of Physical Quantities to Directions in Space. 265 



become volume-strain per unit time (T _1 , or Y _1 Z _ X - ). 

 Electrical force E becomes MXT -2 , and voltage E 

 = MX 2 r 2 (energy). Since m=ET, m becomes MX 2 T _1 , 

 and magnetic moment ml = MX 2 YT -1 . Again, B 

 magnetic induction becomes ?n(XZ) -1 = MXZ _1 T _1 > and 

 H magnetic force (Y _1 T _1 ). Again, in the second case, we 

 have B = m(XZ) _1 = volume-strain per unit area; E = MT _ 

 = T _1 = volume-strain per unit time; e = MY 2 T -1 ; = 

 MYV 2 (energy) and C (current density) = MY 2 (YZ) _1 T" 2 . 

 These formulae, although it may be possible to give them in- 

 terpretations, are at present unintelligible, and do not suggest 

 any connected relation between the various quantities. 



The cause of the unintelligible character of these latter 

 formulae lies in the fact that the formula MXYZ -1 is not sym- 

 metrical with respect to the dimensional axes X, Y, Z. Since 

 the above formula is independent of T, the corresponding 

 quantity must be of the dimensions of some property of the 

 medium depending ultimately upon the inertia of the medium 

 alone. It is difficult, however, to conceive what property 

 depending upon the inertia of the medium can involve the 

 three dimensional axes unsymmetrically except the rotational 

 inertia, or moment of inertia of a unit volume. The above 

 formula, however, does not admit of such an interpretation. 

 Thus, whether MXYZ -1 be the dimensional formula of fju or k, 

 the results are either incapable of interpretation (as, for ex- 

 ample, fi and k), or the interpretations are unintelligible. 



Thus there are left only cases 1 and 2. If the dimensions 

 of fi be those of 1, that is M(XYZ) - , //, becomes the inertia 

 of unit volume, or the density of the medium, and magnetic 

 energy is kinetic. If the dimensions of /jl be 2, those of k 

 are 1, and k becomes the density of the medium, and electrical 

 energy is kinetic. There are thus two cases to be discussed. 



I. Magnetic Energy Kinetic. — /jl the density of the medium. 



1. Magnetic force = H =^- | [M*RT~ 1 (XYZ)" 1 ] = RT" 1 = 

 YT _1 , since R must now coincide with Y. This is the linear 

 velocity directed along Y the magnetic axis. 



2. Magnetic induction = B = Intensity of magnetization, 



I = / u,H =( vy 7 W = Linear momentum per unit volume. 



3. Magnetic moment -ml= I (XYZ) =MYT _1 = Linear 

 momentum. 



4. Current strength = C = HY=Y 2 T" 1 . 



