The general solution of Chaplygin's equation for the motion of an inviscid compressible fluid is obtained for ‘simple wedge flows’. Some particular examples are given and a discrepancy in earlier Russian papers explained. After a discussion of the properties of the velocity potential and the expression for the physical coordinates in terms of the hodograph variables, a general theorem on sonic jets is proved, namely, that the physical changes due to the presence of solid boundaries in the flow are completed within a finite distance in those directions in which the flow becomes finally a sonic jet.

The general solution of the Chaplygin equation for ‘simple wedge flows’ is used for the particular case of Réthy flows. The drag coefficient is evaluated and comparisons made with the results obtained from the approximate hodograph equations of Tricomi and of Tomotika and Tamada. A distinction is made between subsonic and transonic régimes and the limitations on the lengths and pressure differences permissible in the various ranges are discussed.