During the year 1906-7 the young rats were graded by the method used by MacCurdy and Castle (1907) that is, the back-stripe was measured and a calculation made of the percentage of the dorsal surface posterior to the hood which was pigmented. But on account of the irregular outline of the back-stripe in many individuals the method of measurement was found to be at best a rough one, as well as extremely laborious. Accordingly in the summer of 1907 a set of arbitrary grades was adopted, which is shown at the top of Plate 1. Each young rat was classed in that grade which it most nearly approached in amount of pigmentation. Skins of rats graded from -3¼ to +4¾ are shown in the middle and lower rows of Plate 1. The grading was done when the rats were about three or four weeks old, at which time selected individuals were reserved as the parents for a later generation, the remainder being discarded. This method has been followed ever since its adoption and the data thus obtained are summarized in the tables, which cover the breeding operations of a little more than six years, 1907-1913. The grouping of the young in a series of generations is only approximately accurate, for practical considerations have often led us to mate together animals which belonged to different generations of offspring. When, for example, an animal of generation 2 was mated with one of generation 4, the question would arise: To what generation do the offspring belong? In deciding this question we simply added one to the mean of the generations to which the respective parents belonged. In the foregoing case this would be (2 + 4)/2 + 1 = 4. In case one parent belonged to generation 2 and the other to generation 3, a fractional result would be obtained, thus (2 + 3)/2 + 1 = 3½. In making up the summaries of the generations as given in the tables, offspring like the foregoing, of generation 3½, were divided equally between generations 3 and 4, alternate litters of young as recorded in the ledger being assigned to each. Offspring belonging to generations 2¾ and 3¼ were tabulated in generation 3; those belonging to generations 3¾ and 4¼ were tabulated in generation 4, etc. While, therefore, the generations as tabulated overlap, it is clear that they include groups of offspring of selected parents each the result of _one additional selection over the preceding group._