The statistical character of kinetic interpretations

The kinetic interpretation of an aerodynamic process, just as any other explanation of a physical phenomenon, consists of the representation of the observed sequence of states by a purely conceptual scheme. A special feature of kinetic interpretations, however, is the statistical character of these schemes. Each single process which takes place in the given gas quantum is made to correspond to a whole group of motions of the gas model. This is done with the help of the following concluding assertion  

Distribution of state and observable data. The representation of the aerodynamic processes formulated in (VIII) reveals the following gap Assertions (V)-(VII) deal with a continuum of motions which are generated by a distribution of state Za prescribed for tA. The actual observations, on the other hand, do not give a distribution of state but determine what might be called the visible state of the gas quantum. It is a rough determination of the distribution of pressure, density, temperature, and velocity of flow inside the gas. 

In the usual treatments this gap is overlooked in the further developments. The procedure is carried out as if the following theorem could be proved  

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