414 THE ELECTROMAGNETIC FIELD. [PT. III. CH. XI. 



212. Dimensions of the Units. If we denote the numeric 

 of a quantity when measured in the electrostatic system by the 

 suffix e and when measured in the electromagnetic or magnetic 

 system by the suffix m, we have for the magnetic potential 



(1) n m = ^/ e ft> = / m ft>, 



(2) l e = I e co=-l m a>. 



Consequently the number A denotes the ratio of the numeric of a 

 certain current when measured electromagnetically, to the numeric 

 of the same quantity measured electrostatically, or I/ A is the 

 number of electrostatic units of current in one electromagnetic 

 unit. If m denote a magnetic charge, we have the dimensional 

 equation, by 190, 



the quantities being measured in either system. Also since the 

 dimensions of solid angle are zero, the dimensions of ft are the same 

 as of /, and 



rT -t r^-, f m 

 (4) [f] ' 



Since the unit of electric charge in either system is obtained 

 from the unit of current multiplied by the unit of time, 



and we accordingly have for the ratio of the two units of electricity 

 or of current, inserting the suffix m in (5)* 



Now the fundamental assumption in defining the magnetic system 

 was that the dimensions of p were zero. Also the assumption 

 defining the electrostatic system was that the dimensions of e 

 were zero. Accordingly the dimensions of e e , and of m m , both 

 belonging to the Gaussian system, and defined by precisely the 

 same considerations, namely 



(7) 



* Evidently any dimensional equation holds when either suffix e or TO is inserted 

 on both sides. 



