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



The limit 50403 and S= 1787'01 require the smallest changes and seems prefer- 

 able, although limit 50410 and S = 1786 is perhaps possible. Both 1787*87 and 

 1785*26 would appear excluded. The numerical work to follow will be based on the 

 limit 50403, i/ t = 53707 + rfi' 1) v a = 2649*5 + dV 2 , S(e) = 50403*00 + These make 

 A!= 72820, A 2 = 32166. 



With these more exact values of S ( o ) and v l it is now possible to obtain the 

 important constants, the ^-links. They are found to be 



a= -'*+ > +e, c = 6277'21-6 > 16a?-*020+l*347di> 1 



b = 537070-5'Olx d = 7399*60-7'67cc-*046+l*822(Z' 1 



e = 23678'42-22 1 96a;-'056+4 < 912d*, 



where the terms in x denotes the changes for a displacement of xSi in S ( oo ). 



To determine the u, v links requires a knowledge of S, (l). Tt is impossible to obtain 

 really definite information on this point from direct observations. In default of this 

 the following considerations will give some indications, and will serve to illustrate how 

 the laws of relationship already determined can give clues indirectly. In the cases of 

 A, Kr, X the lines for S x (l) are respectively -42642, -42469, -42153. The corre- 

 sponding line for RaEm should therefore be looked for about 41800, with s (l) = 

 P(oo) about 50403 + 41800, or, say 92200. The e link unfortunately is too large to 

 test for the lines for it would reach back to lines about 11103 2649'5 12751*5 

 5370'7 ] 8 122*2, of which the last only would be in the observed region. Con- 

 sequently no evidence can be obtained with reference to it from the v } , v 2 separations. 

 There is a strong line at (8) 17909'9. It would give Sj (l) = 41586, smaller than 

 seems likely. Also it has a 5637 link not usually connected, so far as we yet know, 

 with S lines. It however is the only strong line in the neighbourhood, and it will be 

 probably wiser to conclude that the S (l) line has no linked e line to it. The above 

 value for P ( ) gives a v link about 13660, and this link on the supposed S (l) should 

 produce a line about 28140. We find the set 



(2) 201637 2645 (4) 22808*68 [28183*7] 



in which the last is extrapolated by the normal i/ t + v, from the first. 



It falls in the large gap where no lines have been observed and the spectroscopic 

 apparatus was defective. If this be really the S (l) v set, it is possible to calculate 

 what the u, v links are. ThusS,(l) =-(281837 + v), s(l) = P(oo) = 785867 + v, and 

 v is produced by the A t displacement in the denominator of this. As v by a rough 

 determination is in the neighbourhood of 13660, it can be put = 13660 + ce where x is 

 not very large and can be determined by the condition that 13660 + * is the change 



