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The value of in terms of thus becomes

. | (17) |

Equation (11) now becomes

, | (18) |

so that instead of the cylindrical coordinates and we, can take and where

. | (19) |

From (18) we have in terms of and

Hence

, | (20) |

, | (21) |

, | (22) |

I now pass on to calculate the total energy possessed by the ellipsoid when in motion along its axis of figure. In making the calculation I shall suppose that , i.e., that is positive. The case in which can be deduced by the appropriate mathematical transformation.

I have shown {§ 22} that the total energy, viz. the volume integral of , due to the motion of a charge on any surface, is

where is the value of the convection-potential at the surface of the body, and T is the magnetic part of the energy, viz., the volume integral of .