442 OHM ON THE GALVANIC CIRCUIT. 



disproportion between the members of a differential equation, 

 belonging nevertheless necessarily to one another, is too remark- 

 able not to attract the attention of those to whom such inquiries 

 are of any value ; an attempt therefore to add something to the 

 explanation of this aenigma will be the more proper in this place, 

 as we gain the advantage of rendering thereby the subsequent 

 considerations more simple and concise. We shall merely take 

 as an instance the propagation of electricity, and it will not be 

 dilBcult to transfer the obtained results to any other similar 

 subject, as we shall subsequently have occasion to demonstrate 

 in another example. 



6. Above aU, it is requisite that the term goodness of conduc- 

 tion be accurately defined. But we express the energy of con- 

 duction between two places by a magnitude which, under other- 

 wise similar circumstances, is proportional to the quantity car- 

 ried over in a certain time from one place to the other multi- 

 plied by the distance of the two places from each other. If 

 the two places are extended, then we have to understand by 

 their distance the straight line connecting the centres of the 

 dimensions of the two places. If we transfer this idea to two 

 electric elements, E and E', and call s the mutual distance of 

 their centres, g the quantity of electricity, which under accu- 

 rately determined and invariable circumstances is carried over 

 from one element to the other, and x the conductibihty between 

 them, 



X ss g .s. 



We wiU now endeavour to determine more precisely the quan^ 

 tity of electricity denoted by g. According to § 4 the quantity 

 of electricity, which is transferred in an exceedingly short time 

 from one element to the other, is, the distance being invariable, 

 in general proportional to the difference between the electrO' 

 scopic forces, the duration, and the size of each of the two ele 

 ments. If therefore we designate the electroscopic forces of the 

 two elements E and E' by u and u', and the space they occupy 

 by m and m', we obtain for the quantity of electricity carried 

 over from E' to E in the element of time d t the following 

 expression : 



a m ml [u' —■ u) d t, 

 where a represents a coefficient depending in some way on the 

 distance s. This quantity changes every moment if «' — « 

 variable ; but if we suppose that the forces u' and u reraaii 



