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 But this is identical with the form which was obtained for a field due to permanent and temporary magnets. It thus appears that in all cases the stored energy of a system of electric currents and permanent and temporary magnets is

where the integration is extended over all space.

It must, however, be remembered that this represents only what in thermodynamics is called the "available energy"; and it must further be remembered that part even of this available energy may not be convertible into mechanical work within the limitations of the system: e.g., the electrokinetic energy of a current flowing in a single closed perfectly conducting circuit cannot be converted into any other for so long as the circuit is absolutely rigid. All that we can say is that the changes in this stored electrokinetic energy correspond to the work furnished by the system in any change.

The above form suggests that the energy may not be localized in the substance of the circuits and magnets, but may be distributed over the whole of space, an amount (μH2/8π) of energy being contained in each unit volume. This conception was afterwards adopted by Maxwell, in whose theory it is of fundamental importance.

While Thomson was investigating the energy stored in connexion with electric currents, the equations of flow of the currents were being generalized by Gustav Kirchhoff (b. 1824, d. 1887). In 1848 Kirchhoff extended Ohm's theory of linear conduction to the case of conduction in three dimensions; this could be done without much difficulty by making use of the analogy with the flow of heat, which had proved so useful to Ohm. In Kirchhoff's memoir a system is supposed to be formed of three-dimensional conductors, through which steady currents are flowing. At any point let V denote the "tension" or "electroscopic force"—a quantity the significance of which