Energy in the Electrodynamic Field. 403 



Thus, whereas in Poynting's theory the transfer o£ energy 

 in the distant field always exists and is directed outwards if 

 the rate of change of the moment of the doublet is accelerated, 

 there is, on the general form of the new theory, no such thing 

 as a radiation of energy away from the vibrator in the distant 

 field : all that happens is a rearrangement taking place by 

 flux in the spherical surfaces round the vibrator as centre 

 and generally along the lines of electric force at all parts of 

 the field. 



This conclusion agrees generally with that obtained in the 

 case of the simple radiation field, and explains the accumu- 

 lation of the kinetic energy in the field near the vibrator. 

 In fact the only difference between the present theory and 

 Poynting's is that on the latter theory the energy supplied 

 to the field at the vibrator is transferred outwards and 

 radiated away, whereas on the former theory it is stored up 

 in the field surrounding the vibrator and counted there in 

 the kinetic energy. 



Macdonald's own theory forms a sort of mean between 

 the two general theories, and although the energy in the 

 field is definitely determined for each configuration of the 

 field without reference to the past history of the establish- 

 ment of the field and whether there is real dissipation or not, 

 the energy radiation processes involved in it may be very dif- 

 ferent from those mentioned above. The fact that this theory 

 gives a definite transference of energy radially outwards in 

 the distant simple radiation field surrounding the vibrator, 

 when the motion is oscillatory, is not really in contradiction 

 with the result obtained on the same theory in the simple 

 problem first analysed, that there is no such transference in 

 the direction of propagation. In fact, the fields in the two 

 cases, although alike in their general aspects, are of funda- 

 mentally different mathematical origin : the radial component 

 of the zero electric force in the distant field surrounding the 

 vibrator in reality consists in the difference of two finite 

 parts — the one of dynamic origin derived from the vector 

 potential, and the other of static origin derived from the 

 scalar potential. In the simpler case first examined the 

 field was entirely dynamic in character, there being no 

 static potential. Of course, from another point of view, 

 the difference in the two cases must be considered as a 

 disadvantage in the theory. The scalar and vector potentials 

 are merely auxiliary functions introduced to secure analytical 

 simplicity in the relations of the theory, and cannot therefore 

 represent definite physical entities. The real entities of the 



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