82 



Prof. R. Clausius on the Connexion between 



It is further to be remarked that, if once Ampere's expla- 

 nation is abandoned and the electrostatic unit of magnetism is 

 sought to be determined in another way, by employing one of 

 the forces exerted by a magnetic pole, then Maxwell's formula 

 is not the only possible one. I am induced to make this 

 remark especially by a memoir recently published by Prof. 

 Helmholtz*. 



M. Helmholtz speaks of Gauss's units of electricity and 

 magnetism, which are defined by the following propositions: — 

 (1) The unit of electricity is that quantity of electricity which 

 at unit distance exerts the unit of force upon an equal quan- 

 tity of electricity; (2) The unit of magnetism is that quantity 

 of magnetism which exerts at unit distance the unit of force 

 upon an equal quantity of magnetism. From these proposi- 

 tions result the equations : — 



H = [M*IJT- 1 ],| (7) 



[m] = [MiLiT-'].J 



A system of measures based upon the simultaneous employ- 

 ment of these two equations M. Helmholtz calls the hitherto 

 employed electrostatic system, and in one place also the electro- 

 static magnetic system of Gauss. 



Now I certainly do not believe that Gauss intended to make 

 these two equations the foundation of one and the same co- 

 herent system of measures ; I am much rather of the opinion 

 that he regarded the electric and magnetic systems as two 

 separate and independent systems, of which each would have 

 one of the two equations for its basis. On the other hand, 

 however, I willingly admit that, if we once abandon Ampere's 

 explanation of magnetism, we can just as well combine these 

 two equations into one system as those which underlie Max- 

 well's electrostatic system of measures. 



We have consequently, including the system recommended 

 by M. Helmholtz, three different electrostatic systems of mea- 

 sures, which agree perfectly with each other in relation to 

 the purely electrical quantities, and differ only with respect 

 to the unit of magnetism ; and here, for the sake of distinct- 

 ness, the three formulae representing the latter may be placed 

 side by side. 





Maxwell. 



Helmholtz. 



Clausius. 



K] 



[M*L*] 



[M*L*T- J ] 



[M^UT- 2 ] 



So far as we have to do only with the comparison of mag- 

 * Wied. Ann. xvii. p. 42 ; Phil. Mag. Dec. 1882, p. 433. 



