The applicability of a method to directly deduce the ionospheric Hall conductance distribution &Sgr;H from ground magnetic and ionospheric electric field observations, here called ''method of characteristics,'' is tested by using input data from models of some typical ionospheric electrodynamic situations. We shall show that the method in the form of a fully automatical computer algorithm is able to reproduce well the &Sgr;H distributions of all modeled situations, i.e., a two-dimensional eastward electrojet, a Harang discontinuity, an omega band, and a westward traveling surge. Furthermore, we will show quantitatively that the ambiguity implied by the necessary assumption of the distribution of the Hall to Pedersen conductance ratio has only a small effect on the results obtained. We also prove quantitatively that the assumption of vertical, straight geomagnetic field lines made in the derivation of the method leads only to very small errors if the case of oblique, but straight geomagnetic field lines is taken to be realistic. Moreover, we review the general theory of the method and discuss some additional theoretical aspects. In particular, we will show that isolated points with E↘=0, but nonvanishing ∇h⋅E↘ are associated with extrema or saddle points of the &Sgr;H distribution, and calculate the magnetic field disturbance of an ionospheric current system with oblique, but straight field-aligned currents directly below the ionospheric plane. The method does not require an electrostatic situation; i.e., ∇h¿E↘≠0 is allowed. ¿ American Geophysical Union 1995