it has a 5637 link not usually connected, so far as we yet know, 
with S lines. It however is the only strong line in the neighbourhood, and it wall be 
probably wiser to conclude that the S (l) line has no linked e line to it. The above 
value for P (<») gives a v link about 13660, and this link on the supposed S (l) should 
produce a line about 28140. We find the set 
( 2 ) 20163*7 2645 ( 4 ) 22808*68 [28183*7] 
in which the last is extrapolated by the normal v^ + v^ from the first. 
It falls in the large gap where no lines have been observed and the spectroscopic 
apparatus was defective. If this be really the S (l)—u set, it is possible to calculate 
what the ti, v links are. Thus Sj (l) = -(28183*7 + u), s (l) = P ( “ ) = 78586*7 +'y, and 
V is produced by the — A^ displacement in the denominator of this. As u by a rough 
determination is in the neighbourhood of 13660, it can be put = 13660+ * where x is 
not very large and can be determined by the condition that 13660 + * is the change 
