Report presenting a lecture series that aims to give a survey of the more recent results of the theory of viscous fluids and their importance to actual applications. The primary focus is on the theory of the boundary of frictional layer.

"In the present paper which deals with the heat transfer between the gas and the wall for large temperature drops and large velocities use is made of the method of Dorodnitsyn of the introduction of a new independent variable, with this difference, however, that the relation between the temperature field (that is, density) and the velocity field in the general case considered is not assumed given but is determined from the solution of the problem. The effect of the compressibility arising from the heat transfer is thus taken into account (at the same time as the effect of the compressibility at the large velocities). A method is given for determining the coefficients of heat transfer and the friction coefficients required in many technical problems for a curved wall in a gas flow at large Mach numbers and temperature drops" (p. 1).

"Lamé's wave functions result by separation of the wave equation in elliptic coordinates and by integration of the ordinary differential equations thus originating. They are a generalization of Lamé's potential functions which originate in the same manner from the potential equation. Lamé's wave functions are applied for boundary value problems of the wave equation for regions of space bounded by surfaces of a system of confocal ellipsoids and hyperboloids" (p. 1).

"Lately it has been proposed to reduce the friction drag of a body in a flow for the technically important large Reynolds numbers by the following expedient: the boundary layer, normally turbulent, is artificially kept laminar up to high Reynolds numbers by suction. The reduction in friction drag thus obtained is of the order of magnitude of 60 to 80 percent of the turbulent friction drag, since the latter, for large Reynolds numbers, is several times the laminar friction drag. In considering the idea mentioned one has first to consider whether suction is a possible means of keeping the boundary layer laminar" (p. 1).

From Summary: "The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part. These actual flows show a special characteristic, denoted as turbulence. The character of a turbulent flow is most easily understood the case of the pipe flow. Consider the flow through a straight pipe of circular cross section and with a smooth wall. For laminar flow each fluid particle moves with uniform velocity along a rectilinear path."

"The present report of Mr. Dupleich is the summary of a very extensive experimental study of the well-known mechanical phenomenon: the rotation in free fall (* air, for instance) of more or less elongated rectangles cut out of paper or pasteboard. This phenomenon, the conditions for existence of which depend chiefly on the elongated of the small plate and its weight per unit area, is essentially an aerodynamic phenomenon and as such, raises questions of a certain interest to our department. We believe that the modern concepts of the mechanics of fluids do not have the range attributed to them" (p. 1).

"In the present paper, the motion of a gas in a plane-parallel Laval nozzle in the neighborhood of the transition from subsonic to supersonic velocities is studied. In a recently published paper, F. I. Frankl, applying the holograph method of Chaplygin, undertook a detailed investigation of the character of the flow near the line of transition from subsonic to supersonic velocities. From the results of Tricomi's investigation on the theory of differential equations of the mixed elliptic-hyperbolic type, Frankl introduced as one of the independent variables in place of the modulus of the velocity, a certain specially chosen function of this modulus" (p. 1).