The integrations may also be effected by means of polar coordinates, taking first the integration with respect to 4) so as to obtain the result for an infinitely thin annular aperture.
To transfer the integral equation into the differential equation of continuity, Green's transformation is required again, namely, (++) dxdydz= ff (l +mr t } ndS, (2) or individually dxdydz = f flldS, ..., (3) where the integrations extend throughout the volume and over the surface of a closed space S; 1, m, n denoting the direction cosines of the outward-drawn normal at the surface element dS, and, 77, any continuous functions of x, y, z.
Now these integrations are quite intractable, even for a very simple mathematical assumption of the function f(v), say the quadratic or cubic law, f(v) = v 2 /k or v3/k.
Universally as an " integration of matter and dissipation of motion," and yet mental, social and moral developments are also called evolution, so that, in accordance with the definition, they are also integrations of matter and dissipations of motion.
Such differentiations and integrations of living bodies are the subject-matter of discussions on evolution; some will see in the play of circumambient media, natural or supernatural, on the simplest forms of living matter, sufficient explanation of the development of such matter into the highest forms of living organisms; others will regard the potency of such living matter so to develop as a mysterious and peculiar quality that must be added to the conception of life.