OHM ON THE GALVANIC CIRCUIT. 443 



constant at all times, it merely depends on the magnitude of the 

 instant of time d t, we can consequently extend it to the unity 

 of time ; if we place the present constant difference of the forces 

 v! — u equal to the unity of force, it then becomes 



« in m'. 

 This quantity of electricity is for the two elements E and E' 

 whose position is invariable, constant under the same circum- 

 stances, on which account it may be employed in the determi- 

 nation of the power of conduction just mentioned. For if we 

 understand by q the quantity of electricity transferred from 

 E' to E in the unity of time, with a constant difference of the 

 electroscopic forces equal to the unity of force, we have 



q =z a m m', 

 and then 



X — a. m m' s. 



If we take from this last equation the value of a m m' and sub- 

 stitute it in the expression 



c m m' (u'—u) dt, 



we obtain for the variable quantity of electricity which passes 

 over in the instant of time d t from E' to E, the following : 



K (u' — u) d t / , V 



— s — ' ^^^ 



which expression is not accompanied by the above-mentioned 

 disproportion between the members of the differential equation, 

 as will soon be perceived. 



7. The course hitherto pursued was based upon the suppo- 

 sition that the action exerted by one element on the other is 

 proportional to the product of the space occupied by the two 

 elements, an assumption which, as was already observed in § 4, 

 can no longer be allowed in cases where it is a question of the 

 mutual action of elements situated indefinitely near each other, 

 because it either estabhshes a relation between the magnitudes 

 of the elements and their mutual distances, or prescribes to 

 these elements a certain form. The previously found expres- 

 sion ( (J ) for the variable quantity of electricity passing from 

 one element to the other, possesses therefore no slight advan- 

 tage in being entirely independent of this supposition ; for what- 

 ever may have to be placed in any determinate case instead of 

 the product m ml, the expression ( cj ) constantly remains the 



