Frequency and Atomic Number. 495 



affinity " of the elements, are derived from thermionic mea- 

 surement *, and for the reason stated must be received with 

 some reserve. It is, however, interesting to find that the 

 values of N<£ approximate fairly closely to multiples of 

 13-55 volts. 



§ 6. The Physical Significance of the Empirical Relation, 



The empirical relations here discussed may be summarized 

 in the formula 



NV=..v B 



where v is some characteristic frequency, and n is an integer 

 (or in some cases an integer +i). On multiplying each 

 side of the equation by /i, this gives 



~Nhv=nhv & 

 or, by using the quantum relation hv = eY, 



~NeY = neVT., 



But Ne is equal to the charge, E, on the atomic nucleus. 

 Hence 



EV-n<?V H =0. 



This suggests that in the limiting conditions which arise in 

 all the physical phenomena under discussion, we have to deal 

 with a minimum value of the energy of a system comprising 

 the nucleus and a certain number of electrons f . 



The fundamental electronic frequency, v& is found to be 

 about 154 times the fundamental atomic frequency, v A . It 

 is perhaps worthy of notice that the hypothetical positive 

 electron of Prof. Nicholson, derived from the study of funda- 

 mental spectra in Astrophysics, has a mass 151 times that of 

 the negative electron. 



I 



* 0. W. Richardson, * The Emission of Electricity from Hot Bodies,' 

 p. 69-79, 164-178 (1916); Langrnair, American Electrochemical 

 ociety, pp. 341-396 (1916). 

 t In this connexion it is interesting to note that the frequency number 

 3 is found from the ionization potential of helium. As the helium atom 

 contains only two electrons, this may possibly indicate that a third 

 electron is temporarily associated with the atomic system when it is 

 subjected to bombardment by electrons. In this way an unstable 

 arrangement may be produced and ionization result. 



2N2 



