of Physical Quantities to Directions in Space. 253 



or, the Gaussage of a closed magnetic circuit measures the 

 total electrical current through it. 



(b) Circuitation E = C,»=E = ^- m ; 



ot' 



or, the Voltage of a closed electrical circuit measures the 

 total magnetic current through it. 



The corresponding relations as given by Maxwell are 



(a) ^^-(g-^jrai, 



u being the component current-density along a 9 and ft, 7 the 

 components of magnetic force along y and z respectively, the 

 whole being referred to an elementary magnetic circuit 

 (B#(te)« [The Air in the expression \ttu is dropped, as 

 previously explained.] 



neglecting A and >|r. P is the component electrical force 

 along <r, and b and c the components of magnetic induction 

 along y and z respectively. 



III. Dynamical Relations. — These are relations between 

 quantities whose product express the energy, or energy per 

 unit volume of the medium. 



^E : mfl : pC . . . Energy. 

 DE : BH : AC . . . Energy per unit volume. 

 But D = £E, and B=//,H. Hence 



7bE 2 : /xR 7 . . Energy per unit volume. 



By means of these relations we can express in terms of 

 M, X, Y, Z, T, and one selected quantity the dimensions of all 

 the rest. The only useful cases, however, are those in which 

 the selected quantities are either fi or k, for these express 

 physical properties of the medium at a point, and are in- 

 dependent of the electromagnetic reactions going on there. 

 The dimensions in terms of yu. are obtained by starting with 

 the relation fiW 2 = Energy per unit volume; and similarly 

 for the dimensions in terms of k. 



Since the above dimensions have to be deduced by means 

 of a connected system of equations, it becomes necessary to 

 make a suitable choice of axes of reference. Let X be the 

 axis of the electric displacement, and Y that of the magnetic 

 displacement at a point in the medium. For an isotropic 

 medium (the only case we have at present to consider) these 



Phil. Mag. S. 5. Vol. 34, No. 208. Sept. 1892. T 



