Application of Ohm's Law to Problems of Electrostatics. 327 



may be transformed into questions of propagation, and thus 

 brought within the domain of Ohm's law. The exactitude of 

 this principle has been already demonstrated experimentally 

 (1) in the case of concentric cylindrical condensers, (2) in the 

 case of excentric cylindrical condensers, and (3) in the cas*e of plane 

 condensers*. I have now verified it for a new class of conden- 

 sers, that of concentrical spherical condensers." 



In all these cases the quantity accumulated on the surfaces of 

 the dielectric would be, with a given source, inversely propor- 

 tional to the " resistance " of the dielectric to accumulation or 

 induction; and the term "inductive resistance" has been very 

 frequently employed to express this resistance, in opposition to 

 " conductive resistance." 



In all these examples hitherto mentioned, the source of elec- 

 tric generation is supposed to have one pole connected to one 

 surface of the condenser, whilst the other pole is in connexion, 

 through the earth or otherwise, with the other surface. A single 

 resistance exists ; and the quantity accumulated on the surfaces is 

 inversely proportional to this resistance, in the same way that, if 

 in the galvanic circuit a single resistance exist, the quantity pass- 

 ing a single section of the circuit in a given time will be inversely 

 proportional to the resistance thus supposed to form the whole 

 resistance of the circuit. 



When both poles of the source are connected to conductors 

 insulated from one another and from the earth, new and inter- 

 esting problems arise. The quantity on either conductor will 

 evidently be no longer simply inversely proportional to the in- 

 ductive resistance, separating it from the earth or nearest con- 

 ducting surface ; for in such case, with two conductors of differ- 

 ent dimensions attached to the poles of a source, we should have 

 unequal quantities of electricity generated at the two poles — an 

 acknowledged impossibility. 



If, however, we consider that, just as for conduction to take 

 place in the conductive circuit there must be a continuous 

 chain of conducting matter from one pole to the other, so 

 for accumulation to take place we must have between the poles 

 of the source a continuous chain or series of inductive bodies 

 (or inductive resistances) joined, it is true, by conductors, we 

 shall find the means, by applying Ohm's law for the conductive 

 circuit to what may be termed the " inductive circuit" of solving 

 this and many other problems. 



We have, in fact, only to trace the inductive circuits that exist 

 even to branch or derived circuits, and apply the formula for con- 

 ductive circuits. Thus in the case of a single pair of flat plates 

 (fig. 1), a single Ley den jar (fig. 2), or the spherical shell inves- 

 * Comptes Rendus, February 18, April 29, and June 17, 1861. 

 Z2 



