PEOF. W. M. HICKS: A CRITICAL STUDY OF SPECTRAL SERIES. 77 



These bring all the lines (P(5), S (2), excepted as before) well within the limits of 

 error. Again, it is to be noted that in the S formula a = /3, and the ft of P is negligible. 

 The fact that this relation occurs twice suggests its being a real relation, and not due 

 to the chance choice of the suitable values of p, q, r, &c. The limiting errors in the 

 cases of Rb and Cs are so wide that it did not seem worth while to discuss them in 

 the same detail, especially in view of considerations which will appear later. The 

 evidence so far is strengthened as to the correctness of (F) and (G) in fact ; but, on 

 the other hand, the impression is intensified that there is something not quite correct 

 with the form for the S series. RITZ uses m+"5 instead of TO, although there does 

 not seem any experimental evidence in its favour. As a fact it can be shown that the 

 use of m+'5 in place of m in our formula makes it still more difficult to fulfil 

 conditions (F) and (G). 



(H). The difference betiveen the p.'s of S and P. If we write down the value of 

 /A of P p. of S, we get 



Na . . . . '492885 (5800) or between "498685 and "487085 

 K . . . . -470694 (GG47) "477341 "4G4047 

 Rb . . . . -489489-(l0578) "496331 "478911 



+ (G842) 

 Cs . . . . "493306 ? 



"487 would include all except K. The values point to the possibility of there being 

 a constant difference, if the correct S formula be found. Also it shows conclusively 

 that such difference cannot be "5, a supposition which has suggested the idea that the 

 P and S are similar series, P with even numbers and S with odd. The supposition, 

 moreover, is not borne out by the evidence of other spectra. It is very nearly "5 in H, 

 153 in He', "445 in O. The S { oo ) is always very close to VP (1) wherever it can be 

 tested. If this hold for Mg and Ca, the difference in their cases would be about '34 

 for Mg and "31 for Ca ; Zn, Cd, about the same. There are clearly no valid grounds 

 for the supposition in question. 



(I). The D's of P. A first inspection of the values of JJL given in Table II. makes 

 evident a remarkable approximate relation between the values of /j. 1 of the various 

 elements. They may be written as follows : 



Na . . . 2["074339(238)] Rb . . . 5 ["073280(228)] 



K . . . 4 ["074120(373)] Cs . . . 6 ["075161 ? ] 



The possible variations show that, with the exception of Rb (which, however, very 

 nearly falls in with the others), the values of p. 1 are multiples of a number not far 

 from "074. The case is not really so strong as it looks, for the limits of variation are 

 almost certainly much less than the maximum possible (which has been mentioned 

 before). On the other hand, the relation is so close that a more correct value of N or 

 the true form of the formula might well make the ratios exact. It is clear that the p 



