DR. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 455 



We are justified by its form in taking this as a D(l) set for a preliminary trial, 

 although the satellite separations are not in the usual ratio of 5 : 3. It is not so clear 

 that the particular F ( oo ) just obtained is a d sequent belonging to it, nor, if so, 

 whether it is a d n or a satellite sequent. The latter point, however, will have little 

 effect for our immediate object --the attainment Aj..A 2 .e as the differences are 

 small and may be included in an undetermined The probability is that as this 

 seems the only prominent D triplet set, it belongs to the normal group and that our 

 F ( oo ) belongs to it, although on this point something will have to be said later. 

 We shall take on trial that F ( oo ) = d n . In this case 



D! (oo) = 21230'll + 3185ri3 = 53081'24 + 



This should also be Sj ( oo ) and should give the separations by oun multiples in the 

 denominator of the sequent. The three S or D limits would then be 



53081'24. + 49-24 53130'48 +<&', + 19-71 53150*19 -I- c^ 



where may be considerable, owing to uncertainty as to 31851 being of d n or satellite 

 type. The mantissa? of these are 



437428-13-540^, 436752-13'521 436485-13'514 



which give as differences 



A! = 6G6--019^-M3'5^, = 46 (1 



in which it must be remembered that calculations with seven-figure logarithms give 

 uncertainties of a unit in the last digit. The direct calculation of S from the atomic 

 weight has already given J=14'47'01. This gives 46(5 = 665'6'46, 18^ 

 = 267'69'18. Thus these limits give without any doubt the true oun multiples 

 in A!, A 2 , and the calculated A a then gives a closer value of 267 7 '2. No possible 

 change in can affect these results. Further, these multiples are quite in step with 

 the march in the other gases. The remarkably close agreement sustains the allocation 

 of the F ( oo ) to the d sequence of this set, although not necessarily to d u . 



As a further test the satellite separations should be due to oun displacements in the 

 sequences. These separations are 29'21 and.45'19, taking the latter because 21224 is 

 a good measure (B. and W. agree) and the observed v 2 = 1971 agrees so closely with 

 the A 2 value and the ^ is subject to the very common triplet modification. These 

 separations require displacements in the sequence mantissse of 851 '040+29di/,* and 

 1313-'060+29di/. Now 59<S = 85371'2, 90f<S = 131311'8. This is sufficient to 

 give the satellite multiples, but as the oun is so small, S l = 3 '62, the close agreement 

 cannot serve as evidence one way or the other as to the satellite nature of the doublet 



* WATSON'S value of the separation 29-30 makes this 2-6 larger = 853-6. 

 VOL. CCXX. A. 3 Q 



