250 The Mathematical Electricians of the 



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 



-' dxdydz, 



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 form 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 distri- 

 buted over the whole of space, an amount (pH 2 /Sir) 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 



*Ann.d. Phys. Ixxv (1848), p. 189: Kirchhoff's Ges. AbhandL, p. 33. 



