42 
DR. W. M. HICKS: A CRITICAI. STUDY OF SPECTRAL SERIES. 
These last arrangements- are, of course, no argument in favour of the constant ratio 
'21520. They can only be regarded as suggestions of the way in which the 1— 
term may enter if we know that the constant ratio has a real existence, and that this 
modified sequence is the correct form. But in the present state of our knowledge 
nothing is to be gained by attempting a closer approximation. It may, however, be 
noted that the general agreement between the two arrangements A and Ag is due to 
Lhe fact that except for Ba A is roughly SA^. Also as affecting the argument in 
favour of the arrangement, it may be mentioned that a change of unity in the 
multiples of A or Aa in the most favourable dii-ection towaixls the value '21520 affects 
that ratio in the two cases as follows, viz. 
For Mg. . '21380,-21626; Ca. . '21054, '21697; Sr. . '19588, '21960 ; 
and, of course, very much larger deviations for Ba. 
A glance at Table I. sliows that in A1 and the Ga sub-gi’oup the a is always larger 
than '215/4. In fact, the actual ratios of a //4 are 
A1 . . '2528 ; Ga . . '2641; In . . '2419; T1 . . '2664. 
These cannot be the same within observation limits, and even in the Ga sub-group 
In IS too far out to l/e due to mere erroi's of observation. It is clear, therefore, that 
no terms in can occur in the same way as in the other cases. 
In the discussion of the alkalies the term W (l—was supposed to be based on 
the F-sequence, which was taken to be m-i-l—2W^ (l—Here we have only two 
lines each m A1 and 'll allocated to the F^ series by Bitz, whilst those for the other 
elements of this group have not yet been observed. The limits of the F series are the 
values of VD(2). Using this, the denominators of the F series are found to be 
A1 = m+i-•043761 (1-m-i), 
[25A = 50W = '043850±(24)], 
T1 = 791-M--037389 (1-w-i). 
If now as before the ji-seqiience be supposed based on the F-sequence, but that the 
factor i—rn ^ does not now occur, the denominator for A1 may be written 
m 
-1-1-'043761 A-294286 (1-'21526m-0. 
Unfortunately wo are not able to compare with the other elements of the A1 sub¬ 
group (Sc, Y, La) to see if tliey follow an analogous rule ; Ijiit the appearance of the 
C.alled by some German writers Bercmann’s 
alkalies. 
series, as he discovered the analogous series in the 
