438 Prof. H. Helmholtz on Si/stems of Absolute 





Electric. 



Electrokinetic. 



Magnetic. 



Potentials ... 



Forces 



Densities . . . 





r i r L ' M i 

 m-gSl 





H = [CT] 



These are the determinations which, without any further 

 limiting equations, result from the above fifteen. These can 

 be applied to any definition of the units of m and e, and there- 

 fore also to the electrostatic-magnetic system of Gauss. 



Now follows, in Maxwell, § 623, " These fifteen equations 

 are not independent of each other; and in order to deduce 

 from them the dimensions of all the twelve units they contain, 

 we require one more equation." In fact we require two, 

 since e and m must be determined singly by recurring to two 

 facts of observation regarded as fundamental phenomena. The 

 one here wanting, not expressly mentioned by Maxwell, but 

 from the connexion self-evidently presupposed, we can write 

 as above:— M = [0]. 



Clausius has chosen for it the less perspicuous 



But, since one of the fifteen determinations in § 622 reads 



[m.O] = [^.C], 

 each of the two follows from the other. 



Just on this account, however, the closing words of § 623, 

 " All the above-given determinations are correct for any sys- 

 tem of units we may choose," must be altered, and limited to 

 electromagnetic systems, and, indeed, to such only as are 

 derived from the meaning, as defined by Maxwell, of the fun- 

 damental law of electromagnetism. For that coucluding sen- 

 tence applies neither to the electrostatic system nor to the 

 system set up by Clausius. Of the possibility that another 

 conception of the electromagnetic fundamental law might here 

 lead to other consequences Maxwell probably did not think ; 

 and in this respect Clausius has indeed, in his most recent 

 memoir, given a thankworthy enrichment of our ideas. 



Finally, we must speak of the reason why Prof. Clausius is 



