Vasyliunas (1972) showed that, for steady state lossless ion convection in the inner magnetosphere, the effects of region 2 field-aligned currents generated by the pressure gradients of the magnetospheric plasma could be represented by an equivalent magnetospheric Hall conductance Ci. We examine in the framework of a linearized fluid theory how ion losses modify the formalism introduced by Vasyliunas. The equivalent magnetospheric Hall conductance Ci is decreased and a new term Cr is added to the ∑&phgr;&phgr; component of the ionospheric conductance tensor ∑. An evaluation of this new term shows that the eastward rotation of the convection potential pattern induced by Ci is reduced and that Cr contributes to a nonnegligible part of the shielding effect. This linear formalism is compared with the nonlinear model of C. Peymirat and D. Fontaine (Numerical simulation of the magnetospheric convection including the effect of field-aligned currents and electrons precipitation, submitted to Journal of Geophysical Research, 1993), showing that the effect of the field-aligned currents on the magnetospheric convection is reproduced up to first order in the linear formalism. The liner formalism presents a simple way to include the effects of region 2 field-aligned currents into models of ionospheric electrodynamics for steady state conditions. ¿ American Geophysical Union 1993