the Units of Magnetism and Electricity. 81 



the employment of an equation which differs from Ampere's 

 with respect to its attitude towards the electrostatic and elec- 

 trodynamic systems. For a distinction must be made between 

 equations which belong exclusively to one of those systems 

 and those which are applicable to both. Exclusively electro- 

 static or electrodynamic equations are those which represent 

 an electrostatic or an electrodynamic force by the formula of 

 mechanical force. 



Now, as to Ampere's equation, it certainly resulted from the 

 consideration of electrodynamic forces — that is to say, from 

 the comparison of the forces exerted by a magnet and by 

 an electric current ; but it does not represent these forces 

 either by the mechanical-force formula or by any other for- 

 mula, but merely expresses that the magnet and the current 

 are, in respect of the forces exerted by them, equivalent to one 

 another. It is therefore not to be regarded as an exclusively 

 electrodynamic equation; much rather, since it expresses only 

 the relation which, according to Ampere, subsists between 

 magnetism and electricity, to it must be ascribed, so far as 

 Ampere's theory is at all recognized as correct, a general 

 validity independent of the system of measures employed: and 

 this justifies my application of it. 



Maxwell's equation, on the contrary, was produced by repre- 

 senting an electrodynamic force, namely the force which a 

 magnetic pole exerts upon an electric current, by the mecha- 

 nical-force formula. It consequently has in itself the cha- 

 racter of an exclusively electrodynamic equation ; and its 

 employment for the determination of the electrostatic unit of 

 magnetism cannot be acknowledged as justified. 



On the reasons alleged by various English authors in sup- 

 port of this mode of determination I have already expressed 

 myself in my above-mentioned article in the ' Philosophical 

 Magazine,' and will not repeat what I have there said, but 

 will confine myself to noticing some points which appear to 

 me to furnish a standard for judging the mutually contrary 

 modes of determination. 



Maxwell's determination is not only carried out without regard 

 to Ampere's explanation of magnetism, but is even in contra- 

 diction to it, as will readily be seen if the formula (6) above 

 given for [w s ], and at the same time formula (4) for [^ s ], be 

 inserted in equation (3), because then on the two sides there 

 will be different expressions, and, indeed, expressions of differ- 

 ent dimensions. And I must say that, if Ampere's explana- 

 tion of magnetism, by which the great department of science 

 embracing electricity, magnetism, and electromagnetism is so 

 essentially simplified, were given up again, I should hold that 

 a decidedly retrograde step had been taken. 



