For the treatment of a supersonic flow over a wedge, it is particularly suitable to employ the so-called shock polar diagram which summarizes all velocities appearing in flows with compression shocks. In the corresponding axial case of supersonic flow over cones which is very important in ballistics, an adiabatic compression takes place in the conical field extending from the compression shock to the surface of the cone. The velocities appearing in this case on the surface of the cone are found on the line which encloses the shock polars. Let this line be called the Apfel curve, a diagram of which was published recently by Busemann. For an exact analysis of supersonic flows over cones, however, it is necessary to know the curves corresponding to the adiabatic compression which connect the shock polars and the Apfel curves. These curves are presented in the report. They are determined by a graphical-numerical integration of the differential equation of the axially symmetrical conical field in the hodograph for all cone angles and for all free-stream velocities. The pressures on the surface of the cone thus obtained are represented in diagrams and compared with the two-dimensional case.