110 PROF. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 



within errors of observation. The chief exception is for the first line of the sharp 

 series, which is shown to be probably due, on other evidence, to a change in N. 



2. The existence of a new fundamental sequence F (in) whose denominator is either 



/ I \ 

 m+/j, 2W (RiTz) or m + //, 2W (1- -), where W, the atomic weight term, is a small 



fraction of the square of the atomic weight. The dependence of the fraction on the 

 element is not at present determined, but if w denote the atomic weight divided by 

 LOO, the fraction of n? is '0141 for Na and about ,s/(.v 1) x '0141 for the others. 



.1 That the D of the P sequence is found by adding '074560 (\.- ' 21521 \ 9 to 



V m J 



' 1 \ 

 1 W ( 1 ), as found from the F sequence, where s has the values 2.4.5.6 for Na 



\ !>* / - 1 ' 



I/I 



K, TCb, Cs. In the case of Cs, however, in which satellites appear in the D series, 



the term in W ( 1 ) does not occur. 



4. The 1) of the P 2 sequence is found by deducting 2W, or approximately 



0141W 2 Fl + - I, from that of P,. 



L m(.s-l)J 



5. The fj. of the U sequence is found by deducting the same quantity '074560s 

 from 1 W(l j/r 1 ). The form of the term in a has not been determined. When, 

 however, satellites occur, and there are two D sequences, as in Cs, the W missing in 

 the P sequence must be put in here, and the above quantity '074560x6 deducted 

 from 1-2W instead of from 1-W. This gives the p. for D 21 or D 12 . The /* of 

 D n (2) is found by adding i-W to that for D 12 , i.e., W (1-mT 1 ). 



6. In the same way as the P sequence forms a doublet D series, VPi(l) VD (m), 

 Vl } 2 (1) VD?n, so do the D sequence produce a F series doublet when D has 

 satellites viz., VD n (2)-F (m), VD ia (2)-F (m). 



7. The values for the S series show that its ^ is obtained by deducting quantities 

 somewhat smaller than '5 from that for the P, and that its a is always considerably 

 less than that of P. Also, although KYDBERG'S relation S ( QO ) = VP (1) is very 

 closely verified, the other, P(oo) = VS(1) cannot be true with the formulae used. 

 Moreover, the formulae fail to reproduce S(2) within limits of error. Evidence is 

 given that this is due to a change in value of N in the S sequence. A suitable 

 change makes P ( o> ) = VS (1), the difference of the /A of S and P the same for 

 each element, a the same for S and P, and the values of S (2) within the limits. 

 Moreover, in using the He spectra to obtain a more exact value of N than can be 

 expected from H, it is found that N is greater than 109675 for S, by about the same 

 amount in both the singlet and doublet series, whilst close to it for the D', D", and 

 P". The evidence in favour of this explanation is therefore very strong, and the D 

 of S would then be found by subtracting -5-x, where x is small of order '1 from 

 that of P. 



8. The spectrum of Li is abnormal. It is a singlet series in which what has been 



