Energy in the Electrodynamic Field. 401 



part of the energy in the field near the vibrator gradually 

 increases with the time, even to the extent of becoming- 

 infinite if there is no damping. On such a theory, therefore, 

 the process of increasing or reducing an electromagnetic 

 field is an irreversible one, and in order to destroy a field by 

 reducing the forces in it to zero, a certain amount of work is 

 necessary, depending essentially on the process adopted to 

 secure the vanishing Meld, and the equivalent energy remains 

 stored in the space previously occupied by the field. Such 

 a conclusion involves an idea which is now generally re- 

 garded as inconceivable in any physical theory of these 

 matters. 



The discrepancy in the result obtained on Macdonald's 

 form of the theory for the energy in the distant field is 

 further emphasized by comparing it with the distribution of 

 potential energy. On all forms of the theory the density 

 of the potential energy is taken to be 



at any place, and this is easily seen to correspond to a 

 value W r o> for the potential energy stored between the 

 spheres r and r -f o>, where 



W;.= ~ (//"* + 2t*ff' + r'3f* + 2ff" + Srff + 3/ 2 ), 



which in the distant field reduces to 



w, = i/" 2 . 



Thus on Poynting's theory and the general form of the 

 new theory, the kinetic energy density in the distant 

 radiation field is equal to the potential energy density, 

 but on Macdonald's own form of his theory these are not 

 equal except in the case of simple harmonic oscillation. 



10. The radiation phenomena in the different theories are 

 also essentially different. According to Poynting the energy 

 flux at the typical field point is given simply by the 

 components 



47T 



c 2 sin 6 cos 9 



Phil. Mac. S. 6. Vol. 34. No. 203. Nov. 1917. 2 F 



