384 Prof. R. Clausius on the different Systems of 



further, the little electric currents which, according to Ampere, 

 must be assumed to flow in the interior of a magnet are like- 

 wise closed, we have in magnetism to do with forces of the 

 same kind, and hence we can also select as the standard the 

 force exerted upon one another by two quantities of magne- 

 tism. This latter is the most convenient, because magnetic 

 forces can be more simply expressed than the forces exerted 

 between larger closed currents. Accordingly, in the electro- 

 dynamic system the unit of magnetism is determined, in pre- 

 cise correspondence with the unit of electricity in the electro- 

 static system, by the following definition: — The unit of mag- 

 netism is that amount of magnetism which exerts upon an equal 

 amount of magnetism at the unit of distance the unit of force. 



For the mathematical representation, we, again with Max- 

 well, denote the unit of magnetism by a square-bracketed m ; 

 but, in order to indicate that the unit in question is the 

 dynamic unit, we annex a d as index, so that the symbol has 

 the form [m rf ] ; and with this we form the equation 



« ] = [MLT-], 



whence results 



[m d ] = [M^L?T- 1 ] (2) 



§ 2. The Relation between Electricity and, Magnetism. 



By equations (1) and (2), for the static system the unit of 

 electricity, and for the dynamic system the unit of magnetism, 

 are determined. There is now the further question, How is 

 the unit of magnetism to be determined for the static system, 

 and the unit of electricity for the dynamic? For this the 

 well-known proposition of Ampere respecting the substitution 

 for a closed galvanic current of two magnetic surfaces, which 

 has also been adopted by Maxwell in its utmost generality 

 and irrespective of any particular system of measurement*, is 

 available. 



For the sake of simplicity, the current-curve may be sup- 

 posed plane, and the area of the plane figure inclosed by it 

 assumed as the surface-unit. Besides the plane containing 

 this figure, let us now imagine a parallel plane placed at an 

 infinitesimal distance, and upon this a figure delimited con- 

 gruent with the first figure and lying perpendicularly opposite 

 to it. Now let these two plane figures be uniformly covered 

 with equal quantities of north and south magnetism — that 



* See Maxwell's ' Treatise on Electricity and Magnetism/ vol. ii. part 3, 

 chapter iii. 



