Page:Zur Dynamik bewegter Systeme.djvu/23

 For those values applying to q = 0, by definition (§ 13) the expressions follow:

and with their aid by (39), (40), (43) and (46) the values valid for any velocity q follow:

in accordance with the equations of § 1

By momentum G, also its inertial mass is determined. This quantity, which plays in pure mechanics such a fundamental role, is degraded to a secondary expression within the general dynamics. For, once the momentum is no longer proportional to the velocity, the mass of a body is no longer constant; also we are led to completely different dependencies of mass on velocity, depending on whether we divide momentum G by velocity q, or if we differentiate velocity q, where in this case it is necessary to specify particularly the manner in which the differentiation took place: whether isothermal, adiabatic, etc. Again, a different value for the mass is found in general, if we start from the energy E and differentiate it to $$\frac{q^{2}}{2}$$. How to designate these different expressions, is of course a matter of definition.

Here, by "mass" M of a body we want to understand that quantity of a body independent of velocity, which is obtained if the momentum G is divided by velocity q and where we set the ratio q = 0, thus in our notation by (46):

This quantity in general depends on the temperature T and volume V of the body.

If we set in the expression $$\frac{G}{q}$$ the velocity q not to zero, then we call the ratio, as usual, the "transverse"