of Plitjskal Quantities to Directions in Space. 25& 



7. C«=mT- 1 =:E. 



8. m = B(XZ). 



9. C^BT- 1 . 



10. E, B = H(Y) = C=^T- 1 = D(YZ)T- i . 

 The energy of the medium at any point may be expressed 



where r is the instantaneous linear displacement upon which 

 both the electric and magnetic displacements at that point 

 d-epend, for the two laws of circulation express that the 

 electric and magnetic displacements at a point in the medium 

 are not independent, but originate from the same dynamical 

 cause. Expressed diinensionally, this becomes 

 M(X 2 + Y 2 + Z 2 )T~ 2 or MR 2 T" 2 , 

 and the dimensions of energy per unit volume are 



MR^XYZ)- 1 !- 2 . 

 Since the axes of reference (X, Y, Z) and the displacement 

 R are both instantaneous with respect to any point, the 

 direction of R must be definitely related to the axes, the 

 relation being dependent upon the dynamical mechanism of the 

 field. It will be convenient, however, to express the dimen- 

 sions of electromagnetic quantities, first, in terms of M, X 5 

 Y, Z, T and R ; and afterwards to determine the relation 

 between the direction of R and the axes. The fact that the 

 formulae of some of the quantities involve R, while others do 

 not, then simply means that in the former cases the corre- 

 sponding quantities depend upon and involve the instanta- 

 neous linear displacement specified by R ; while in the other 

 cases they are independent of the displacement and express 

 only physical properties of the medium. 



I. Electromagnetic System : — 



f cH 2 = MR 2 T" 2 (XYZ)- 1 . 

 Hence 



1. H=f^[M4lT- (XYZp*]. 



2. B^H^^RT-^XYZ)- 1 ]. 



3. 77i=^ = B(XZ)=^[M^RT- 1 (X l Y- | Z l )] t 



4. E ^mT-^/^M^RT-^Y^Z 1 )]. 



5. E ^ECX-^^^RT-^X^Y^Z 1 )]. 



T2 



