Differential Inductometer and in the Electrophorus. 133 



These formulae, which are the same as those for the divided 

 current, are only absolutely true for plates of an infinite size. 

 They signify that the inductive capacities of the two con- 

 densers which form the differential inductometer are in- 

 versely proportional to the distances of the plates. If we 

 use the term " inductive resistance " to denote the reciprocal 

 of the inductive capacity in the same way as conductivity is 

 the reciprocal of resistance, then, in the case of infinite plates, 

 the inductive resistance is directly proportional to the dis- 

 tance. In such a case of infinite plates the equipotential 

 surfaces are planes parallel to the plates, and the tubes of 

 force are cylinders at right angles to them. 



This electrostatic condition is converted into the corre- 

 sponding electrodynamic one if a conducting liquid is placed 

 between the plates. If, then, the plates are kept at the same 

 electrical level by (say) a battery, then a divided current 

 would pass from the middle plate through the liquid to the 

 two side plates; so that the middle plate would be an anode, 

 and the side plates kathodes; and the division would then 

 take place in such a manner that the strength of the two 

 branch currents would be inversely proportional to the re- 

 spective resistances ; or, since the latter are proportional to 

 the distances, the currents would be inversely as the distances *. 

 Just as we incur an error when we pass from the law that 

 the divisions of the current are inversely proportional to the 

 distances in the case of infinitely large plates, to the case 

 where the plates are simply very large, so we incur a similar 

 error in electrostatics when we apply the formula for infinitely 

 great plates to the inductometer. 



The case in electrodynamics which corresponds to the 

 inductometer (which we regard as an apparatus for the 

 division of induction) would be the branching of the current 

 between three round plates. If we imagine the differential 

 inductometer to be plunged into a conducting liquid and the 

 potentials to be constantly maintained, then a current would 

 pass from the middle plate as anode to the external plates as 

 kathodes. Further, if in both cases we construct the system 

 of the surfaces of equal potential, then, if their equation be 



V= constant, 



V in both cases (that is, by the branching of the current and 

 in the inductometer) would satisfy the same differential equa- 

 tion, and the same limiting conditions must be fulfilled. We 

 should get in both cases the same system of surfaces of elec- 

 trical level; and the perpendiculars to these surfaces would 



* See Currents between Plates, Wied. Galv. § 116. 



