DR. 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(co) = 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 Si (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 Sj = 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 ( oo). 
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 Ag is 18|- or = 267'70±‘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 
mantissas. 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 (1) 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 f 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 
o 
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-figiu'e 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 K = 31852-1816 I. N = 109678-6. Put A^ = 267-70 + a:, therefore 
^ = 14-4703-1--054a: 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 8, but of 
Si = The correct value of a wave-length will be taken as the observer’s value 
—-001 xjo, so that dn = -1-... . 
