Arkell’s mating between Dorsets and Merinos (tables IX and XVI) corroborates his view “that the knob of the Merino female is represented in the germ-plasm by the double determiner.” The 5 F₁ sons had long horns, 3 F₁ daughters had horns present, and 2 had them absent (table XVI). If some of the Merino mothers used were homozygous for a factor that inhibits the development of horns in the female we can account for the hornless daughters, and if other mothers did not have this factor (or were heterozygous for it) we can account for the horned daughters. Evidently more evidence is needed. Arkell himself assigns a corresponding difference to the mothers in these cases, based on the observed fact that the mother that had knobs or scurs were the ones that gave birth to the horned daughters. If the above suggestion proves true, it shows that the Merino condition dominates the Dorset condition. The result is in harmony with the view that both have a common factor for horns, but that in addition the Merinos have a non-sex-linked modifier that holds down the development of the horns in the ewe. What bearing have these results on the theory of sexual selection? Clearly the Merino male, as constituted at present, develops horns because he is a male, but only in the sense that his testes secrete some substance that makes his horns grow. That maleness does not in itself necessarily produce horn is shown by the absence of horns in the Suffolk breed. Is it the same factor, present in the Merino, that produces horns in both sexes of Dorsets when homozygous and in the male only when heterozygous? If originally the ancestral race had no horns, the appearance of factors for horns would, even in a heterozygous condition, have sufficed in the males for the development of horns. If this gave them any advantage either over the enemies of the race or in the eyes of the female, such factors might be perpetuated, and through transferrence to the females ultimately become homozygous in both sexes. Both would then have horns, whether horns were or were not of any advantage to the female, which would have them because they have an advantage to the other sex. Because the genetic evidence shows that a single factor difference between the breeds with and without horns accounts for the horned condition in one of them, it by no means follows that horns as they exist arose as a single mutant factor change. True, they may have arisen as a new single factor difference, but the Mendelian evidence can not be claimed as evidence for this view. The _a priori_ argument based on the relation of horns in an adaptive sense to the rest of the body would appear rather to indicate that they could not have arisen at a single mutational step.