A simple Mendelian explanation covers the results. If we assume that the Dorsets, both male and female, are homozygous in a factor for horns, H, that is not in the sex chromosome, and that the Suffolks “lack this factor,” _i. e._, that they have an allelemorphic factor for hornlessness, the germ-cells are H-H and h-h, respectively. Only one kind of individual, Hh, results in F₁. Since the male with this formula develops horns, we must conclude that the presence of the testis (through its secretions) causes horns to develop, while in the female of this same composition horns are not produced because of the absence of the testes. The sex-cells in these F₁ individuals are H-h and H-h. Chance meeting of these gametes will give 3 classes of individuals, irrespective of sex, namely, (1) HH, (2) Hh, (1) hh. The expectation for the males is that those of the composition (1) HH and (2) Hh will develop horns, while those of the composition hh will not develop horns. There should be 3 horned to 1 hornless male. In the females we expect those with the composition (1) HH to develop horns, since they have the same formula as the pure Dorset; those with the formula Hh are not expected to develop horns, because the F₁ females of this composition do not have horns; those with the formula hh are not expected to develop horns, because they have the same composition as have the pure Suffolk. There should be 3 hornless to 1 horned female. Combining both sexes, the expectation for F₂ is 4 horned to 4 hornless. Arranged according to sex, these give the classes realized: Horned male, 3; hornless male, 1; horned female, 1; hornless female, 3. That this is the correct explanation is borne out by back-crossing the hornless F₁ female to a hornless Suffolk ram. The former has two kinds of gametes, H and h, the latter only gametes that bear the h factor. Half the sons should be horned, half hornless, because half of them are Hh and half hh. But none of the daughters should have horns, because neither the Hh nor the hh females produce horns. This is the result realized, viz, 3 hornless offspring to 1 horned.