The article reports the development of a new method of calculating electrical conditions in wire-duct electrostatic precipitation devices. The method, based on a numerical solution to the governing differential equations under a suitable choice of boundary conditions, accounts for the effect of space charge and is applicable over the entire range of current and voltage before sparkover. The procedure yields voltage-current characteristics and determines the electric potential and electric field strength as functions of position for each current and applied voltage. Predictions of the theory are compared with existing experimental data and the agreement is excellent.