Condensation of supersaturated water vapor on monodisperse submicrometer SiO2 and TiO2 particles is investigated in a flow cloud chamber (FCC). The dependence of the critical supersaturation S-cr on particle size in the range of 15 to 120 nm and on temperature in the range of 10 to 50 degrees C are determined experimentally. The results show that the experimental S-cr decreases with increasing particle size, at a rate in reasonable agreement with that predicted by Fletcher's version of Volmer's theory of heterogeneous nucleation, but decreases with increasing temperature at a rate higher than that predicted by Fletcher's theory. The experimental S-cr is smaller than the theoretical prediction even with the line tension and surface diffusion taken into account; the particles induce heterogeneous nucleation better than theory predicts even for perfectly wetted particles. The discrepancy cannot be fully accounted for by the effects of line tension, surface diffusion, or the curvature dependence of the physical properties. The condensation of supersaturated vapor on singly-positively-charged particles with diameters of 30, 60, and 90 nm is also examined. No obvious effect of charge on S-cr is observed, in agreement with the theoretical prediction. The law of corresponding states was extended to heterogeneous nucleation, and a simple correlation was obtained.