Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/424

382 $$R,$$ and let a current be passed along this series from left to right.

Let us first suppose the plates $$B_0,\, B_1,\, B_2,$$ each insulated and free from charge. Then the total quantity of electricity on each of the plates $$B$$ must remain zero, and since the electricity on the plates $$A$$ is in each case equal and opposite to that of the opposed surface they will not be electrified, and no alteration of the current will be observed.

But let the plates $$B$$ be all connected together, or let each be connected with the earth. Then, since the potential of $$A_1$$ is positive, while that of the plates $$B$$ is zero, $$A_1$$ will be positively electrified and $$B_1$$ negatively.

If $$P_1,\, P_2,$$ &c. are the potentials of the plates $$A_1,\, A_2,$$ &c., and $$C$$ the capacity of each, and if we suppose that a quantity of electricity equal to $$Q_0$$ passes through the wire on the left, $$Q_l$$ through the connexion $$R_1,$$ and so on, then the quantity which exists on the plate $$A_1$$ is $$Q_0-Q_1,$$ and we haveand so on.

But by Ohm's Law we have

If we suppose the values of $$C$$ the same for each plate, and those of $$R$$ the same for each wire, we shall have a series of equations of the form