The theory of characteristics will be presented generally for quasilinear differential equations of the second order in two variables. This is necessary because of the manifold requirements to be demanded from the theory of characteristics.

This paper includes the following topics: 1) Characteristic differential equations; 2) Treatment of practical examples; 3) First example: Diffuser; and 4) Second Example: Nozzle.

"So far, very careful investigations have been made regarding the flight properties, in particular the static and dynamic stability, of engine-propelled aircraft and of untowed gliders. In contrast, almost no investigations exist regarding the stability of airplanes towed by a towline. Thus, the following report will aim at investigating the directional stability of the towed airplane and, particularly, at determining what parameters of the flight attitude and what configuration properties affect the stability" (p. 1).

Contents include the following: Characteristic differential equations - initial and boundary conditions. Integration of the second characteristic differential equations. Direct application of Meyer's characteristic hodograph table for construction of two-dimensional potential flows. Prandtl-Busemann method. Development of the pressure variation for small deflection angles. Numerical table: relation between deflection, pressure, velocity, mach number and mach angle for isentropic changes of state according to Prandtl-Meyer for air (k = 1.405). References.

In an attempt to follow the time rate of change of the processes in turbulent flows by quantitative measurements the measurement of the pressure is often beset with insuperable difficulties for the reason that the speeds and hence the pressures to be measured are often very small. On the other hand, the measurement of very small pressures requires, at least, considerable time, so that the follow-up of periodically varying processes is as goad as impossible. In order to obviate these difficulties a method, suggested by Prof. Prandtl, has been developed by which the pressure distribution is simply determined from the photographic flow picture.

We have set ourselves the problem of calculating the laminar flow on a body of revolution in an axial flow which simultaneously rotates about its axis. The problem mentioned above, the flow about a rotating disk in a flow, which we solved some time ago, represents the first step in the calculation of the flow on the rotating body of revolution in a flow insofar as, in the case of a round nose, a small region about the front stagnation point of the body of revolution may be replaced by its tangential plane. In our problem regarding the rotating body of revolution in a flow, for laminar flow, one of the limiting cases is known: that of the body which is in an axial approach flow but does not rotate.

With an unsymmetrical wing and a rotating Magnus cylinder, the lift is produced by the superposition of parallel and circulatory flows. An explanation of the circulatory flow is furnished by the boundary-layer theory of Prandtl and the consequent vortex formation. According to this explanation, it must evidently be possible to increase the circulation either by increasing the size of the stronger (lower) vortex or by decreasing the size of the weaker (upper) vortex.

Many treatises in regard to construction of airship sheds are lacking in data on air currents, for which reason this phase of the problem will be here thoroughly discussed in connection with the accompanying photographs of currents.