On the Dimensions of a Unit of Magnetism. 125 



the way in which he has brought into the calculation the force 

 acting between an electric current and a magnetic pole deter- 

 mined the derivation of his formula. 



If we suppose given an electric current of intensity i pass- 

 ing along a straight line of infinite length, the force exerted 

 by the current upon a magnetic pole m at the distance L of 

 the straight line will be represented by 2iniL~ 1 , provided that 

 i and m be measured in electrodynamic measure. If, then, 

 each of the three quantities i, m, and L is a unit of the kind 

 of quantity in question, the expression takes the value 2 and 

 represents 2 units of force. Hence, introducing the formula 

 of the unit of mechanical force [MLT~ 2 ], we can write 



2[^L-'] = 2[MLT- 2 ] ? 

 from which follows 



[M»] = iML 2 T- s ], 

 and, if for [i] we substitute [eT _1 ], 



[«»] = [MLT- 1 ]. 



This is the equation of Maxwell's, cited in my preceding 

 paper, in which for [e~\ he has inserted the expression of the 

 electrostatic unit of electricity in order to get the electrostatic 

 unit of magnetism. 



It is, however, to be remarked that in forming this equation 

 the formula of the unit of mechanical force is put for an elec- 

 trodynamic force, and thereby the equation obtains the cha- 

 racter of an electrodynamic equation, into which we must not 

 directly put electrostatic units. 



In opposition to this, Mr. Everett says that my equation 

 derived from Ampere's proposition stands, in respect of the 

 property of being electrodynamic, on a par with Maxwell's. 

 But this I must controvert. Ampere's proposition enunciates 

 that the forces exerted by a magnet and by the corresponding 

 electric current are equal to one another, but does not represent 

 those forces by any formula. Maxwell's equation, on the con- 

 trary, rests, according to the above derivation, upon the intro- 

 duction of a definite formula for the electrodynamic force, 

 namely the formula of the unit of mechanical force ; and it is 

 this circumstance that makes it an electrodynamic equation, 

 in the sense that it is not suitable for application to electro- 

 static units, as the determination of the latter rests upon the 

 representation of a quite different force (the electrostatic force 

 exerted by two quantities of electricity upon each other) by 

 the formula of the unit of mechanical force. 



In Mr. J. J. Thomson's article another objection appears, in 



