358 Dr. 0. J. Lodge on the Dimensions of a Magnetic 

 capacity K, we have the general equation 



r ~ Kr 2 

 Now all that is solemnly essential with respect to the dimen- 

 sions of the quantities here involved is that e 2 /K must be a 

 force into an area, or that 



M=[L][KF]* 



If we proceed to define the unit of electricity so as to make K 

 of no dimensions and to equal 1 for air, that is a convention, 

 and it is the basis of the electrostatic system ; but the above 

 statement is no convention, but a natural truth. 



Precisely the same kind of thing is true in magnetism; and 

 we now know that the force between two magnetic poles is not 

 independent of the medium surrounding them, but that if the 

 torsion-balance were full of, say, ferric chloride, the force 

 between the two poles would be measurably less than if it 

 were full of mere air. Thus we again need a factor for com- 

 pleteness ; and the real law is that 



or that 



Ws[L]|>F]* 



The conventional magnetic system of units is based on the 

 definition of m in such a way that fx. the magnetic inductive 

 capacity of the medium, shall be of no dimensions, and shall 

 for air be simply 1. 



All then that is objectively and physically fixed about th<- 

 matter is that the dimensions of e/v/K and of m/^/fi are 

 absolutely and mechanically definite, being each of them a 

 length into the square root of a force, or 



But observe that the two system of units, the electrostatic 

 and the magnetic, the arbitrary definition of e and the arbi- 

 trary definition of m, are in their origin utterly independent ; 

 not that they are unrelated, but their relation must be a matter 

 for future and experimental investigation. All we can so far 

 say about them is, that,in every possible consistent system that 

 can be adopted, 



[«K-*] = [fn^]=[LF + *]= [MiT*]. . . (1) 



(The last term of this triple identity is added for the sake of 

 completeness, though it does not directly belong to the present 



