1 96 On the Mechanical Values of Distributions of Electricity, ^c. 



III. Electricity in motion. 



If an electric current be excited in a conductor, and then left 

 without electromotive force, it retains energy to produce heat, 

 light, and other kinds of mechanical effect, and it lasts with 

 diminishing, or it may be with alteruatel}' diminishing and in- 

 creasing strength, before it finally ceases and electrical equili- 

 brium is established ; as is amply demonstrated by the experi- 

 ments of Faraday and Henry, on the spark which takes place 

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

 Weber, Helmholtz, 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 electromotive force ceases 

 may be ascertained, 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 

 conductor (a bent wire, for instance) of any form. To do this, 

 in the first place it may be remarked, that a current once 

 instituted in a conductor, will circulate in it with diminishing 

 strength after the electromotive 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 cncuit. 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 ineriia either do not exist for electricity in motion, or 

 arc but small compared with those which, in a suitable arrange- 

 ment, are produced by the " induction of the cm-rent upon itself." 

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

 determined 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 deter- 

 mined 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 

 conductors, with a current sustained in each by a constant elec- 

 tromotive force, be slowly moved towards one another, and there 

 be a certain yuin of icork on the whole, by electro-dynamic force 

 operating during the motion, there will be twice as much work 

 as this spent by the electromotive forces (for instance, twice the 



