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as it moved through space, and it might be possible to account in this way for some of the energy which is ordinarily thought of as totally dissipated.

Another conclusion which is suggested by the foregoing is that, assuming the loss of mass accompanying dissipation of energy, the sun's mass must have decreased steadily through millions of years. If too, our conclusion respecting the gravitating quality of confined energy be correct, the gravitation constant of the sun has also decreased and the distances of the planets must have increased accordingly. This last increase of planetary distance can be calculated by making the angular momentum of the planet about the sun a constant, and allowing the mass of the planet, together with the gravities of both sun and planet, to grow less with time.

So little is known as to the former radiating power of the sun that no even approximate calculation can be made, but it is not difficult to show that the order of magnitude is such as might make the increase in the planetary distances not altogether negligible during great lapses of time.

A Proof from a different Point of View.

16. The proof of expression (17) which has been given has the advantage of entering intimately into the structure of the general system and showing the part that non-electrical forces in the form of constraints must play if the fundamental laws of electrical action are to hold for every infinitesimal element of the finite volume occupied by any electrical system. Although this is assumed in every mathematical derivation of the mass of an electron, and in fact in all problems of a similar nature, many will doubtless object to this assumption on the ground that probably the ordinary electrical laws do not apply when the distance between "elements of charge," so called, is comparable with the diameter of an electron.

Although it is difficult to see how a coherent mathematical theory of electricity can at present be formed without this assumption, yet it was thought best to add a more general proof of (17). The following is therefore given as avoiding the explicit use of constraints.

17. The statement of the law of the conservation of energy for an element of volume in any electrical system possessing electrical charges in motion, is the well-known expression

${\frac {\partial w}{\partial t}}=-\left({\frac {\partial S_{x}}{\partial x}}+{\frac {\partial S_{y}}{\partial y}}+{\frac {\partial S_{z}}{\partial z}}\right)-(v_{x}\rho \Im _{x}+v_{y}\rho \Im _{y}+v_{z}\rho \Im _{z})$

(23)