4'2] 



and tlie magnetic energy have changed their parts. It is clear that 

 it must be difficult to combine the two theorems into one. 



I must not omit to saj that Whittaker does not want to attacli 

 too great importance to the special form of his model. He aptly 

 remarks that, after having obtained a satisfactory system of equations, 

 we may discard the model by which we have been led to it. What 

 is especially interesting in Whittaker's idea seems to me to be this, 

 that it shows the possibility of a sharp criterion by means of which 

 it can be decided whether an encounter is effective, or. otherwise. 

 Such a criterion there must certainly be. 



^ 9. Generalization of the model. Suppose that there is in the 

 atom a definite closed circuit s, in which a magnetic current 2 may 

 circulate, the energy being 4 LP. Then we have the differential 

 equation 



di 



dt 

 or, if an electron moves near the atom, 



di e du) 



dt ijtc dt 

 Take this instead of (8), and combine it with (11). The amount 

 of energy that is transmitted in an effective encounter (initially 

 { = 0) is now found to be 



-^ (16) 



In order to obtain a "vibrator" ^) we can link the circuit s with 

 another circuit .s', in which an electric current can circulate (no 

 resistance, energy h L' i'^); indeed, we have 



di 1 ., ^di' 1. 



L — z:^ —i' , L — =:: i. 



dt c dt c 



The frequency is given by 



at f 



L-= Ih.ds, 



V = 



If now an electron passes through the circuit 5 in a time that is 

 short in comparison with the period, the vibrator receives the 

 amount of energy (16) and this amount will subsequently be radiated. 

 It will be equal to hv if 



c 



'I XL' 



1) Gf. Whittaker, I.e. § 5, p. 139, 



