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



for m = 6 to be 716474, and this is 23931 below the observed denominator for D 2 (5). 

 Now, 50S = 23850, which is the same as the difference for m = 4 and 5 instead of 

 being less, as analogy with others would lead us to expect. But the observation 

 errors are large (maximum of order 18<5, about) so that room is allowed for this. 

 There would then be one step from m = 5 to 6 of something less than 50(5 combined 

 with a collateral displacement of ( + 2^) on D ( oo ). To indicate the explanation this is 

 entered in the table, a difference of 50S making the denominator for D (6) = 6716653. 

 The observed abnormality as between D u (6) and D 21 -i/ = D 12 (6) is that the wave 

 number of D n is 1'26 less than D 12 , whereas it should be 8 or 9 greater, with a 

 denominator about 32 S greater instead of 1721 less. There is, in fact, a further 

 defect beyond the normal value of about 36d Thus, if the difference for D 2 (5, 6) is 

 xS, that of DI (5, 6) is (x + 36) S. The lines would then be represented as follows : 



d, = 755767, d 2 = 740503, 



D,(m) = 



The collateral addition intensifies D 2 and explains its continuance, but in Dj the 

 increase, owing to addition of 2^ to D ( oo ), is overweighted by the diminution of the 

 excess 36S in the VD part, and so, after the first, the rest are too faint to observe. 

 At least, that is a suggestion of a possible explanation. 



Tl. 



In Thallium the satellite separations appear to be the following multiples of <^ : 

 24, 27, 28, 28, 28. But so far as limits of error permit, they might be 24, 27, 27, 

 27, 27. A peculiarity appears in the D lines in that the doublet separation for the 

 first set is 7793'08 (48), whereas the normal value is very close to 7792'39. The 

 difference is therefore real and not attributable to observation errors. Moreover, the 

 next four show a gradual diminution, although still remaining normal within extreme 

 permissible errors. The doublet values beyond this depend for the measurements of 

 the second line on measurements of CORNU. They give separations 15 to 20 less 

 than normal, but little reliance can be placed on deductions from them, for COBNU'S 

 results may err possibly by several units in the first decimal place, and with these 

 small wave-lengths any error in X is multiplied by 22 to 23 in the wave numbers. 

 I have, therefore, not brought them into the discussion. 



The table is based on = '3, though no attempt has been made to find the best 

 value. The mantissa of the first line is abnormal, since it is less than the second 

 instead of greater, and, moreover, its difference from it cannot be a multiple even of S^ 

 Since the satellite difference is very close to such a multiple (9048 = 6<S + 4) it is 

 probable that the abnormality affects both in the same manner. Now the arrangement 

 may be made normal by regarding the first line as a collateral (<!,) Dj (2). The 



