The basic concept of the present paper is to use a tangent line to the adiabatic pressure-volume curve as an approximation to the curve itself. First, the general characteristics of such a fluid are shown. Then in Section I a theory is developed which can be applied to flows with velocities approaching that of sound, whereas the theory of Demtchenko and Busemann only give an approximation for flows with velocities smaller than one-half of the sound velocity. This is done by a generalization of the method of approximation to the adiabatic relation by a tangent line, conceived jointly by Th. von Karman and the author. The theory is put into a form by which, knowing the incompressible flow over a body, the compressible flow over a similar body can be calculated. The theory is then applied to calculate the flow over elliptic cylinders. In Section II the work of H. Bateman is applied to this approximate adiabatic fluid and the results obtained are essentially the same as those obtained in Section I.

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