246 Prof. G. A. Schott on Bohr's Hypothesis 



and inquire whether it is possible to modify the equations of 

 the electromagnetic field in such a way as to annul the radia- 

 tion derived from the Poynting energy flux. We cannot 

 change the Maxwell-Hertz equations for the distant field 

 without risking the loss of the, accepted theory of electro- 

 magnetic waves together with all that it implies ; but 

 perhaps it may prove possible to modify the electromagnetic 

 equations for the interior of the electron so as to attain the 

 desired object. The retarded potentials do depend on the 

 form of the equations within this region, and there appears 

 to be no reason a priori why a suitable modification should 

 not enable us to annul the radiation from the electron. Only 

 a calculation can decide, and we shall proceed to carry it 

 out ; it may, however, be stated at once that the result will 

 prove to be negative. 



We shall make use of a method of calculating the radiation 

 on the basis of electromagnetic equations modified for the 

 interior of the electron, together with the Poynting flux, a 

 method developed for another purpose by Oseen *. For the 

 outside space we write as usual 



curlh-~=0, curl d + 4^=0, divd = 0, divh = 0, 

 c^t cot ' 



where d and h denote the electric force and magnetic force, 

 and c the speed of light. For the interior of the electron 

 we write 



curlh--^=C, curld+~ = K, divd=e, divh = ^. (1) 



cot cot v ' 



The equations (1) may be regarded as defining the scalar 

 quantities e and /a and the vector quantities C and K for the 

 interior of the electron, and every part of space where they 

 do not all vanish is to be regarded as part of an electron. 

 They may be interpreted as densities of electric and magnetic 

 charges and currents, but this must be regarded as a matter 

 of terminology, in the usual electron theory we have 



^ = 0, C = ev/c, K=0, 



where € denotes the electric density of any element of the 

 electron, and v its velocity. These relations are not sup- 

 posed to hold in the present investigation, and in fact the 

 only relations which will be assumed to subsist between 

 the four quantities e, /x, C, and K are the following two 



* Oseen, Ann. d. Phys. ser. 4, vol. xliii. p. 639 (1914). 



