For two- and three-dimensional flow in a compressible medium, a simple relation is given by which, to a first approximation, the quantitative influence of compressibility upon the velocities and pressures can be understood in a clear manner. In the application of this relation the distinct behaviors of two-dimensional and axially symmetric three-dimensional flow with increasing Mach number are brought out. For slender elliptic cylinders and ellipsoids of revolution, calculations are made of the critical Mach number; that is, the Mach number at which local sonic velocity is achieved on the body. As a further example, the lifting wing of finite span is considered, and it is shown that the increase of wing lift with Mach number at a given angle of attack is greatly dependent upon the aspect ratio b(exp 2)/F.