894 Prof. Thomson on TVamient Electric Currents. 



we have do ., v 



''^-di • • (^^- 



Now, if C denote the electrical capacity of the principal conductor, 

 that is, the quantity of electricity which it takes to make the 

 potential within it unity, the mechanical value or the " potential 



1 Q^ 



energy '' of the distribution of a quantity q upon it is - ^. As 



this diminishes from the commencement of the discharge, and 

 varies during the whole period of the discharge, corresponding 

 mechanical effects must be produced in the discharger according 

 to the general law of "vis viva,*' or of the preservation of mecha- 

 nical energy. The mechanical effects in the discharger are of 

 two kinds, — first, the excitation or alteration of electrical motion ; 

 secondly, the generation of heat. To estimate the first of these, 

 it is necessary to know the mechanical value or the ** actual 

 energy " of an electrical current of given strength established 

 and left without electromotive force in the discharger. In inves- 

 tigations which I have made towards a mechanical theory of 

 electro -magnetic induction, I have found that the mechanical value 

 of a current in a closed linear conductor is equal to the quantity 

 of work that would have to be spent against the mutual electro- 

 magnetic forces between its parts in bending it from its actual 

 shape into any other shape, while a current of constant strength 

 is sustained in it by an external electromotive force, together with 

 the mechanical value of the current in the conductor thus altered. 

 According to Faraday's experiments (Experimental Researches, 

 § 1090, &c.), it appears that the actual energy of a current in a 

 linear conductor doubled upon itself throughout its whole extent, 

 is either nothing, or such as to produce no sensible spark when 

 the circuit is suddenly opened at any point ; that is, that what 

 can be obviously interpreted as inertia of electricity either does 

 not exist, or produces but insensible effects compared to those 

 which have been attributed to the " induction of a current upon 

 itself." According to these views, the actual energy of an 

 electric current of given strength in a given closed linear con- 

 ductor would be determined analytically by calculating the 

 amount of work against mutual electro-magnetic actions required 

 to double it upon itself throughout its whole extent ; but it may 

 be that a more complete knowledge of the circumstances will 

 show a term depending on electrical inertia which must be added 

 to the quantity determined in that way to give the entire mecha- 

 nical value of the current. However this may be, and whether 

 the linear conductor be open or closed, it is obvious that the actual 

 energy of a current established in it and left without electromotive 

 force must be proportional to the square of the strength of the 



