At high Mach numbers instationary shock waves may be described by the so called „Homologielösungen”︁. The determination of the „Homologieparameter”︁nis quite simple for shock waves originating by explosion in a fixed point or a fixed wall (as it may be in a shock tube), but must be done by automatic computers for plane waves with a free streaming of matter behind the front (as in astrophysical objects). The methods of computing the Homologieparameter for an adiabatic plane wave in the latter case are extended to include also energy losses in the front, which is more realistic expecially for high Mach numbers. It can then be shown, that there exist Homologieparameter in the whole region between adiabatic and isotherm fronts. The numerical values, computed by an Type „Ural. III”︁ c