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



For the first three, the factors are easily equal within limits, say 074560-'016120/ni. 

 If we remember that the limits for Kb were based for P(l) on LEHMANN'S estimates 

 of error, which are rather too small, we may represent the degree of closeness of the 

 above numbers by attaching a possible error of about (80). With the above numbers 

 the ratio /(/*-!) is '21521. The formula for Na, K, Eb, is therefore 



m \ m. 



with uncertainties in the two last digits in each number. The new arrangement has, 

 however, thrown Cs quite out of order. Not only is the factor too large, but the ratio 

 of a to it is also too large, viz., '2276. If the term in W be omitted 



=6(-075161?)(l-- 2000n 



m ' \ m 



To bring this into agreement with the above would require a change in /A of about 

 003600, which might just be possible. As we shall see later, the series appear to 

 depend on fundamental types in which p. = 1pW where p are integral. It is just 

 possible that in Cs the type changes from one to the other. 



The preceding arguments may appear unsatisfactory, as they apparently lead to 

 two different results with equal evidence, but there is reason to think that if the 

 values for the atomic volumes are known with greater accuracy, they will be found to 

 agree. If not, then the second argument stands, and the former falls, as based on 

 incorrect values of the atomic volumes. 



(J). The D's q/"P 2 . A glance at the table shows that the a. are practically the same 

 for both P] and P a . The doublet separations, therefore, are due to a change in //, alone. 

 In determining the values of fj-i^ use may be made of the values in the table ; but 

 as the doublet separations are much more accurately known than the wave-numbers 

 of the lines from which the constants have been determined, it will be better to 

 calculate the differences between the D's of Pj and P 3 on this basis, assuming the 

 D of PI (l) correct. Any small error in the latter will have an infinitesimal effect on 

 the difference in question. Taking the following values of v as the most probable, 



, K = 57'87l, Eb = 236784, Cs = 5522, 

 and taking N = 109675, there result for the differences of the D's of Pj and P a 



Na. K. Rb. Cs. 



000744(4) -002933(50) '012887(215) '032435(116) 



or 



01406 ('23) 2 (-01920(33)) (-3910) 2 (-01765(30)) ('8545) 3 (-01839(7)) (T328) 1 



