PROF. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 81 



We might have expected that the differences would have come out proportional to 

 the squares of the atomic weights. It is not so, however ; nor is there a regular 

 progression, as the order of increase is Na, Rb, Cs, K. 



In the original calculation the limits of P 2 were found from the observations, and 

 not by making P 2 ( oo) = P, ( oo), except, of course, for Na, where only two lines of 

 NaP 2 had been measured. In this case the difference of the D's of P! and P 2 involved 

 a as well, and an inspection showed that the ratio of Sa to S/t was about | for K, 

 \ for Rb, and \ for Cs. If this apparent rule be made exact and put in the form 

 ku?\l lfm(s 1)], where .<?, as before, denotes the element multiple, we find the 

 following values of k : 



K. . -014391(22); Rb . . '014121(23); Cs. . -015321(6), 



whilst the result for Na is -01406w 2 without a term in l/m. This points to the 

 probability that the change in p. is accompanied with a change in , and that the 

 change in p. is a constant multiple of w 2 , whilst the change in a depends in a more 

 complex way on the properties of the element. The term 1 l/m (x 1) looks like a 

 first approximation from a complete formula. In many cases, for instance, the form 

 of denominator m + /i + a/(m + //,) reproduces the lines with great accuracy. If the ^ 

 were decreased by kw 2 the change in D would not be in a constant ratio to a?, but 

 would involve a and /M, i.e., s. The doublet separation is given by the difference, 

 when m 1. In the approximation arrived at above it is -0141tt> 2 for Na, 

 and - 0141w a s/(s 1) for K and Rb, and Cs, but second order terms are required for 

 the large w 2 of Cs. 



(K). D's of S ( QO ). Since the S ( oo) are very close to VP (l), we should expect to 

 find a similar relation between the D's of S(oo) as for the P series. The actual 

 numbers are, writing down only the fractional parts, 



Na = -1169861(165) = 2 [-0584931(82)] 



K = 234G25(]59) = 4 ['0586561(40)] 



Rb= -292398(218) = 5 ['0584801(44)] 



Cs = -361214+ 1 =6 [-0602021 ? ] 



but there is here an additional uncertainty owing to the fact that, in calculating the 

 S series, the means have been taken and the Si (GO), S 2 (oo) determined from their 

 means by an estimated value of v. The limits of the D series are much closer to the 

 VP. Naturally, therefore, they bring out the relationship rather more clearly. 



(L). The D's of S. -The p!s of S, as we have seen, suggest that we have to do 

 with ^ = '5 + f. If we write down the fractions, we get 



Na . . . -1557931(5368) = 2 [-0778961(2684)] 

 K . . . -3257861(5155) = 4 [-0814461(1289)] 

 Rb . . . -376910-(9438) = 5 p075382-(l888)l 

 + (5702) L +(H40)J 



Cs . . . -4576611 ? = 6[-076277i ? ] 



VOL. OCX. A. M 



