..,,, |, K . w. M. HICKS: A CIMT1CAL STUDY OF SPECTRAL SKRIKS. 



not prok-il>l.- that the error is one of observation. In Group 2 the Zn sub-group can 

 be repn|iirr<l fairly well with a formula in <x/(2w-l) in which a is negative. M^ 

 can H!HO be reproduced within error limits by a formula of the same kind, but it is 

 impossible to do so for Ca, and Sr and Ba require additional terms in l/m a . In 

 Group 3 Al is quite intractable, and if really depending on a formula, appears to 

 require complicated algebraic or circular functions. In and Tl also are not amenable 

 to formulae in // only or a/m + P/m". Nevertheless, the general build of the series 

 is so similar to that of the others that it would seem probable that the wave numbers 

 should also be of the form S(oo) N/(wi + f? m ) 3 . If so it is possible to calculate d m 

 from the observations and a comparative study may throw some light on the origin of 

 the different lines. The attempt to deal with these series from the formulae point of 

 view, however, brought out the fact that the satellites are related to the strong lines 

 in a similar way to that in which the Principal line doublets are, viz., by a constant 

 difference in the denominators and that their differences probably depend on 

 multiples of the " oun," as is the case in the Principal series. As the evidence 

 depends also on a comparison of the numerical values of d m , this point will also be 

 considered now. 



The actual values of d m will depend on the accuracy of the value S ( oo ) (or D ( <x> )) 

 of the limit. In the calculations below the most probable value has been used (see 

 note under each element) and the true value has been taken to be that + In order 

 to be free from mental bias these have been in general taken to be the same as S ( oo), 

 which involves the theorem that D(o) = S(oo). But of this little doubt can be felt. 

 The true values of d n can then be given in the form d m + kg where k is small. For 

 high orders of m, k is comparatively large and can only be used when is very small. 

 It is however generally the case that errors made in this way are only a fraction of 

 the observational errors. 



As in the normal type where there are no satellites VDj = VD 3 = VD 3 , and where 

 there are satellites VD 1:J = VD al , VD 13 = VD.,,, it is only necessary to tabulate the 

 values of d m for the case of VD, or VD U , VD 12) VD, : , respectively. When this is done 

 certain regularities are clearly apparent, which can be made more exact by allowing 

 small observational errors and giving a small permissible value to It would cumber 

 the space at disposal to give both sets of values, especially as it is possible to easily 

 indicate the differences on the one set of tables. Table II. then gives the values of D m 

 with the modified value of with the maximum errors attached in the usual way 

 in ( ), and the calculated value given as a correction to the selected value. Thus for 

 NaD (3), D (3) = 3-986626 (l33)-289-104, 3'986626 is the selected value, 133 

 possible change in last three digits in this, -289 is change for = + 1 , and the observed 

 value is 104 less than the selected. The values of the errors of observed wave-length 

 over calculated (O-C), and of possible observed errors (O) are given in each case on 

 the right. The tables for the different elements are collected together and discussion 

 of each is given later when considering the ordinal relations of the denominators. 



