Abstract: Based on the Jeans's theory of persistence of velocity, a number of new conceptions, such as inverse persistence of velocity and successive movement of molecules and so on, is presented. The theory on velocity-persistence is extended. The available persistence of velocity at different levels and the corresponding equivalent free path of the molecule L are obtained. Finally, when L takes the place of l, good results are got with the elementary theories of the transport phenomena. This shows that, the completed theory of persistence is a success.