Measures for Electric and Magnetic Quantities. 385 



which, if we imagine ourselves going with the current round 

 the figures, we have on the left hand with north, and the other 

 with south magnetism. The quantity of the magnetisms is 

 determined by the intensity of the current and the mutual 

 distance of the planes. Let the latter be denoted by e[L], in 

 which [L] , as always, signifies unit length, and e an infinite- 

 simal numerical value. Then, if a current-unit be assumed as 

 the current-intensity, each of the two quantities of magnetism, 

 apart from the sign, is to be supposed equal to a unit of mag- 

 netism divided by e. The pair of magnetic surfaces thus 

 formed can replace the current in regard to all the forces 

 exerted by it. 



To express this mathematically, we have to multiply the 

 intensity of the current by the area round which it flows, to 

 multiply the quantity of magnetism present on one of the sur- 

 faces by the distance between the surfaces, and then to equate 

 the two products. Now the current-intensity is a current- 

 unit, which is a unit of electricity flowing through the cross 

 section in unit time, and which is therefore represented by 

 [eT -1 ] ; and the area round which it flows is a unit of surface, 

 therefore [L 2 ]. Accordingly the first product is [<?L 2 T -1 ]. 

 Further, the quantity of magnetism coming into consideration 



is — -, and the distance between the surfaces e[L]; so that 

 the second product reads -*=-^ e [L] or [mU\ . We have con- 

 sequently to form the following equation: — 



[mL] = [eL 2 T" 1 ], 

 from which results 



X^^LLT" 1 ] (3) 



This equation, which is only an expression of the relation 

 established by Ampere between magnetism and electric cur- 

 rents, must hold good for every system of measurement ; and 

 hence we can form from it two special equations referable to 

 the static and the dynamic systems respectively, namely: — 



^J=[LT-i], (3a) 



6H LT -] (-> 



If we bring these two equations into connexion with the 

 equations (1) and (2), for [ej and [w*d], we thereby arrive 



