Application of Ohm's Law to Problems of Electrostatics, 333 



Q= ,; and when the two lengths are equal, the quantity in 



r -\-r 



each will be half that which would be accumulated in one, if the 



other pole were connected to earth. 



In the charging of a series of Leyden jars arranged in cascade 



(fig. 8), with the last jar connected to earth, the reason that the 



accumulation in each jar is not quite equal, but is less in each jar 



nearest the earth connexion than in the preceding one, is easily 



seen by considering the problem as one of branch circuits. The 



first jar in a cascade of two jars is a resistance common to both 



Fig. 8. 



A\ 



branches ; and the branches consist, first, of the dielectric inter- 

 vening between the outer armature of the first jar and the sur- 

 rounding conductors, and, secondly, of the glass of the second jar. 



The quantity in the first jar must be equal to the quantity on 

 the outside of the outer coating of the same jar (or what is 

 sometimes termed the " free electricity ") added to the quantity 

 in the second jar, just in the same way that the current in any 

 part of a conductive circuit (containing a branch) must, before 

 bifurcation, be equal to the sum of the currents in the two 

 branches after bifurcation. The quantity in the second jar will 

 be therefore less than that in the first by exactly this quantity 

 of "free electricity " on the outside of the first jar. And as this 

 quantity can be increased by lessening the resistance of this 

 branch of the circuit, as, for instance, by approaching conductors 

 to the outside of the jar, it follows that the disproportion in the 

 charges of the jars will depend on the proximity of surrounding 

 conductors to the whole series. 



Many other problems can be thus considered and explained, 

 and, where the inductive resistances are defined, worked out by 

 the formula ; so that what will occur in cases hitherto never 

 before treated, can be accurately foretold. Moreover it will be 

 seen that all the most ordinary phenomena in electrical experi- 

 ment regarding generation and accumulation can be explained 

 without any recourse to the earth as a " common reservoir." 



In a future communication I propose to detail some experi- 

 ments with submarine cables grouped to the two poles of a bat- 

 tery, in illustration of the subject. 



