PROF. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 79 



a much nearer approximation to equality than before; in fact, '1950 well within all 

 limits. 



We are therefore led to surmise that the P series of all the alkalies can he 

 represented by a formula, 



VS (l)-N/{m+'986 + &x atomic volume fl- H', 



/ I \ m l\ ' 



the numbers inserted being only very roughly approximate. In other words, the 

 knowledge of four constants (N, '486 ? '195 ? and k) gives all the lines of all the P 

 series of the alkalies (Li not considered). 



On the other hypothesis, viz., the excesses of p. over 1, exact multiples of a 

 constant, and the ratio of a/(/x 1) also a constant, p + a 1 ought to exhibit a similar 

 relation. Now p- + a is determined with a far less error than either ^ or a separately, 

 and hence the values of jii + a ought to show the relationships more clearly. The 

 respective values are 



Na . . . 2 [-058451 (35)] Kb ... 5 ['058369(3)] 



K . . . 4['058492(264)] Cs . . . 6["060148 ? ] 



which is very strong evidence in favour of the multiple law for the first three at 

 least. 



The limits of possible variation are so close, the exactness of the equality within 

 those limits so absolute, that there can be no doubt that the relation is an absolute 

 law. We have found already that the same law is indicated for p and a, but with 

 greater deviations ; in the case of Rb outside the permissible limits. It is clear, 

 therefore, that the inequalities of JJL and a must counterbalance one another when 

 m = 1, i.e., there is probably a term x(l l/m) in addition to the term sb(lc/m). 

 (Here and for the future s stands for the integer proper to the particular element, 

 2, 4, 5, 6, b for the factor, and c for the constant ratio of a to p 1.) Later, evidence 

 will be given of a new type of series (the F sequence) based on an atomic weight term 

 which (and multiples of which), as will be seen immediately, determines the second 

 (or second and third) of the doublet (or triplet) series. The values of these terms are 

 determined in the next paragraph. If x in the above be taken, one-half of these 

 values, and deducted, it will be found to give the perfect agreement required for Na, 

 K, and Rb. If W denote this atomic weight term, W for the four elements are 

 000370, '001466, '006444, '016267, and the values of D for these elements are then 

 1 W(l 1/ni) + the following terms : 



Na. . . . 2 {074524(238)-wr 1 [-016073(203)]} 



K . . . . 4{'074486(373)-m- 1 [-015992(637)]} 



Rb. . . . 5{-074569 (89)-nT 1 [ > 016199 (85)]} 



Cs. . . . 6 {'077872+ (?) -w- 1 ['017724 (?) ]} 



