Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/410

368 equal to that due to a system of charges placed in air at certain points along the normal to the plate through $$S.$$

Make then we have two series of points at distances from each other equal to twice the thickness of the plate.

318.] The potential in the first medium at any point $$P$$ is equal to  that at a point $$P'$$ in the second and that at a point $$P''$$ in the third where $$ I,\, I', $$ &c. represent the imaginary charges placed at the points $$I,$$ &c., and the accents denote that the potential is to be taken within the plate.

Then, by the last Article, for the surface through $$A$$ we have,

For the surface through $$B$$ we find

Similarly for the surface through $$A$$ again, and for the surface through $$B,$$ If we make we find for the potential in the first medium,