26 



Prof. W. M. Hicl 



vS on the 



The lines are collected in the following table, together 



with the deduced wave-lengths : — 





A. 



n. 



V(\)-p{m\ 



x f 10R 

 llOR 



267605 



37357-62 





2428-06 



41172-94 





Ht 



1756-0 



56947*61 





1725-5 



57954-22 



(4)16781-73 



3 { 



1582-48 



63191-04 



(1)25834-32 



1572-5 



63500-80 





*{ 



1516-23 



65953-07 



(2)28595-47 



1511-16 



66149-06 



(3)24977-02 



*{ 



1483-12 



67425-21 



(1)30067-59 



1480-5 



67540-65 





•{ 



1464-00 



68301-68 



(An) 30944-04 



1462-75 



68369-80 



(1)27202-44? 



n 



1451-28 



68904S8 



(2)27731-94 



«{ 



1443-6 



69272S8 



(2;-)28104-65? 



The considerable number of combination lines of a very 

 common type p(l) ~jK m ) strongly supports the supposition 

 that the set form an actually related series. The question pre- 

 sents itself whether the objection raised as to the limit not 

 being s(l) can be met. In the foregoing treatment of the set 

 as a P series, 29469 is p(l), and the series is regarded as pro- 

 duced by deducting the sequence p(m) from a limit 70642. 

 We have shown that 70642 cannot be the true P(qo ) or 5(1). 

 This difficulty may, however, be possibly explained by re- 

 garding 70642 as composite — in other words, by regarding the 

 series in question as linked to the true P series and 70642 = 

 P (go ) + links (that is, as forming a parallel series to the P). 

 For instance, it it was the single e link the P(ao) would 

 be 70642-79 — 172523 1=53390-68 =N/(l-4335) 2 , which is 

 within possible reach of s(l). In this connexion the large 

 number of — v links noted above in sounding is suggestive. 

 To these may be added the following for the orders m = l, 2, 

 in which also the linkages v + c are included : — 



(2r) 21629-62 4606-98 (2^)26236-60 14936-34 41172-94 P^fl) 



(1)3741003 460660 (1)42016-63 14930 98+3 3^ 56947-61 +3-3p P' 2 (2) 



(1^)38418-54 4606 + 14929 68 + 3 Zv 57954-22 4-3 3/; V\ (2> 



