486 Mr. 0. Heaviside on Resistance 



finds the impulsive permittance from the conductance-operator. 

 L C and — S Z V are equivalent expressions for the electro- 

 motive impulse. 



If Z should he infinite, ihen use Y. For instance, the 

 insertion of a nonconducting condenser of permittance S x in 

 the main circuit of the current makes Z infinite, since the 

 resistance-operator of the condenser is (Si/?) -1 . There is no 

 final steady current, and L is infinite. We should then use 

 (26) instead of (24), especially as the energy is wholly electric 

 in the steady state. 



7. To connect with the energy, multiply (23) by C, the 

 final current, and, for simplicity, let V be steady ; giving 



j(Y-Er)C^=Z / C 2 =JV(C-r)^. . . (27) 



It may be anticipated from the preceding that these equated 

 quantities express twice the excess of the magnetic over the 

 electric energy. 



In connexion with this I may quote from Maxwell, vol. ii. 

 art. 580. A purely electromagnetic system is in question. 

 " If the currents are maintained constant by a battery during 

 a displacement in which a quantity of work, W, is done by 

 electromotive force, the electrokinetic energy of the system 

 will be at the same time increased by W. Hence the battery 

 will be drawn upon for a double quantity of energy, or 2W, in 

 addition to that which is spent in generating heat in the 

 circuit. This was first pointed out by Sir W. Thomson. 

 Compare this result with the electrostatic property in art. 93." 

 The electrostatic property referred to relates to conductors 

 charged by batteries. If " their potentials are maintained 

 constant, they tend to move so that the energy of the system 

 is increased, and the work done by the electrical forces during 

 the displacement is equal to the increment of the energy of the 

 system. The energy spent by the batteries is equal to double 

 of either of these quantities, and is spent half in mechanical, 

 half in electrical work." 



Although of a somewhat similar nature, these properties are 

 not what is at present required, which is contained in the fol- 

 lowing general theorem given by me*: — Let any steady 

 impressed electric forces be suddenly started and continued in 

 a medium permitting linear relations between the two forces, 

 electric and magnetic, and the three fluxes — conduction current, 

 electric displacement, and magnetic induction (but with no 

 rotational property allowed, even for conduction current); the 

 whole work clone by the impressed forces during the establish - 



* ' Electrician/ April 25, 1885, p. 490. 



