DR. W. M. HICKS: A CRITICAL STUDY" OF SPECTRAL SERIES. 325 



Hg 19, and, further, that in many cases A, and A a were also themselves multiples of 

 the same number. As, however, Mg with a difference of 450 and Zn of 543 could not 

 possibly be brought into line with the others, this line of attack was given up. But 

 later the case of Zn, which at first had seemed to stand in the way of an explanation 

 on these lines, gave cause for encouragement. The series for Zn are well defiued, the 

 measures good, and the formulae reproduce the lines with great accuracy.* Great 

 confidence can thus be put in the values for A, and A 2 , and it was noticed that they 

 were both extremely exact multiples of the difference Aj 2A a . In fact, the values 

 are A, = 31 x 543'446?0 3 and A., = 15 x 543'476t0*. This relation could hardly be due 

 to mere chance, especially when it was also noticed that 543'44 is very close to 3/2 the 

 former 360, and, further, the 450 of Mg is about 5/4 tin- same. In other words, with 

 the rough values used 360 = 4 x 90, 450 = 5 x 90, and 540 = 6 x 90. This looked so 

 promising that a systematic discussion of all the data at disposal with limits of 

 possible variation was undertaken. The theory to be tested then is that the A of 

 any element which give its doublet or triplet separations are multiples of a quantity 

 proportional to the square of the atomic weight. We will denote this by $ = qu?. 

 It will be convenient, in general, to deal with the 360 quantity, and S will be used to 

 denote this. If other multiples are dealt with as units a subscript unit will be used 

 giving the multiple of the 90. Thus <?, denotes the smallest, S t = 542710*, and so on. 

 The results are given in Table I. below. 



The value of A is obtainable as the difference of two decimals with six significant 

 figures. It is convenient therefore to tabulate the values of 10"A. The exactness of 

 the calculated value depends on (l) the correctness of the adopted value of S(o), 

 (2) the exactness with which v is measured, and (3), when expressed in terms of 70*, 

 the exactness of the value of W or the atomic weight. In the case of the latter the 

 value W/100 = w is used and the values of ItfA/iv 3 are tabulated. The method 

 adopted may best be seen by taking an actual example, say that of calcium. The 

 values of ,, v a as found by least squares from the S-series are 105'89, 52'09. The 

 value of S(oo) as given in Table I. of [II.] is 33983'45, and the correct value is 

 supposed to be larger. The numbers 33983'45, 34089'34, 34141'43 are then thrown 

 into the form N/D a , and the denominators are 1796470, 1793679, 1792310, giving 

 for differences A, = '002791, A a = '001369, which are tabulated as 2791, 1369. The 

 corrections for the error are found to be '2f and '! Moreover, the last digits 

 of 10*D may be '5 wrong and the value of the A be 1 out. In cases where the v 

 are known to three decimal places, the calculations are carried out with 9-figure 

 logarithms, and the values of A determined without this ambiguity. The values of v 

 may be wrong by dv, i.e., \05'89 + dv, &c. This will produce; ;i variation in A, of 

 26'Sdv in general dv is a fraction <'l. Thus 



A, = 2791l-'2+26'3cZ<. 

 * See Table I. of Part II. 



