DR. W. M. HICKS : A CRITICAL STUDY OF SPECTRAL SERIES. 343 
would seem that in this case we are not dealing with precisely the same entity in the 
two cases. 
Special F Series .—There appears to he a remarkably stable triplet series of the F 
type apparent in most of the gases, but more especially evident in X, in which 
element it was first noticed. Not only are the lines strong and present in a large 
number of orders, but they appear, at least in X, to be little susceptible to displace¬ 
ments such as are common in other types. The separations are 1864, 829. The 
occurrency curve for 1864 is shown in Plate 2, fig. 3, In this, in strong contrast to 
other such curves, it rises to a very high single peak and is practically symmetrical 
on both sides of the peak. The similar curve for A is shown in Plate 2, fig. 5. 
Summation Series .—In the investigation of this XF series a quite new type of 
series was brought to light. The hitherto recognised series appear as the differences 
of two terms A —B. The new one has its wave-numbers of the form A + B. In other 
words, where the old series are difference frequencies the new ones are the corre¬ 
sponding summation frequencies. The notation adopted is to write the corresponding 
terms in Clarendon type. Thus 
F (m) = A—f{m), F(wr) = A.+f{m). 
The list of the lines in X is given on p. 385 up to m = 30. For low orders, m < 3, 
the lines are in the ultra-violet and have to be. sounded for. Similar summation 
series coupled with other F series are also common. It probably explains also the 
crowding of F separations in spectra like that of Cu in short wave regions far beyond 
the F limit which has always appealed to me as a difficulty. It is possible that 
summation series may also exist for the P.S.D. series in all elements, but, as a rule, 
the limits of these are far larger than the F(co), with the consequence that any 
P.S.D. lines must lie very far in the ultra-violet, a fact which explains why such types 
if existing have not hitherto been recognised. The existence of these summation 
series is thoroughly established and their importance as bearing on theories of the 
origin of spectral lines is evident. They would seem difficult to explain on any of the 
current theories. But apart from this the existence of the type is of great value for 
quantitative determinations. This is fully dealt with on p. 384 and it need not be 
recapitulated here. Its importance for this purpose may be realised when it is seen 
that it forms the starting point in the analysis of the BaEm spectrum, that it settles 
in a quite definite way a difficulty arising in the evaluation of the oun in Kr, and 
that it fixes a very accurate value for the limit of the 1864 series in X, thus 
simultaneously fixing a particular d sequent subject only to observation error in one 
line. 
Groups q/D and S Series .—^Not only do we meet with different groups of D series 
depending on different multiples of Aj,* but in the case of Kr there appear to be two 
* As an example, see p. 403, in X with groups depending on 7 OA 2 and 79 A 2 . 
VOL. CCXX.-A. 3 B 
