230 Dr. J. Larmor. On the Elcdrodynamic and [Jan. 2, 



barrier surface. This is equal by Green's theorem to the volume- 

 integral 



i:T(>*+p+y)4r 



extended throughout all space. This latter integral is in fact taken 

 in most forms of Maxwell's theory to represent the actual distribution, 

 in all circumstances whether steady or not.* of the electrokinetic 

 energy among the elements of volume of the aether, in which it is sup- 

 posed to reside as kinetic energy. 



2. The most definite and consistent way to treat magnetism and 

 its energy is to consider it as consisting in molecular electric currents : 

 so that in magnetic media we have the ordinary finite currents, 

 combined with molecular currents so numerous and irregularly 

 orientated that we can only average them up into so much polarisation 

 per unit volume of the space they occupy. So far in fact as the 

 latter currents are concerned, the only energy that need or can 

 occupy our attention is that connected with some regularity in their 

 orientation, i.e., with magnetisation, the remaining irregular part 

 beino- classed with heat. If there were no such molecular currents, 

 the magnetic force (a, j3, y) in the aether would in steady fields be 

 derived from a potential cyclic only with regard to the definite number 

 of circuits of the ordinary currents. But when magnetism is present this 

 potential is cyclic also with respect to the indefinitely great number of 

 molecular circuits. The line integral of magnetic force round any 

 circuit is -}--t'), where 2t' refers to the practically continuous dis- 

 tribution of magnetic molecular currents that the circuit threads. 

 This latter vanishes when these currents are not orientated with some 

 kind of regularity. If we extend the integral from a single line to an 

 average across a filament or tube of uniform cross-section 6S, with 

 that line for axis, by multiplication by SS, we obtain readily the 

 formula 



8s[(ad&e+ fidy+ydz) = &4ir2i + 4-| {Adz + Bdy + G/:)6S 



in which (A, B, C)oV represents the magnetisation in volume or. 

 Thus, after transposition of the last term, and removal of the factor 

 SS after the average lias now been taken, we obtain 



j {(a - 4irA) dx + (fi- 4:rB) dij + (y - 4ttC) dz] = &r2i 



In other words this new vector (a - 4-A, fS - 4~B, y - 4-C), is derived 

 from a potential which is cyclic in the usual manner with regard to 

 the ordinary currents alone. 



* In tlie previous electric specification, the fictitious electric currents of aethereal 

 displacement must be introduced when the state is not steady. 



