102 



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



RAYLEIGH'S results were published. The work of applying the method to the six 

 series is exceedingly laborious, and as the corrections themselves are not quite free 

 from doubt, it did not seem worth while to recalculate. In any case, it is not probable 

 that the actual values of N would be greatly altered. All six series have been treated 

 in the same way, the observations being weighted in accordance with R. and P.'s 

 estimates. In the case of the S series, however, the top line (m = 2) has been omitted. 

 This was done because there is some doubt as to the correct form for the S formula, 

 and any term /B/m 2 has much less effect on the lower lines. Consequently the,, value 

 of N is less likely to be affected. 



The resulting formulae are : 



Singlet Series. 



32033-094- 109814'G/(w + 1'014593-wr 1 x "004392) 2 

 27l74-917-109726-0/(m+ -SGllSl-m^x -007809) 2 



27l74-627-109672'5/(m+ 996369 + 7~ 1 x '002917) 2 



P'. . . 



S'. . . 



D'. . . 



Doublet Series. 



P" . . . 38453-347- 1096G6-2/(r/i + -929442 + wr 1 x '007792) 3 



S" . . . 29222-696- 109719'6/(m+ 705092-m~ 1 x '013408) 2 



D" . . . 29222-595-109689'2/(m+ '996347 + m~ l x -002200) 2 



The values of obs. calc. are given in the following table, with the corresponding 

 values from llrrz' formula, although they are not comparable on the same basis, 

 except possibly in D', P", and D'', where the N is practically the old N, but RITZ 

 gives no formula for the D series : 



