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The part of the kinetic energy we are concerned with will evidently be

Let us take the first integral first, and take the term depending on p; this is


Integrating by parts this becomes


The surface-integrals are to be taken over the surface of the sphere; and the triple integral is to be taken throughout all space exterior to the sphere.

If the sphere be so small that we may substitute for the values of F', , &c. at the surface their values at the centre of the sphere, the first surface-integral , where is the value of at the centre of the sphere; the second surfaceintegral vanishes, and the triple integral also vanishes, since