DE. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 461 



These numerous F and D relations render it certain that the sets of lines adduced 

 belong respectively to sets of F series and the D series. Moreover, it suggests that 

 the source of the 1429, 417 separations is the d sequent or F(oo) = 31851'13. 



A possible supposition is that their source should be in the S ( oo ) limit. If so we 

 should expect it to appear strongly in the S lines, and so in the S t (2) lines considered 

 above. As a fact, however, there is no sign of such in either of the S groups adduced, 

 except a very dubious one 1425 between two L.D. lines each of which has an 

 ambiguity 4. It takes place between S, = 27964 and 26539 backwards, so that if 

 its source were here it would be a positive displacement on S ( oo ) or a negative one 

 on s(2), both unusual. The strongest argument for its source being in the 31851 is 

 that the separations in question show themselves in all orders of F (m) in other 

 words, occur in the limit F ( co ). 



The Value of the Oun. It has already been found that the value of the oun 

 calculated from the chemist's atomic weight is 14'47'01 and that the oun 

 multiple for A 2 is 18|- or A 2 *= 26770 '02. This is too small or the inexactness too 

 large to obtain a more accurate value as in the other cases directly from the F or D 

 mantissae. It is, however, possible to arrive at an extremely accurate estimate by 

 proceeding step by step with successive approximations, and for this purpose the F 

 separations are clearly at disposal. The wave-lengths of many of the F(l) lines are 

 very accurately known (B.M.M. will be used), they are so large that the dn are small 

 multiples of d\, and being of order m = 1, an oun displacement will produce a 

 comparatively large change in n. In spite, therefore, of the smallness of the oun it is 

 possible to get some definite information. The reliability of the information will 

 depend on two assumptions 



(1) That the lines employed are F lines parallel to the series F (l) = 17081. 



(2) That no displacements occur in the / sequents themselves. 



If the assumption (2) is not satisfied the series in question will not show constant 

 separations from the corresponding Fj (m) lines, but will converge or diverge with 

 increasing order. The lines we shall make use of have been measured probably up to 

 a few thousandths of an Angstrom, and the accuracy is greater than one in the 

 seventh digit in the value of n. Moreover, in calculating with seven-figure 

 logarithms, in which also we have to do with differences between two numbers, errors 

 amounting to unity or more are liable to enter. Consequently where these very 

 accurate numbers occur nine-figure logarithms have been used. As the wave-lengths 

 are given in I. A. the calculations have been made on that basis. The limit 

 31851-1300 R = 318521816 I. N = 109678'6. Put A 2 = 26770 + *, therefore 

 S = 14'4703 + '054x where at present x lies between '2. It should be noted that in 

 the d sequences, the satellite displacements are not in general multiples of S, but of 

 S L = S. The correct value of a wave-length will be taken as the observer's value 

 '001 x jt>, so that dn = +... . 



