The collecting efficiency of an electric precipitation may be effected with electrical conductivity of some industrial dust under treatment. The conventional theory predicts much higher efficiency for the electrical precipitation of particles of electrical conductivity higher than 10^<-4>mho/cm. In fact the measurements of actual performances give far low efficiencies in such cases. To make the physical meaning about the phenomena clear, the author carried some improved works. The author suspended a model particle of convenient electrical and physical properties as a pendulum system, in an electric field consisting of a positive plate electrode and a negative multi-needle electrode where the moderate corona was setting up. The model particle was held so close to the plate electrode surface that the condenser energy flashed through the air gap as the condenser terminals connected across them. Varying the energy stored in the condenser, the behavior of the particle was observed. Then the author found following facts newly. (1) When a condenser energy given as 1/2 CE^2 flashed through the air gap δ_2,the particle gained a first kick with an equivalent potential energy, and there existed some definite relation between them. (2) The author called the force that gave the kick as ”Discharge pressure”. (3) The cinematographic analysis about this phenomena gave the relation as ”The discharge pressure gap increases by E^4 proportionally as the condenser charging voltage E increses”. (4) The same result had been derived from different experiment. Namely, the discharge gap length δ_2 increased by I^2 proportionally under steady corona discharge current I. While I increased by E^2 proportionally as had been previously mentioned. And then, δ_2 varied with corona discharge energy E^4 proportionally too. (5) After all, the conventional theory giving collecting efficiency of an electric precipitation handling higher conductivity dust should be corrected after those results newly investigated. (6) At this, the author proposes to introduce the term ”K_2(ρ/ρ_0-1)E^4” to the conventional efficiency equation as for conductive dust precipitation. Where, K_2 is a constant mainly depending on the shape of the particle, ρ denotes the electric conductivity of the particle, ρ_0 is the critical value from which the inconvenient phenomena appear and E is the applied voltage.