284 PiJOFESsou Thomson 07i the Distribution of Electricity. 



A will express such a functioa of the inductive capacity that if a ball of 

 similar substance be placed in a magnetic field where the force is F, the 

 intensity of the magnetization induced in it will be — 



F 



2?v + -t^ 



III. Electricity in Motion. 



If an electric current be excited in a conductor, and then left without 

 electro-motive force, it retains energy to produce heat, light, and other 

 kinds of mechanical effect, and it lasts with diminishing, or it may be 

 with alternately diminishing and increasing strength : before it finally 

 ceases an electrical equilibrium is established, as is amply demonstrated 

 by the experiments of Faraday and Henry, on the spark which takes 

 place when a galvanic circuit is opened at any point, and by those of 

 Weber, Helmholz, and others on the electro-magnetic effects of varying 

 currents. The object of the present communication is to show how the 

 mechanical value of all the effects that a current in a close circuit can 

 produce after the electro-motive force ceases, by a determination, founded 

 on the known laws of electro-dynamic induction, of the mechanical value 

 of the energy of a current of given strength, circulating in a linear con- 

 ductor (a bent wire, for instance) of any form. To do this, in the first 

 place it may be remarked, that although a current, once instituted in a 

 conductor, will circulate in it with diminishing strength after the electro- 

 motive force ceases, just as if the electricity had inertia, and will diminish 

 in strength according to the same, or nearly the same, laws as a current of 

 water or other fluid, once set in motion and left without moving force, in 

 a pipe forming a closed circuit. But according to Faraday, who found 

 that an electric circuit consisting of a wire doubled on itself, with the 

 two parts close together, gives no sensible spark when suddenly opened, 

 compared to that given by an equal length of wire bent into a coil, it 

 appears that the effects of ordinary inertia either do not exist for electri- 

 city in motion, or are but small compared with those which, in a suitable 

 arrangement, are produced by the " induction of the current upon itself." 

 In the present state of science it is only these effects that can be deter- 

 mined by a mathematical investigation ; but the effects of electrical 

 inertia, should it be found to exist, will be taken into account by adding 

 a term of determinate form to the fully determined result of the present 

 investigation which expresses the mechanical value of a current in a linear 

 conductor, as far as it depends on the induction of the current on itself. 



The general principle of the investigation is this ; that if two conduc- 

 tors, with a current sustained in each by a constant electro-motive force, 

 be slowly moved towards one another, and there be a certain gain of 

 work on the whole, by electro-dynamic force, operating during the motion, 

 there will bo twice as much as this of work .spent by the electro-motivo 



