In the previous reports (Part I and II), the calculating methods of various solid vortex type flow patterns were presented. In this report, the expression of efficiency of the solid vortex types is introduced. For the free vortex flow, the manometric efficiency of blade combining rotor and stator becomes maximum for the case of symmetric velocity diagram at the geometrical mean radius. Though the flow conditions which are both solid vortex in the inlet and the outlet of rotor, are two-dimentional in the rotor, back flow occurs at the root of rotor for the multistage axial compressor. But they might be used for pre-rotors. Then the general methods of obtaining velocity profils which are comparatively similar to free vortex by putting the stages which the pressure increase in rotor is not constant at the inlet of compressors suitably, are presented. Finally an example for the outlet solid vortex type is expressed.