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A surface integral is developed which yields solutions of the linearized partial differential equation for supersonic flow. These solutions satisfy boundary conditions arising in wing theory. Particular applications of this general method are made, using acceleration potentials, to flat surfaces and to uniformlyy loaded lifting surfaces. Rectangular and trapezoidal plan forms are considered along with triangular forms adaptable to swept-forward and swept-back wings. The case of the trangular plan form in sideslip is also included. Emphasis is placed on the systematic application of the method to the lifting surfaces considered and on the possibility of further application.

The problem of the build-u of lift on two- and three-dimensional wings flying at high speeds is discussed as a boundary-value problem for the classical wave equation. Kirchhoff's formula is applied so that the analysis is reduced, just as in the steady state, to an investigation of sources and doublets. Some simple applications of this method are considered, including the determination of the starting lift of a three-dimensional wing and the potential functions for some types of unsteady vortex motion.

Analytical and numerical methods are developed that predict the flux of radiant energy from a family of thin, planar, conducting fins. For a symmetrical array of fins, extending out from a common edge, conducting heat internally, and radiating diffusely, a nonlinear integro-differential equation is derived and solved. Specific results are given for parametric variations of conduction, emissivity, fin geometry, and base temperature. The techniques of calculation are studied with possible extensions in mind.

The spanwise and chordwise distribution of loading, the lift, and the induced drag of a swept-back wing of slender plan form are developed by means of linearized lifting-surface theory. The results are applicable for all free-stream Mach numbers. The term slender implies that the ratio of the reduced span to over-all length of the wing is small.