436 Prof. H. Helmholtz on Systems of Absolute 



moreover gives definitions according to which the electro- 

 kinetic units are determined without any consideration of 

 magnetism. But in § 621 he introduces magnetic quantities 

 without in any way saying expressly that, in all his determi- 

 nations of the ratio between electric and magnetic quantities, 

 the electromagnetic determination discussed in the chapters in 

 question, 



47rJ = n, 

 will be retained. 



In this respect Maxwell's intention in sketching different 

 systems was exactly the same, and as limited, as that more 

 recently carried out by Clausius, although, from the cause 

 above discussed, the manner of carrying it out by the two has 

 turned out different. 



The matter being so important, I will take leave to give 

 here a summary of the connexion of the equations of the cor- 

 responding paragraphs (621-623) of Maxwell's Treatise on 

 Electricity and Magnetism. In § 621 he arranges the quan- 

 tities for which the dimensions of the unit are to be determined. 

 I place them here in a somewhat different order, and with the 

 notation of their meaning which is more usual in Germany- 

 There are four electrostatic, namely: — 



e, electric quantum; 



E, electrostatic potential-function ; 



3), dielectric polarization," measured by the electric density 

 at the surface of the dielectric ; 



(5, the electric force in a point, acting upon the unit of s. 



The four corresponding magnetic quantities he denotes, in 

 the same order, by wi, XI, 23, «£). 



To these are added four more corresponding quantities, 

 namely: — 



C, the intensity of a current ; 



(£, current-density ; 



p, the electrokinetic momentum of a current ; 



51, the vector-potential of electric currents. 



As regards the meaning of the last two quantities, p is 

 Neumann's electrodynamic potential of the other currents 

 present, referred to the entire conductor (passed through by 

 the unit of current) for which it is calculated ; and 51 . ds is 

 the same potential referred to a conductor-element ds situated 

 at a determined place. 



I remark further that the quantities denoted by German 

 capital letters are vectors, i. e. quantities having direction and 

 resolvable into components according to the law of the paral- 

 lelogram of forces, — and that the selection of them resulted 

 from Maxwell's endeavour to introduce, as far as possible, only 



