Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/259

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We may now write the hyperbolic sines in terms of ; thus

Proceeding to the actual calculation we find, either by this process or by the direct calculation of the successive images as shewn in Sir W. Thomson's paper, which is more convenient for the earlier part of the series,

174.] We have then the following equations to determine the charges and of the two spheres when electrified to potentials and respectively,

If we put

and

whence

then the equations to determine the potentials in terms of the charges are

and , and are the coefficients of potential.

The total energy of the system is, by Art. 85,