434 Prof. H. Helmholtz on Systems of Absolute 



rately what we can now, in the manner stated, express in con- 

 formity with nature, by a suitably chosen fiction ; namely, he 

 imagined a surface bounded by the conductor, dividing the in 

 this case doubly connected space covered with a double mag- 

 netic layer. If the magnetic moment of each unit of surface 

 of the double layer is denoted by fi, according to well-known 

 principles the leap of potential between the two sides must be 



0=47T//,, 



and therefore /u, = J. With this form of expression of Ampere's 

 law Prof. Clausius stops. 



Both forms are perfectly equivalent and equally justified, 

 so long as we measure the magnetic quanta according to 

 Gauss's rule. This Prof. Clausius also admits ; but he thinks 

 an extension of Maxwell's expression to other systems of mea- 

 sures must be rejected ; he explains this as an oversight on 

 Maxwell's part, and the equations and determinations of mea- 

 surements derived from it as erroneous. 



The only reason which, in this respect, he alleges against 

 Maxwell's definition is the following, in § 3 of the memoir 

 above cited: — "The force, however, which a current exerts 

 upon a magnetic pole is electrodynamic ; and from this it fol- 

 lows that an equation of which the deduction is based upon 

 this force can be regarded as valid only in the dynamic system 

 founded upon the electrodynamic forces, and not in the static 

 system based on the electrostatic forces." 



But even if one, as an adherent of Ampere's hypothesis, 

 entertained no doubt respecting the first part of this proposi- 

 tion, I do not see why the conclusion should be urged against 

 Maxwell only, and not against the interpretation of Ampere's 

 law adopted by Clausius himself, since the latter is, after all, 

 nothing but another way of expressing the same facts. Both 

 quantities, Maxwell's potential-period ft as well as Ampere's 

 magnetic momentum of unit surface, are, in Gauss's system of 

 measurement, of the dimension [?/i/L] ; both have a physical 

 meaning only in " the representation of the force which a cur- 

 rent exerts upon a magnetic pole." 



The true reason of the difference moreover appears to me to 

 lie in quite another circumstance — namely, in Maxwell's defi- 

 nition of the magnetic potential ft. This is with him not the 

 form of calculation 2[m/V], but he defines it in this case, as 

 also in the corresponding applications to electrostatics and 

 electrodynamics, by stating that ft . m is a work — which defi- 

 nition also underlies Gauss's definition of m. 



The differential quotient —d£ljdx is, corresponding to this, 

 the force which acts upon the unit of magnetism, and therefore 



