the Units of Magnetism and Electricity. 83 



netic quantities with one another, all three formulae can serve 

 equally well as formulae for the unit of magnetism ; but if we 

 compare magnetic with electric quantities, the question arises, 

 to what relations between magnetism and electricity do the 

 different formulae lead ? 



In the electrodynamic system, between the units of mag- 

 netism and electricity the following universally accepted equa- 

 tion holds : — 



[mJ^LT-]. ..... (8) 



With this we will compare the equations which in the electro- 

 static system have to be formed, according to the three differ- 

 ent conceptions of it, between the units of magnetism and 

 electricity. 



According to my conception we must put 



[m s ] = [, s LT-]. ...... (9) 



This equation has the same form as that which holds good in 

 the electrodynamic system ; and consequently with this con- 

 ception we get a definite relation between magnetism and 

 electricity, independent of the system of measures employed. 

 In the equations it is expressed that the unit of magnetism is 

 a quantity having the dimension of a product of the unit of 

 electricity and the unit of velocity. The occurrence of a velo- 

 city as a factor expresses that magnetism is to be placed in the 

 same rank, not with resting (static), but with flowing (current) 

 electricity, in accordance with Ampere's explanation. 

 According to Helmholtz's conception we must put 



K1 = W _• ■ • (9a) 



This is quite another equation than that which is valid in 

 the electrodynamic system ; and I must confess I know not 

 what idea is to be formed of the nature of magnetism if in one 

 system of measures the unit of magnetism appears as a quan- 

 tity having the same dimension as the unit of electricity, and 

 in the other system as a quantity having the dimension of a 

 product of the unit of electricity and the unit of velocity. 

 According to Maxwell's conception we must put 



K]=p}ri] ( 9fi ) 



This is likewise a different equation from that current in the 

 electrodynamic system. Instead of a product of the elec- 

 tricity- and velocity-units, here is a fraction having the 

 electricity-unit for the numerator and the velocity-unit for the 

 denominator; and the question again arises, What idea of the 

 nature of magnetism is to be formed from two expressions so 

 different ? 



Bonn, September 1882. 



