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.
u]] or ffudxdy in terms of the values of u for certain values of x in combination with certain values of y; these values not necessarily lying within the limits of the integrations.
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.
If we have a continuous distribution of matter, instead of a system of discrete particles, the summations in (6) are to be replaced by integrations.