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



The table shows that where triplets occur the multiples are those of A 2 and not of 

 A,, except in the case of the oxygen group of elements, in which A! clearly takes the 

 place of A 2 . If the law of multiples is correct, the values of the A obtained in this 

 way must clearly be far more exact than those obtained direct from the separations. 

 A glance at the deduced values of the oun compared with the former values shows 

 how much closer to the mean value 361 '9 the new ones are than the old, and to some 

 extent this adds to the weight of the evidence. The cases where the multiples do not 

 appear to enter are those of lib, Cs, In and Tl. The case of Rb has been considered 

 above and a natural explanation offered. Cs, In and 'I 1 ! have all large values of S, in 

 which case we have already seen a tendency for the spectra to depend on smaller 

 multiples of the oun than the A. In the case of Cs, the oun is smaller than the 

 multiple and it can give no evidence nor data for the oun. The case is different 

 however for Tl. If the oun enters, the multiple can be no other than that given, 

 and as is seen the value of the oun is improved. All the elements of the Al group 

 show a deviation from the normal type in that the first satellite separations are much 

 smaller for the first order lines than for the second, and seem to point to some 

 displacement. As the Al orders differ by multiples of A, any irregularity in the 

 multiple between the first and second orders does not alter the dependence of the 

 denominator on the multiple of A. In In and Tl, however, the differences go by 

 multiples of or S l} and any irregularity on them will throw out the dependence of 

 the first denominator on a multiple of A. As was shown above the addition of 16(5 in 

 In not only produces the multiple, but at the same time shows a more usual march of 

 differences for the orders. In Tl the observed denominator for D 12 (2) is less than that 

 for D, 2 (3) and quite abnormal. The other anomalies occur in that in Sr, D 12 appears 

 to take the place of D 13 , and in Cd, D u . RaD (2) is in the ultra red and has not been 

 observed. The elements Na and Mg must be left out of account because the 

 ratio denom./A must be so large that a number of multiples can be found all giving A 

 within observation limits. Cu shows a multiple, but the theory of the constitution of 

 the series of Cu and Ag is doubtful and must also be left out. 



With the above doubtful cases the values for K, Ca, Sr, Ba, Zn, Cd, Eu, Hg, Al, S 

 and Se, are clearly exact multiples, and the large values of A in Ba, Cd, Eu and Hg 

 show that these multiples are real. This rule, exhibited as it is in so many cases, and 

 in by far the majority of the elements comparable, must correspond to a real relation 

 and cannot be due to mere coincidence. Against the reality of the relation is the 

 antecedent improbability that those elements with the smallest value of A should 

 have the largest values of the denominator, as e.g., in the case of Na and Mg. A 

 possible explanation is that the mantissa is the nearest multiple of A 2 to some group 

 constant. But see also under discussion of the F series. It might however have 

 been expected on this ground that the denominators would be of the form l-M(A). 

 But the case of Na is clearly against this. Its denominator "988656 = 1 '01 1344 

 and 11344 is 15'26A and cannot be a multiple. It would seem conclusive that the 



