Both sexes in Dorset sheep have well-developed horns; in the Suffolk breed both sexes are hornless. If the breeds are crossed, all the rams in the first (hybrid) generation have horns and all the ewes are hornless. If these hybrids are mated, the resulting male offspring averages three horned to one hornless; but the females are the reverse of this ratio—one horned to three hornless. This is an example of Mendel's principle of segregation—factors may be mixed in breeding, but they do not lose their identity, and hence tend to be sorted out or segregated again in succeeding generations.
In the horned Dorsets, we must suppose that both males and females carry a dual factor for horns—technically, are homozygous for horns. The hornless Suffolks, on the contrary, are homozygous for absence of horns. Thus the dual factor in the zygotes or fertilized eggs at the basis of the first filial (hybrid) generation consists of a single factor for horns and a single factor for their absence. If we represent horns by H and absence of horns by A, Dorsets have a factor HH, Suffolks AA and the hybrids HA.
All the males in this generation have horns, which means that a single "dose" of the factor H will produce horns in a male, or that they are dominant in males. But a single dose will not produce horns in a female—that is, horns are recessive in females—the factor is present but unexpressed.
Mating two HA hybrids, the H and A of course split apart in the formation of the gametes, as the HH and AA did in the previous generation; so that we get an equal number of single H and A factors. In reuniting in fertilized eggs, the chance is just half and half that an H will unite with another H or with an A—that an A will unite with an H or another A. Thus we have two chances of getting HA to each chance of getting either AA or HH. Half the zygotes will be HA, one-fourth HH and one-fourth AA.
If we consider four average males, one will have two A's (absence of the factor for horns) and will thus be hornless. One will have two H's, or the double factor for horns, and hence will exhibit horns—as will also the two HA's since a single dose of horns expresses them in a male. So we have the three-to-one Mendelian ratio.
But four females with exactly the same factors will express them as follows: The one HH (double factor for horns) proves sufficient to express horns, even in a female. The AA, lacking the factor entirely, cannot have horns. Nor will the two HA females have horns, a single dose being insufficient to express them in a female. Again we get our three-to-one Mendelian ratio, but this time it is three hornless to one horned.
Especially Goldschmidt's carefully graded experiments point to a similar difference in the strength of the dose or doses of the sex factors. Instead of the two doses of horns required to express them in the presence of the female secretory balance in Professor Wood's sheep, Goldschmidt found it took six doses of maleness to completely express it on a female basis in his moths. But even with three doses, the female was incapable of reproduction. A single dose in excess of the ordinary combination to produce normal females modified the type of body, also reducing the number of eggs.
In the case of the horns, only two types were possible, absence or presence of the character. Likewise there are only two types of primary sex, i.e., of sex glands proper. But seven different types or grades of body for each sex were found to exhibit themselves in the moths. In more complicated bodies, we should of course expect many more, and where many races (instead of two) are mixed, as in man, a classification merely on the basis of physical characteristics would be much more complicated. Indeed, we may well be sceptical as to the possibilities of cataloguing differences of the sort between men and women by body type alone.
In society, however, we are much more interested in the mental than the purely physical qualities of the two types of bodies, especially since the use of machines has so largely replaced brute strength with skill. Most employments do not even require a muscular skill beyond that possessed by ordinary individuals of both sexes.
Even this ignores the primary consideration in the sex problem in society, the first of the following two parts into which the whole problem may be divided: (1) How to guarantee the survival of the group through reproduction of a sufficient number of capable individuals; and (2) How to make the most economical use of the remaining energies, first in winning nutrition and protection from the environment, second in pursuing the distinctly human values over and above survival. The sex problem as a whole is concerned with adjusting two different general types of individuals, male and female, to the complicated business of such group life or society. The differences between these two sex-types being fundamentally functional, the best way to get at them is to trace the respective and unlike life cycles.