496 Dr. S. R. Milner on the Internal 



The net effect of the fiux must of: necessity be exactly 

 such as will transfer uniformly forward, along with the 

 nucleus, the electromagnetic energy associated with the 

 moving electronic field. In fact, at any point ahead of 

 the equatorial plane the convergence of the flux will express 

 the rate of increase there of the density of the energy, 

 which is continually increasing as the nucleus of the electron 

 gets nearer to the point. But the actual Poynting flux is 

 not equivalent simply to a bodily transference of the energy 

 of the field in the direction of motion of the electron. At 

 the point r, the flux is directed along the instantaneous 

 meridian of longitude, and, except in the equatorial plane, 

 it has a component perpendicular to the axis. Poynting's- 

 theorem, although, of course, it does not require that electro- 

 magnetic energy should be a material thing which moves 

 bodily from one place to another of the field, does demon- 

 strate that the local variations of energy are mathematically 

 the same as if this were the case. The flux can therefore 

 be expressed as the product of the energy density of the 

 field and the velocity with which it is (virtually) moving. 

 From this point of view the total flux (along the meridian 

 of longitude) must be decomposable into two — one ivy which 

 transfers the energy bodily forward in the direction, and 

 with the velocity v, of the electron's motion, and the other 

 mu such that 



wil=P — wv (6) 



Since 



divwv= =- = divP, 



dt 



the wu flux has no divergence anywhere ; from the symmetry 

 of the field it must pass through the nucleus of the electron. 

 Poynting's theorem thus requires that the electromagnetic 

 energy of the field, in addition to taking parr in the forward 

 motion of the whole system, is also travelling round and 

 round through the field, passing on each journey into the 

 nucleus at one face and out of it at the other. 



The magnitude and direction of the circuital flux uu is 

 easily determined by substituting in the vector equation (6) 

 the values of w and P given in (4) and (5). The lines of 

 flow are portions of ellipses of eccentricity 8 which have 

 their major axes in the equatorial plane, and all pass through 

 the centre of the nucleus. They are illustrated in the 

 accompanying figure, in which is the centre and BAO 

 the upper half of the surface of the nucleus, moving in the 



