PROF. W. M. HICKS: A CRITICAL .STUDY OF SPECTRAL SERIES. 109 



If the condition that a/^i, should be the same as for P be applied, say about "2, the 

 values of SN, come to about 382 for Na and 650 for the others. 



In the present state of the observations, it is useless to attempt to arrive at 

 anything more definite than that a very small proportionate increase of N for the 

 S series will satisfy relations (F and G), make better agreement in general for the 

 lines S (2), and bring the ratio /(/u '5) into close agreement with that for P. 

 Possibly some constant value for SN, would make a the same as for the P series, in 

 which case the /A of S would be formed, not by adding the term sb to '5, but to a 

 number > - 5. For these combined reasons it would appear, so far as our knowledge 

 at present extends, that the required improvement in the S formulae should be looked 

 for in a change of the value of N. The evidence shows that at least the greater part 

 of SN, does not depend, like W, on the square of the atomic weight. It might, 

 however, depend on s. Thus apparently SN for NaS is about 300, for KS about 600, 

 and the corresponding multiple law would make it 750 for Rb and 900 for Cs, quite 

 in agreement with the actual numbers found. If this were so, the P sequence would 

 be formed by adding a multiple term to the denominator, and the S sequence by 

 adding a corresponding multiple term to the numerator. 



A further argument in support of this theory is found from the discussion on the 

 various He series. It was there found that using least squares to these very 

 accurately measured spectra, rich in lines, that the F and D sequences have values 

 of N very close to the value 109675 generally adopted, but that the S series in both 

 cases require a value of N about 50 larger, and this when the lines corresponding to 

 m = 2 were not used. In this case they do not reproduce the values of S (2). It is 

 probable, therefore, that if they were introduced the values of N would be still more 

 considerably increased. The case of HeP' requires a still higher value of N, and in 

 this case HeP' ( 1 ) agrees with the observed. It seems a clear case for an increased N 

 if the form m + fji + a/m is absolute. The argument that it is so is that in cases of 

 elements where //, and a are comparatively large, it is sufficient to give practically 

 all the lines within limits of observation errors, and that if -(3/m 2 be added, fi 

 comes always a small fraction of a and capable of being wiped out by errors of 

 observation. Now the a in the He spectra are all very small, and /3 would be very 

 much smaller, and exert scarcely any influence on the lines beyond the first two or 

 three. Nevertheless N is increased for the S sequences. 



Summary of Results. 



The principal results arrived at in the foregoing discussion may be summarised as 

 follows : 



1. A modified RYDBERG'S formula, in which the denominator is of the form 

 /m, is found to be capable of representing practically all the observed lines 



