DR. W. M. HICKS; A CRITICAL STUDY OF SPECTRAL SERIES. 
375 
arrangement in the AgD (4) linkage shown in the c, d, e columns of the map for 
AgPiii [IV.]. The series is in fact continued further than is shown in the present map. 
Starting from 26727 we find a — c + h—d + a—c + a—c (and +d) = Sa + h — {3c + d), the 
actual separations being 770'92 —803’607 + 787'51 —821’81+771‘07 —803'66 + 770'68 
— 80316 (and +825'35). Further, it should be noted that each successive pair is a 
parallel inequality, one in excess and the other in deficit of normal value. It means 
an increased displacement 2^^ in each alternate line. But if the observation errors are 
small, there appear to be indications of simultaneous displacements in the f sequences 
as well as on the limit. In fact a similar phenomenon is indicated in the two next 
orders though naturally some elements are wanting. A precisely similar connection 
is shown by AgS (3), [IV., p. 382], in a still more striking and regular series of 
changes. The elucidation of the laws governing displacements is of the first 
importance and should be one of the immediate objects of investigation. For this 
purpose examples of continuous series of simultaneous and like displacements will be 
of the utmost value. For this reason maps of certain near lines (Plates 4, 5), are 
given for all the orders from 3 up to m = 8, but no attempt has been made to indicate 
exact displacements involving unity. The parallel series F' about 16 below F exist 
for m = 5,'6, 7. The sets connected with F' (7) all show the displacement unity. In 
the lists the true lines are entered as 1 less for m = 6 and 2 less for 7, 8, 9, 10 (fie., 
^ about —2) than the calcidated values. As is seen it makes the observed separations 
more normal and in so far supports the putting of the limit about 2 less. Later the 
actual change in the limit is found to be —1’34. 
KrF. During the work of examining the X spectrum a new type of series, 
associated with the F series, came to light. Whilst the known F type depends on 
the differences of two sequences d(l)—/(m), the new type has a series of lines whose 
frequencies are given by d (l)+/(m). We shall denote the lines of these series by F, 
so that F will denote a difference frequency and F a summation. 
We have already referred to the general properties of these series in the intro¬ 
duction. Some of the material from the Kr spectrum bearing on the subject are here 
collected. In the following lists each order is considered by itself. The examination 
has not been exhaustive so as to involve displaced values, but it is believed all the 
direct observed lines have been included. A few abnormal ones, with considerable 
displacement m the f sequence, have also been entered, as they raised questions which 
require future investigation. The F and F lines are arranged m parallel columns. 
The mean of the two corresponding lines is entered in thick type between them. 
That for the first corresponds to the fundamental limit. The succeeding ones are 
given in the form mean of the first-l-diSerence, and the difference only (which settles 
the denomination of the set) is entered. Thus for m = 2 the first mean is 30674 77, 
that for Fg, Fg is 30976’55 = 30674774-30178 and 30178 is entered. Also over each 
line the difference from Fj or Fj is entered. Notes on detail are appended below the 
lists. The evidence is clear as to the existence of a series of the form A +f (w). If 
3 F 
VOL. CCXX.-A. 
