386 Prof. R. Clausius on the different Systems of 



at the expressions for [?n J and [e d ~] . From (1) and (3 a) we 

 get by multiplication, on which [e s ] vanishes, 



M = [MlLfT- 2 ]; (4) 



and from (2) and (3b) is obtained by division, [m d ~] vanishing, 



M = [M*M]. ....... (5) 



§ 3. Maxwell's Incorrect Equations. 

 Instead of the relation between electricity and magnetism 

 deduced in the foregoing section from Ampere's proposition, 

 and expressed in equation (3), in the equations constructed 

 by Maxwell another relation between electricity and magne- 

 tism is implicitly expressed ; for at page 240 of the second 

 volume of his work, under (1) and (3) are found the equa- 

 tions 



[^] = figlandgl = [T]. 



Here [e] signifies, as with us, the unit of electricity, and 

 [C] represents the unit of current. By [p] is understood the 

 unit of a quantity which he calls the electrokinetic moment 

 of a current, into the meaning of which, however, we need 

 not here enter, since he himself, further on, puts [p] = [?w], 

 and therefore we can in the first of the above equations sub- 

 stitute [rn\ for [/>]. If we then multiply the two equations 

 together, we obtain the equation 



[«]-[Muri (6) 



This, according to Maxwell, holds good for every system of 

 measurement; hence in his developments it plays the same 

 part as equation (3) does in ours. 



The way in which he arrives at his equation rests upon his 

 bringing into calculation the force exerted by a current upon 

 a magnetic pole, in a similar manner to that in which we, in 

 deducing equations (1) and (2), have brought in the force 

 acting between two units of electricity, and between two units 

 of magnetism, respectively. The force, however, which a cur- 

 rent exerts upon a magnetic pole is electrodynamie; and from 

 this it follows that an equation of which the deduction is based 

 upon this force can be regarded as valid only in the dynamic 

 system founded upon the electrodynamie forces, and not in 

 the static system based on the electrostatic forces. 



Indeed it is also manifest that Maxwell's equation (16) leads 

 to the same result in the dynamic system of measurement as 



