DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SKRIffi. 397 



for m = 3. Any lines -corresponding to m = 2 would have wave numbers about 500, 

 and to m = 1 negative wave numbers m the neighbourhood of 16000. Now PASCHKN 

 has noted lines which may be treated as the actual lines in question. They depend 

 on terms S' ( )- VD (2) where S' ( ) is the limit of his singlet series, and of course 

 VD(2) is the F(oo) of the above. Using sequences for the 8' series of the form 

 ft. = 1 +f, the limits of the series are 



Zn. Cd. 



29019-96 28843'40 



The lines in question are 



Zn. Cd. 



A = 0238-21 G325'40 



n = 10025*87 15804'98 



Hg. 

 30114-33 



Hg. 



5769-45 

 17327-96 



If these wave numbers be added to F a (oo) m each element, there results 29018'62, 

 28846-14 and 30115-71, i.e., the value of the S' ( oo) above. The corresponding lines for 

 F! ( co ) do not seem to exist. There is no d priori reason to take F,( oo ) rather than 

 Fj ( co ) for Zn. In Cd, however, the case is settled in favour of F 2 , as the other lines 

 exist, viz., -15520'84, -15793'05, -15804'98, giving the differences 266'21, 1T93 

 corresponding therefore to the companion series to D 13 (2), to D 13 (2) and D la (2), D,, 

 not appearing. But in Hg -17327'9G, -17264'98, -17223'97, with differences 

 62 "98, 41 "01 would seem to assign 17327 to the F 3 term. Nevertheless to get the 

 limit of PASCHEN'S S' series it is necessary to take F a ( oo ). 



If these be regarded as the first lines of the F series, the denominators are 

 Zn, 1-943072-33-5^; Cd, l-949840-33'9^; Hg, T908346. In Hg the line 

 n = 17121 '30 would seem to stand in a normal relation to the F,, as it comes into 

 line with the others as is seen below. With this the apparent limit with F, would 

 be 29874*37, giving denominator 1 "916040 32"0 The question now is, are these 

 denominators related in any way to those for m = 3. The differences of their 

 mantissas are, using our new Hg line 



Zn. 



34557-254 

 10(34557-25-4^) 

 = 10A 2 



Cd. 



20547-252 

 2(10273-126$ 



Hg. 



59565-254*5^ 



2(29782-127-2^) 



2A, 



well within errors, it being also remembered that can only be a fraction. The value 

 of A 2 for Hg adopted is the corrected one 29765, from $= 36r85w*. This is a 

 striking connection. It shows that the limits for PASCHEN'S singlet series are either 

 VF(1) or are formed from VF(3) by deducting 10A 3 for Zn, 2A, for Cd, and 

 apparently 2A 2 for a normal type in Hg which then receives some displacement. 



