Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/75

 Rh second magnetic shell whose strength is φ', the values of F, G, H will be where the integrations are extended once round the curve s',  which forms the edge of this shell.

Substituting these values in the expression for M we find where the integration is extended once round s and once round s'. This expression gives the potential energy due to the mutual action of the two shells, and is, as it ought to be, the same when s and s'  are interchanged. This expression with its sign reversed, when the strength of each shell is unity, is called the potential of the two closed curves s and ''s'. '' It is a quantity of great importance in the theory of electric currents. If we write ε for the angle between the directions of the elements ds and ds',  the potential of s and s'  may be written It is evidently a quantity of the dimension of a line.