324 MB. S. H. BURBURY ON THE INDUCTION OF ELECTRIC CURRENTS. 



and, since K varies inversely as c 8 , 



flj f! 2 oc AX (cj 3 c., 3 ) sin \t, 

 Pi - P* <* M c i 3 - C 2 8 )- 



42. In any case of induction, if the primary or external system become after a 

 while constant, the induced currents will decay by resistance, and the electrostatic 

 charge, whose potential is \}>, will disappear also. Both the induced currents and the 

 electrostatic charge in disappearing generate heat in the conductor ; and this heat is 

 obtained at the expense of the chemical energy of the batteries of the primary 

 system. We know that the closed currents on the conductor, coming into existence 

 and decaying, cause on the whole more chemical energy to be spent in the batteries of 

 the primary system than is accounted for by heat generated in that system, the 

 excess being equal to the energy dissipated in the induced system of currents. 

 The energy of the electrostatic charge, if such exist, must also be obtained at the 

 expense of the batteries. We should then expect to find that charging a conductor 

 electrostatically in the neighbourhood of a closed battery circuit, or moving a charged 

 body in the neighbourhood of the circuit, tends to retard or accelerate the current ; 

 that is, to increase or diminish the chemical energy spent per unit of time in 

 maintaining the current constant. 



