OHM ON THE GALVANIC CIRCUIT. 489 



the repulsive farce between these two elements is proportional 

 to the time d t, to the product u u', and, moreover, to a 

 function dependent on the position, size, and form of the two 

 pai'ticles, which we wiU represent by F'; we accordingly ob- 

 tain for the repulsive force between two particles the expres- 

 sion 



F uu' dt. 



If we here proceed in the same manner as in § 6, and signify- 

 by the moment of action x' between two places, the product of 

 g', which expresses the force produced under perfectly deter- 

 mined circumstances between both, and its mean distance s', so 

 that 



and determine q' by putting u = u' = 1 '\\\ the expression 

 F' u li d t, and extending the action to the unit of time, we have 



x' = F' 5', 

 whence it follows that 



Let us now imagine, as we did in § 11, the prismatic circuit 

 to be divided into equally large, infinitely thin discs, and call 

 M', M, M; those immediately following one another, which 

 belong to the abscissae x + d x, x, x — dx; then, according to 

 what has just been shown, the pressure which the disc M' 

 exerts on the disc M is 



F' uu' dt; 



and if we admit that the position, size, and form of the particles 

 remain in all discs the same, the counter pressure, which the 

 disc M^ exerts on the disc M, is 



F' uu^ dt ; 

 the difference between these two expressions, \-iz. 



F' u (u' —Ml) dt, 

 gives accordingly the magnitude of the force, with which the 

 disc M tends to move along the axis of the circuit. This force 

 acts contrary to the direction of the abscissae when its value is 

 positive, and in the direction of the abscissae when it is ne- 

 gative. 



If we substitute for u'—u its value proceeding from the deve- 

 lopments given in § 11 for u' and u^, the expression just found 

 changes into the following : 



