444 OHM ON THE GALVANIC CIRCUIT. 



same, this peculiarity being solely referrible to the power of 

 conduction x. If, for instance, F designate, as was stated in 

 § 4, the function, corresponding to such a case, of the dimen- 

 sions and of the mean distance of both elements, the expression 



a m nJ {u' — u) d t 



not merely changes apparently into 



F (?/ -u) dt, 

 but also the equation 



X = a m m' s 

 into the other, 



x = F.«, (O) 



so that if we take the value of F from this equation and place it 

 in the above expression, we always obtain 

 X {u' — u) dt ^ 

 s 

 Moreover, the circumstance of the expression ( S ) stiU remain- 

 ing vahd for corpuscles, whose dimensions are no longer inde- 

 finitely small, is of some importance when the same electrosco- 

 pic force only exists merely at all points of each such part. It is 

 hence evident how intimately our considerations are allied to 

 the spirit of the differential calctJus ; for unifonnity in all points 

 with reference to the property which enters into the calculation 

 is precisely the distinctive characteristic required by the differ- 

 ential calculus from that which it is to receive as an element. 



If we institute a more profound comparison between the pro- 

 cess originating with Laplace and that here advanced, we shall 

 arrive at some interesting points of comparison. If for instance 

 we consider that for infinitely small masses at infinitely short 

 distances all particular relations must necessarily have the same 

 weight as for finite masses at finite distances, it is not directly 

 evident how the method of the immortal Laplace — to whom 

 we are indebted for so many valuable explanations respect- 

 ing the natui'e of molecular actions, — according to which the 

 elements mus* be constantly treated as if they were placed at 

 finite distances fi'om each other, could nevertheless still afford 

 correct results ; but we shall find on closer examination that it 

 acts in fact otherwise than it expresses. Indeed, since Laplace, 

 when determining the changes of an element by all surrounding 

 it, makes the higher powers of the distance disappear compared 

 with the lower, he therewith assumes, quite in the spirit of the 



