384 
DR. W. M. HICKS; A CRITICAL STUDY OF SPECTRAL SERIES. 
separation occurs with 18447 or i/j, 1/3 with 17615. But provisionally that was set aside 
for the moment. If they represented a special D set, the separations ought to 
reappear in a triplet series of the F type, and in the reverse order. From the sets 
already excerpted the lines ( 8 ) 1860779, (lO) 2391572, (5) 26365*19 appeared to 
have all the signs (Bydberg’s tables) of belonging to one series. The formula 
calculated from them brought to light a whole long series of observed lines. The 
limit found was 30724, close to the value already found (30713) as of the 
order of magnitude to l)e expected. This so far supported the supposition of the 
D relation, hut there also came to light another result of evident importance in 
general theory—-viz., the F series already referred to. The ordinary form of a series 
is one in which successive lines obey a formula of the type A —(p [m). In this case 
we find series associated with it whose successive lines are given by A- 1-0 [m). 
This holds for each of the triplet sets, so that the complete series are given by 
A±<pm, B + 0 [m), C ±0 (m), where B = A+1864, C = A-l-1864 + 830. Quite apart 
from the importance of this fact in the theory of spectral series the phenomenon is of 
special use in calculating the various constants on which the series depends. For 
instance the sum of the wave-numbers of two corresponding lines gives 2 A, 2 B, 2 C, 
thus determining the values of the limits quite independently of the nature of the 
series formula used. Moreover, the displacements which so frequently occur in the 
F and I) series in the sequence term introduces uncertainties. This happens in two 
ways. First through the modified values in which it is not always possible to say 
whether the displacement is produced in the Di or the D 3 line. , Secondly because 
the typical line in any order is often wanting and only appears with a very large 
displacement of multiples of A 2 on the sequence term. This effect, however, 
provided it occurs for l)oth sets (F, F), does not influence the values of A, B, C 
thus determined. Cases in point are the Kr sets F ( 2 ) {7A' 2 ), F ( 2 ) (IOA 3 ), 
Fi ( 2 ) ( 16 A' 2 +A 2 ) given on p. 380. In consequence it is possible to determine the 
separations B —A, C —B independently of satellite or other displacements. That such 
sequence displacements occur in these 1864 series is shown by separations which 
deviate from the normal by more than observation errors. 
But, further, the diflierence of two corresponding F and F lines, say Fj — Fj, F 2 —F 2 , 
Fg—Fg, should each give 2/(m), if as is the normal rule the sequence term is the 
same for each line of a triplet. When however—as we have seen in Kr, and shall 
find even more markedly in X —there are displacements in f{m) for successive lines 
in a triplet, these differences will not be the same, and the observed separations will 
vary from the normal values. For instance, suppose y’(?n) becomes f[m)—xfov the 
second set, and/(m) — ^ for the third. The lines are A±f{m), B + (y’(w)— x)... . 
The values of A, B, C calcidated from the sums are not affected, and the real vahies 
of the separations given by A — B, C — B are not affected although the observed 
separations are v-\-x, v -[-y and v—x, v —y. In some cases we shall find evidence from 
close lines with different x or y — hut the results are quite tlefinite. If, however, in 
