1. The basic principle in Mendel's discoveries is that of the purity of the germ-cells; in accordance with this a cross-bred animal or plant produces germ-cells bearing only one of each pair of characters in which its parents differ. From it follows the occurrence in the second and later hybrid generations of a definite number of forms in definite numerical proportions. 2. Mendel's principle of dominance is realized in the heredity of a considerable number of characters among both animals and plants. In accordance with this principle, hybrid offspring have visibly the character of only one parent or the other, though they transmit those of both parents. 3. In other cases the hybrid has a distinctive character of its own. This may approximate more or less closely the character of one parent or the other, or it may be entirely different from both. Frequently the distinctive hybrid character resembles a lost ancestral character. In some cases of this sort, as in coat-color of mammals, the hybrid character probably results from a recombination of the characters seen in one or both parents, with certain other characters latent (that is, recessive) in one parent or the other. 4. There have been observed the following exceptions to the principle of dominance, or to the principle of purity of the germ-cells, or to both: (a) Mosaic inheritance, in which a pair of characters ordinarily related as dominant and recessive occur in a balanced relationship, side by side in the hybrid individual and frequently in its germ-cells also. This balanced condition, once obtained, is usually stable under close breeding, but is readily disturbed by cross-breeding, giving place then to the normal dominance. (b) Stable (self-perpetuating) hybrid forms result from certain crosses. These constitute an exception to both the law of dominance and to that of purity of the germ-cells. For the hybrid is like neither parent, but the characters of both parents exist in a stable union in the mature germ-cells produced by the hybrid. (c) Coupling, i. e. , complete correlation may exist between two or more characters, so that they form a compound unit not separable in heredity, at least in certain crosses. (d) Disintegration of characters apparently simple may take place in consequence of cross-breeding. (e) Departures from the expected ratios of dominants to recessives may be explained in some cases as due to inferior vigor, and so greater mortality, on the part of dominants or recessives respectively. (f) Cases of apparent reversal of dominance may arise from 'false hybridization' (induced parthenogenesis). Possibly in other cases the determination of dominance rests with circumstances as yet unknown.