of Physical Quantities to Directions in Space. 257 



1. The velocity of propagation of an electromagnetic dis- 

 turbance in the medium is given by 



V=-^|= = ZT- 1 (dimensionally), 



which is of the dimensions of a velocity along Z, the normal 

 to the plane of displacements (XY) . 



2. The flux of energy at a point is given by 



W = (EH) ; 



and expressing E and H dimensionally in terms of /x or k 



we get 



/ MR 2 T-2 v / MR 2 T~ 2 \ Z 



I XY / 1 XYZ JT -L W J> 



the bracketed factor being of the dimensions of energy per 

 unit volume, and the other a velocity in the direction Z, the 

 axis of flux of energy. 



3. The force between two poles m is given by 



where H is the strength of the field produced at the one by 

 the other. Expressed dimensionally, this becomes 



which is of the dimensions of the space rate of variation of 

 energy along Y, that is, the force along Y, as is evident from 

 the equivalent algebraic expression 



Putting R=?\L, and Y=JL, where r and j are unit vectors 

 in the directions R, and Y, and L the scalar unit length, we 

 have 



n _ MR 2 T- 2 M(rL) 2 T- 2 _ ML 2 T~ 2 _ MLT~ 2 

 LJJ J" - Y~- jL ~ jh ~ j 



= M(jL)T- 2 =MYT~ 2 . 



Thus, the force between two poles is in the direction of 

 magnetization. The reason why the force is expressed in 

 terms of the energy of the system is that it is a mechanical 

 force arising in some way from the mutual reaction between 

 matter and the medium. The quantities m and H in terms 

 of which the force between the two poles is expressed refer to 

 the medium alone, and since nothing is known as to the rela- 

 tion between the medium and matter, the relation above 



