DR. W. M. HICKS; A CRITICAL STUDY OF SPECTRAL SERIES. 
411) 
separations become normal also, but as they stand Fi and F give the true mean limit. In other words 
they have the same sequent, or the sequent is modified in the same way for both. The normal Fi should 
be as much greater as the normal Fi is smaller, and we do find such indications. The value given for Fi 
was found as the mean of two observed lines 32211’10 and 32213'80, supposed as ± displacements from 
the true line. If 32213'80 be taken as normal Fi it gives as mean limit with X ...92’80. The whole set 
of F and F in this order affords good illustrations of the remarks on p as to the general properties 
of these series. All the F lines show link connections. Thus F.2, -{u-'l), )/.- •!; F 3 , +n- '73 • 
F4, - (u - • 32), M - 2 • 33, V - • 9 ; Fj, + r + 1 '7 ; Ff„ +u+ • 2 . 
214.56, 21462 
e- - 29±2-38 
24638 32912 
ri + 1 ■ 87 Ti + 1 ’ 86 
Fi 
V--70 v + 206 
24346 33203 
e - 44 • 0 
36083 
e.X, e.X(2/:) 
70 X X{2k).u 
K{k) 
v.X{k) X{2k).v 
X (- k).e 
In the preceding table the wave-nnmbers where deduced are entered as depending 
on one given line. But in nearly all cases these are substantiated also by links or 
other displaced limit lines. Although in an exhaustive treatment of the spectrum all 
these must be considered, this is not required for the illustration of general theory, 
and the notes do not go beyond m = 7. The number of the associated lines is 
remarkable. The proof of the existence of these lines depending on other d sequents 
as limits is so important, as a matter of general theory, that a large number have been 
adduced up to m = 7 . To go beyond would be to overload the present communication 
with detail. The prevalence of the u.v. links over e may be noted in the F series. 
In dealing with the 1864 series the mean of the common F and F limits for different 
orders was treated as giving the true value within a very small possible error of 
about ^ = '3. It may be interesting to see how in the present cases the corresponding 
averages deviate from the values which have been established on the 1864 basis. 
The mean values found from the tables and expressed in terms of differences from the 
adopted ones are ‘26, '24, —'33, ‘06, '05, '15 and justify the supposition of the small 
limit of error in The mean separations as found from the same 10 F lines deviate 
from the correct values by ’ 02 , ' 86 , '05, '06, ’ll. The large deviation ’86 is due 
chiefly to the uncertainty of the displacement in F 3 (3). 
The preceding discussion is sufficient to show the excessive number and 
complication of the lines belonging to the F systems in this neighbourhood and that 
the complete problem has only been touched upon. As however the allocation of the 
extrapolated lines 16013 and 16044 as extreme satellites of D series based respectively 
on D ( cxd) = S ( go) and ( —3^i) S ( 00 ) is important, it will be well to consider shortly 
if corresponding F series can be indicated. The two lines referred to give the same 
d sequence, depending on a denominator l + 70Ao. This makes d (l) = 350I2'30. 
