Equation of Electrical Flow. 421 



rate of change of the current ; that is 



-r, T dG LrfE „ t, t,^ 



F = - L A=-R^' forE = RG ' 



where C is the current, R the resistance, and L is the 



coefficient of self-induction. 



The equation already given then becomes 



V-L^=E=RC. 



at 



Multiplying through by C and integrating through a com- 

 plete period, 



The first term represents the work done by the source of 

 the disturbance. 



The second term vanishes. 



The third term represents work done in heating the 

 circuit. 



Hence the whole work done has gone to heat the circuit. 



Now it is admitted on all hands that when the period is 

 sufficiently short a radiation of energy into space takes place. 

 A portion of this radiated energy is sometimes caught by 

 means of a neighbouring circuit and converted into heat. 



A coefficient of mutual induction and a corresponding 

 extra term is then introduced into the equation. But are 

 we to suppose that radiation would not proceed into space 

 were there no neighbouring conductor? It is against proba- 

 bility, against the electromagnetic theory of light. 



If electromagnetic waves are capable of being sent into 

 space, we can no longer look upon the operation of establish- 

 ing a current in a circuit as analogous to bending a stiff 

 spring or displacing rigid wheelwork. The wheelwork must 

 have indiarubber spokes or teeth. 



The above equation takes no account of this radiation which is 

 expended outside the wire, nor of any other work done else- 

 where than in the conductor ; and this latter the equation 

 states to be exactly equal to the energy expended in propa- 

 gating the electromotive force. Even supposing a portion of 

 the field is occupied by some material whose passage through 

 a cycle of magnetization involves the loss of energy, in the 

 form of heat, this, equally with wave-propagation through 

 space occupied by perfectly elastic matter, will not be 

 accounted for by the equation. 



Now of such phenomena as radiation of energy in electro- 

 magnetic waves, or absorption of energy in the field, there is 



