Measure* for Electric and Magnetic Quantities. 433 



bv which latter equation the length L would be given. This 

 svstem would therefore free us from the handing-down of any 

 traditional measure. 



In Gauss's magnetic and electrostatic measure the dimen- 

 sions of the magnetic quantum m and the electrostatic 

 quantum e are determined bv the equations 



M=W = [M-LfT- , ] J 



both based on the phenomenon of repulsion between resting 

 magnetic or resting electric quanta. 



On the other hand, for electromagnetic determinations the 

 ponderomotive action of a closed electric current upon a pole 

 of a magnet was used, the laws of which have been mainly and 

 completely formulated by Ampere. 



The components of the magnetic forces produced in its 

 vicinity by an electric cm-rent can, like those of a magnet, be 

 represented as differential quotients of a potential-function 

 which satisfies the same differential equations as those of mag- 

 nets, and only differs from those of the latter in that it periodi- 

 cally increases in value by the same quantity as often as only 

 one pole is caused to make a whole revolution about the con- 

 ductor of the current. As the electromagnetic forces are pro- 

 portional to the current -intensity of the conductor, the period 

 of the potential is also proportional to that intensity, and inde- 

 pendent of the shape of the conductor. Maxwell on this 

 account employs the value of the period of the potential O as 

 a measure for the intensity of the current C, and therefore, in 

 § 623 of his Treatise on Electricity and Magnetism, puts the 

 dimensions of the two equal : 



[Q]=[C] ; 



The fixed numerical relation between the two follows from an 

 earlier passage of the above-mentioned work, § 479, where T 

 denotes the magnetic force of a very long straight current- 

 conductor at the small distance r from its axis, and J is put 

 forC:— l 



Tr=2J. 

 Since 



o = T.27r>>, 



n = 47rJ, 



by which Maxwell's determination becomes, when (rauss's 

 magnetic measure is employed, equal to the electromagnetic 

 measure proposed by "VT. Weber. 



In Ampere's time a complete theory of potential -functions 

 did not yet exist. He has, however, represented quite accu- 



