640 



Dr. S. R. Milner on the 



In mercury all three series are equally well developed and 

 extensively so. 



This fact is of special interest because it allows an accurate 

 test to be made of one of Ryd berg's empirical laws connecting 

 the different series with each other. The law in question 

 runs as follows : — " The difference of the frequency of the 

 convergence limit of the principal series and that of the 

 common limit of the sharp and diffuse series is equal to the 

 frequency of the first line of the sharp series." This law is 

 known to be very approximately true, but there must always 

 remain a certain amount of doubt about its absolute truth so 

 long as any one of the series is represented by only a few 

 terms all of them remote from the limit. The limit in such 

 a case can only be determined from an empirical equation 

 designed to represent these terms ; at the best this can be 

 but an imperfect representation of them, and the value of the 

 limit will to a certain extent depend on the particular form 

 of the equation adopted. But this difficulty does not arise 

 when so many lines of the series have been measured that 

 the last members of them are quite close to the limit. The 

 extrapolation to the limit itself is then a small one, and any 

 approximate equation will determine it accurately. 



Thus if we apply to the principal series Rydberg's equation 

 in the form 



P(m) = P(x> ) -N/(m + -90845) 2 



we obtain the following values of the limit, P(x> ), for each 

 line of the series : — 



m. 



! 



P(00)-P(Wj. 



P(QO). 



3* ... 



71795 



216517 





4t ... 



45521 



217764 





5{ ... 



31417 



21813-2 





6} ... 



2298-0 



20-4 





7 ... 



1753-6 



233 





81 ... 



13820 



26-3 





9 



11171 



310 





10 



921-8 



31-9 





11 



773-4 



30-4 





12 



658-3 



29-5 





13 



567 



28-9 





14 



493-3 



32-8 





15 



433-2 



297 





lo 



383-4 



308 





* Vim) = 144722. t P(w) = 17224-3. 



J Lower frequency component. 



