Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/158

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If we take the case in which one of the surfaces, say , surrounds the rest at an infinite distance, we have the ordinary case of conductors in an infinite region; and if we make , and for all the other surfaces, we have at infinity, and is not greater than .

In the very important case in which the electrical action is entirely between two conducting surfaces and , of which completely surrounds and is kept at potential zero, we have and .

Hence in this case we have

(18)

and we had before

(19)

so that we conclude that the true value of , the capacity of the internal conductor, lies between these values.

This method of finding superior and inferior limits to the values of these coefficients was suggested by a memoir 'On the Theory of Resonance,' by the Hon. J. W. Strutt, Phil. Trans., 1871. See Art. 308.