PEOF. W. M. HICKS: A CEITICAL STUDY OF SPECTRAL SEKIES. 107 



negative makes this way out of the difficulty very doubtful, and any one using 

 KAYSER and RUNGE'S observations gets to doubt whether many of their actual errors 

 are more than small fractions of the possible. It would probably be possible to satisfy 

 the conditions for Rb and Cs within the present possible errors, but only because they 

 are so considerable. I think, therefore, on the whole, the evidence is against this 

 explanation. As, however, the coefficients and /3 were nearly the same in the 

 numerical examples, this point was tested for Na, using P(l) for S(l), PASCHEN'S 

 S (2), and K. and R/s S (3). The resulting formula was 



n 



= 24477-04-N/[~TO- '651450- "012403 (L + -LY] ; 

 / L \m mVJ 



but the deviations for the other lines were far too great, being several times the 

 possible. 



Term /(TO /). The value of f, as determined from the observations, will depend 

 so much on the exactness of the measures of P (1.2) and S (2.3) that we can expect to 

 learn nothing from considering the cases of Rb and Cs. For Na and K the resulting 

 formulae are 



For Na 



P . . 41445'27-N//m+l'150156- ^4^- V, 



S 24472-4G-N/(m + 'G55055- ' 02278G '" 



\ TO--1!)2 



and for K 



P . 35000'53-N/('TO+1-30255G- 



-1557/' 



S . . 219G3-75-N/L + "824259- ' 39 2 V. 



/\ TO -'27 18; 



These give values of obs. calc. as follows : 



NaP . . 



NaS . . 



KP . . 



KS . . 9-45 000 -05 -18 



By comparison with Table L, it will be seen that now NaP (6) comes outside the 

 limits, NaS (2) is slightly better (but can be brought inside as before). KP^ is much 

 worse, and KS (2) improved, but the relation between the limits now holds. No 

 relationships are apparent between the various constants, except that, allowance 

 being made for possible variations, the / of P in both cases is one-half p.- 1. The 

 inequality between the a for the P and S series is increased. 



P 2 



