of Physical Quantities to Directions in Space. 269 



II. Electrical Energy Kinetic. — k the density of the 

 medium. 



1. E = ^-*[M*RT- 1 (X- | Y"*Z"*)] 



= M-*(XYZ)*M t KT- 1 (X" 1 y-^Z" 1 ) = RT~ ] = XT" 1 



(since R here must coincide with X). 

 Thus, E is the velocity of the medium. 



2. E = EX = X 2 T _1 . Magnetic current. (See below, its 

 interpretation depends upon that of m and B.) 



3. m=ET=X 2 . 



4. B = m(XZ)~ = XZ _l = an angular displacement. Thus, 

 m = product of angular displacement into cross section. 



5. Cm=BT- 1 XZ- 1 T- 1 = Angular velocity. Thus, E the 

 strength of the magnetic current corresponds to the strength of 

 a vortex, C m being the density of the magnetic current. 



6. e = MT~ . This corresponds to magnetic pole in the 

 previous case. 



7. L=,(YZ)- 1 = M(YZ)- 1 T- 1 =^J- 1 =Linear momen- 

 turn per unit volume. 



8. C=DT~ 1 = | YYy ) =: Force per unit volume. 



-2 



9. C = MT . This corresponds to voltage in the previous 

 case. 



10. H = C(Y- 1 )=MY _1 T" 2 . Tangential force per unit 

 area, a quantity of the nature of a torque, corresponding to E 

 in the former case. 



It is thus seen that this system is simply the inverse of the 

 other, and it is unnecessary, therefore, to go into more detail. 



To summarize, therefore, we may say that, of the eight 

 possible systems previously mentioned, only two give rise to 

 dimensions whose interpretations are intelligible, natural, and 

 connected as a whole ; and these interpretations accord with 

 the two rotational theories of electromagnetism which have 

 been hitherto put forward. Of tbe other six, it was shown 

 that four necessitated, in some form or other, fluid theories of 

 electricity or magnetism, and that the interpretation of the 

 formulae of p, and k and other quantities are difficult. These 

 remarks also apply to the other two cases, in which electri- 

 fication and magnetization became respectively volume-strains. 

 All other cases were disposed of by excluding ; — 



(1) All values of fx leading to dimensions involving higher 



Phil. Mag. S. 5. Vol. 34. No. 208. Sept* 1892. U 



