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 be 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-/H, P(m) = A+/(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 ( oo ), 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 RaEm 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 of D and S Series. Not only do we meet with different groups of D series 

 depending on different multiples of A,,* but in the case of Kr there appear to be two 



* As an example, gee p. 403, in X with groups depending on 70Aj and 79Aj. 

 VOL. COXX. A. 3 B 



