204 



Dr. Marshall Watts on a Relationship 



together bv a formula of the form 



1 



= A[l-B«- 2 -Cn- 4 ], 



where A, B, C are 

 1 



constants, and n receives the values 

 . 2, 3, 4, &c. 



The lines in each series, therefore, approach closer and 

 closer together towards the violet, coming to a limit at the 

 oscillation-frequency given by the value of A, which is termed 

 the convergence-frequency. The values of the constants 

 for the principal series of the (dements named are : — 





A. 



B. 



C. 



Lithium 



43584-73 



3-06688 



i 25-24012 



Sodium 



41536-81 



3-12939 



19-33950 



Potassium 



35086-55 



3-61914 



17-82216 



Rubidium 



33762-11 



371781 



16-65343 



Cassium 



31501-56 



3-97050 



15-55107 



i 1 



Here the differences of convergence-frequency of potassium, 

 rubidium, and caesium are nearly proportional to the differ- 

 ences in the squares of the atomic weights : but the same 

 does not hold between lithium, sodium, and potassium. The 

 convergence-frequency of sodium, calculated from those of 

 lithium and potassium on this hypothesis, would be about 

 40810. 



The two rules stated above are probably only approxi- 

 mations to the truth — the results of the calculations made 

 would agree more closely with the known values if the actual 

 law were not more complicated than that assumed. 



The numbers given below will show what amount of accuracy 

 may be expected. 



Example 1. From the atomic weight of cadmium, 111*83, 

 to calculate that of zinc (64- 9). 



The following are the oscillation-frequencies of the lines 

 assumed to correspond : — 





Cadmium. 





Zinc. 





(a) 



30654-4 



10 r 



32500-0 



8r 



(b) 



30734-9 



8b 



32540-1 



10 r 



(c) 



31905-5 



8b 



32928-7 



10 b 



(d) 



32446-8 



6b 



33118-6 



8b 



(e) 



36023-7 



(>b 



34310-8 



4 



(/) 



37334-5 



8 



34791-3 



6 



(.</) 



38851-1 



4 



35285-7 



8r 



(*) 



39280-5 



2 m 



35408-9 



G 



(i) 



43690-5 



10 r 



36934-7 



6 



(.;) 



44086-7 



4r 



37059-2 



2b 



(*) 



44630-0 



6r 



37242-2 



8 b 



(0 



45550-6 



1 



37548-1 



8 



