IN ANALYSES OF BOUNDARY-LAYER FLOW a l o n g b o d i e s of revolution placed with their axis parallel to the stream, the thickness of the boundary layer is generally considered as small in comparison to the body diameter at any cross section, and terms proportional to this ratio are disregarded in the equations. This procedure seems well justified at the forward portion of the body where the diameter is increasing and the boundary layer is spread thin by flow divergence. It may become less accurate if the body has an extended cylindrical section, and it is probably no longer applicable in case of a boat tail where flow convergence produces an excessive thickening of the boundary layer. In the following analysis, which is based upon von Karman's integral form of the boundary-layer momentum equation, the terms originating from the lateral curvature of the surface will be retained. Since the equations become fairly complicated for bodies with variable cross section, the treatment will be restricted to a constant radius of curvature, that is, flow along the surface of a cylinder. This case has been treated in simplified manner for a compressible turbulent boundary layer with uniform free-stream Mach Number in an earlier paper by the author.' Tn the present paper the Mach Number is considered as variable. For slender bodies in free flight there is, of course, little variation in the potential flow Mach Number. A considerable Mach Number gradient can be produced, however, along a cylindrical rod used as test object in a wind tunnel by variation of the test chamber cross-section area; as it has been done, for instance, by Chapman and Kester. Aside from this external flow problem the generalized analysis of the paper opens access to treatment of the internal flow problem, namely turbulent boundarylayer development in a cylindrical channel, which is inherently connected with a variation of the Mach Number of the potential flow core, due to the displace-