448 OHM ON THE GALVANIC CIRCUIT. 



11. This being established, we mil now proceed to the sub- 

 ject, and in the first place consider the motion of the electri- 

 city in a homogeneous cylindric or prismatic body, in which 

 all points throughout the whole extent of each section, per- 

 pendicular to its axis, possess contemporaneously equal electro- 

 scopic force, so that the motion of the electricity can . only take 

 place in the direction of its axis. If we imagine this body 

 divided by a number of such sections into disks of infinitely 

 small thickness, and so that in the whole circumference of each 

 disk the electroscopic force does not vary sensibly for each pair 

 of such disks, the expression J given in § 6 can be applied 

 to determine the quantity of electricity passing from one disk 

 to the other ; but by the limitation of the distance of action to 

 only infinitely small distances mentioned in the preceding para- 

 graph, its nature is so modified that it disappears as soon as the 

 divisor ceases to be infinitely small. 



If we now choose one of the infinite number of sections 

 invariably for the origin of the abscissae, and imagine any- 

 where a second, whose distance from the first we denote by x, 

 then dx represents the thickness of the disk there situated, 

 which we will designate by M. If we conceive this thickness 

 of the disk to be of like magnitude at all places, and term u the 

 electroscopic force present at the time t in the disk M, whose 

 abscissa is x, so that therefore u in general will be a function of 

 t and x\ if we further suppose m' and u^ to be the values of 

 n when x -\- dx and x — dx are substituted respectively for x^ 

 then vS and u^ evidently express the electroscopic forces of the 

 disks situated next the two sides of the disk M, of M'hich we 

 will denote the one belonging to the abscissa x -\- d x by M', 

 and that belonging to the abscissa x -V dx by M^; and it is 

 clearly evident that the distance of the centre of each of the 

 disks M' and M, from the centre of the disk M '\% dx. Con- 

 sequently, by virtue of the expression {$) given in § 6, if x re- 

 presents the conducting power of the disk M' to M, 

 K {u' — u) dt 

 dx 

 is the quantity of electricity which is transfei-red during the in- 

 terval of time d t from the disk M' to the disk M, or from the 

 latter to the former, according as «' — « is positive or negative. 

 In the same manner, when we admit the same power of conduc- 

 tion between M, and M, 



