DopiAers Factor into the Electron Theory. 283 



The volume-integral 



J 



da? <h > 



in which dx, dy, dz are respectively equal to d$ , dy fi , dz 



divided by K, is identically equal to 



d 2 (j> 



i r<pj> 



K J dx* 



dr 



and this holds good even on replacing -= - .,. by *rj, since 



dr Q = Kdr. 



On the other band, in the demonstration of Beltrami's 

 theorem, as in that o£ an analogous theorem of Green's, the 

 point P is surrounded by a sphere whose radius tends towards 

 zero, and the surface-integral 



j4> 



d<T. 



extended over the surface of the sphere, is considered. On 

 substituting, as above, dx Q , dy , dz for dx, dy } dz, the integral 

 becomes 



whence 



and therefore 



i r <v\ 



On now replacing dr by <iT /K 3 , the factor K disappears. 

 Thus, taking into account the field of emission and that of 

 transmission, we see that the factor in question is not 

 introduced, although it was necessary to mention this fact. 



Since, however, it is necessary to complete the expression 

 for (p by the introduction of K into the denominator in 

 order that the analytical results may accord with those 

 obtained directly by Lorentz without the use of the notion of 

 propagation, and with the experimental facts connected with 

 oscillatory and circular motions of the electron, it becomes 

 necessary to have recourse to a mechanical hvpothesis 

 involving this modification. 



I believe that the hypothesis according to which the 



