The effects of partial outcrossing on the genetic variance and heritability in segregating and natural populations were examined, and the methods for estimating the components of variance and heritability were developed, taking into account the effects of outcrossing. 1 . The rate of increase in genetic variance or heritability by the repetition of segregating generation decreases as the proportion of outcrossing becomes large, and in the case of complete outcrossing the genetic variance and heritability in all generations excepting the F1 are the same as those of the F2 generation. In the estimation of the heritability of Fn by the regeression coefficient, it is more rational to use the selfed progenies tnan those obtained by open pollination. It was also found that in the progeny mean selection in the breeding of partially allogamous plants it is effective to make an artificial selfing in one or two generations prior to the selection, and further it was concluded that the limit of outcrossing for an effective bulk-method breeding is 10%.2. In the estimation of variance components by using Mather's method (1949), it is desirable to self-fertilize the F, individuals by some artificial technique when there is any possibility of outcrossing, although if the degree of outcrossing is known the estimates may be obtained by using the fomulas (10)-(15), where )L is the proportion of outcrossmg.