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



95 



is seen not to hold, within at least PASCHEN'S estimates of his errors (possibly under- 

 estimated as compared with K.R.'s scale), but that RYDBERG'S form gives much closer 



approximation. Thus, for Na with /A = '999260 H , the differences of wave- 

 numbers for F(3.4), taking F(o) = 12272'24, would be 0, 1'60, and without the a 

 term with F(oo) = 12273"08 they would be 0, 77, both within the limits of error 

 (4 '97) for the second line. The value of the limit is nearer VD (2) in the first case. 

 There is nothing to decide between the two theories here. But a similar treatment 



.AAoqqq 



for K, where p. = "997067+ - -, gives in the first case with F( oo) = 13454-28 



differences '88 and 2, both close to PASCHEN'S estimates of error ('88 and 1'23), 

 whilst without the a term and F( oo) = 1345673 the differences are 0, '84. This 

 definitely points to the RYDBERG form as the preferable one. On the other hand, 



with Cs, JJL "967565 + - -, where the term is large enough to be really 



I iv 



important, agrees better with the whole set of observations. Comparing the wave- 

 length differences with those for the RYDBERG form we get the following table : 



For Rb, p. = -987113+ 



01 9887 



gvng 



Thus, as between the two suppositions, Rb gives no indication ; Cs is in favour of a, 

 and its large value of a makes it important, but it is not decisive ; Na is satisfied by 

 both, but is better for RYDBERG ; K is the only one strongly in favour of RYDBERG. 

 The question must therefore be left open at present, with leaning in favour of 

 RYDBERG. 



The validity of the supposition, that lines exist whose wave-number is the difference 

 of the V part of the wave-numbers of two other lines, may be regarded as fully 

 established by RITZ,* who calls it the Principle of Combination. Examples have 

 occurred amongst the lines just discussed. It is possible, however, that what really 

 happens is not an addition of unity to m, but an addition of our alkali constant. 

 '987? to the p., e.g., while we write a new limit as N/(2+|u) 2 , it may actually be 

 N/(l +/J.+ - 987) 2 . To settle this requires greater accuracy in the obscure lines than is 

 to hand. 



* "Ueber ein neues Gesetz der Serienspektven," ' Phys. Z.,' vol. 9, p. 521. 



