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



to build up the alkali series. Whether this has any real significance, however, must 

 be at present an open question. 



Further Discussion. 



From the foregoing discussion a few points stand out for further consideration. 

 The most important is the doubt as to the form for the S series. 



The dissatisfaction with the form in afm for the S series arises from the fact that 

 VS (1) does not give P ( oo), and that in some cases the value of S (2) calculated by it 

 from constants determined from 8(3.4.5) is considerably outside the limits of obser- 

 vation, certainly in the case of K, and probably also for Rb and Cs. This second 

 failure, however, clearly is a consequence of the first, and will probably be corrected 

 if the first is. In addition, the /u, '5 of the S is so close to the value of the atomic 

 volume term in P as to point to a real equality if the true form be obtained, whilst 

 the value of a in S is always considerably less than that in P. It has been shown 

 that the VS(l) cannot be made = P( oo) without introducing a term in )8/m 2 , and 

 that in the two numerical examples given for Na and K, the a and j3 come about 

 equal in other words, a denominator = m + p. am~' (1 +m~ l ) would satisfy all the 

 conditions. Also the /x '5 is brought nearer to the atomic volume term, but a 

 becomes about one-half that in the P series. Before considering this clue further, 

 two other ways out of the difficulty may be mentioned. HITZ has systematically 

 used ?>(.+ 5 in place of m in the S series. But the adoption of a/(m+'5) in place of 

 oi/m makes the disagreement between VS(l) and P(oo) greater, although it brings 

 the a. more into agreement with that of P. On the other hand, m '5, which makes 

 the /A of S in the alkalies practically the same as that in P, throws the difference the 

 other way. It is clear, then, that since m integer makes VS(l)<P(oo), and 

 m '5 makes VS(l)>P(oo), that a value of / < '5 can be found, such that a 



denominator = m + p. .would make the limits come correctly. 



m-J 



In all that precedes, not only has the value of N been taken to be a universal 

 constant, but it lias had the special value 109G75 attached to it. The evidence for 

 the universality of its value is not, however, conclusive, and it is clearly possible, if it 

 be not so, to assign values N p , N s to N. so that 



N P /D 2 of P (1) = S ( oo ), N 5 /D 2 of S (1 ) = P ( oo ), 



and such contingency at least requires examination. These three possible solutions 

 will now be taken in order. 



Addition of Term in /3/m 2 .-- We have seen that it is possible to satisfy the required 

 conditions in the case of Na and K, but only by allowing actual errors in the 

 measurements alternately positive and negative, and each a considerable fraction of 

 the possible. The necessity of taking in each case the errors alternately positive and 



