If a heterozygous bird be mated to a recessive the variability of the offspring is much increased, owing to the occurrence in the progeny of both DR and RR individuals (table 40). The offspring do not, to be sure, fall into two distinct and well-defined types, as in typical Mendelian cases; but one part of the range of variation agrees fairly with that of pure RR's, i. e., Brahmas, and the remainder with that of heterozygotes. And if we make the division in the middle of the middle class, viz, 5, we shall find a close approximation to that equality of extracted recessives and heterozygotes that the segregation theory calls for (table 44).

If, again, two heterozygous birds be mated, the variability is still greater and the proportion of clean-footed offspring rises to 12 per cent. These, together with some of the extremely slightly booted offspring, represent the extracted dominants. The whole range now falls into three regions divided by the middle of grades 2 and 5. These regions correspond to the DD's, the DR's, and the RR's of typical cases of segregation, and their relative proportions are approximately as 25: 50: 25.

Finally, if a heterozygote be mated to an extracted dominant the proportion of clean-footed offspring rises to about 30 per cent and the whole range of variation falls readily into two parts, the one comprising grades 0 and 1, the other grades 2 and above. The first includes the DD offspring; the second, the DR's; and their frequency is equal. One will not fail to note that we are not here dealing with a case of blending simply, and the inheritance of the blend; such a view is negatived by the fact of the much greater variability of DR × DR cross over the simple D × R cross of the first generation. One may safely conclude, then, that, despite the apparent blending of booting characters in the first generation of hybrids, true segregation takes place. But this is always to be seen through the veil of imperfect dominance.

A casual examination of table 38 would seem to show a correlation between the grade of booting of the parents and that of the average of their progeny. Thus, on the whole, the parental grades run high in the upper part of the table and run low in the lower part. This relation would thus seem to confirm Castle's conclusion for polydactylism in guinea-pigs that there is an inheritance of the degree of a character. One consequence of such an inheritance would be that it would be possible in a few generations to increase or diminish the grade of a character and fix any required grade in the germ-plasm. A more careful consideration of the facts of the case shows that this relation has another interpretation. The grade of boot of the different parents varies largely because their gametic constitution is diverse. As table 39 shows, the parents of the upper part of table 38 are chiefly extracted recessives, and consequently their booting and that of their offspring are characterized by high grades. On the other hand, the parents of the lower part of the table are heterozygous or extracted dominants and, consequently, their grades and also those of their offspring average low. On account of the lack of homogeneity of the families in table 38, one can draw from it no proper conclusions as to relation between parental and filial grades. On the other hand, from a homogeneous table, like table 39, we can hope to reach a conclusion as to the existence of such a relation. I have calculated, in the usual biometric fashion, the coefficient of correlation between average parental and filial grades, and found it to be -0.17 ± 0.13. This can only be interpreted to mean that in a homogeneous assemblage of families there is no correlation between the grade of booting of parents and offspring.

In my 1906 report I described in detail the form of the nostril in poultry. Usually it is closed down to a narrow slit, but in some races, as, e. g., the Polish and Houdans, the closing flap of skin fails to develop and the nostril remains wide open. This is apparently an embryonic condition. Thus in Keibel and Abraham's (1900) Normaltafeln of the fowl it is stated that the outer nasal opening, which is at first wide open, becomes closed with epithelium at about the middle of the sixth day of development. The Polish and Houdan fowl thus retain in the outer nasal opening an embryonic condition. The question is: How does this embryonic, open condition of the nostril behave in heredity with reference to the more advanced narrow-slit condition?

The wide-nostriled races used were both the Polish and the Houdan. The condition of the external nares is much the same in the two, but is slightly more exaggerated in the Houdans than in the Polish. The open nostril is often associated with a fold across the culmen, apparently due to the upturning of the anterior end of the premaxillary process of the nasal bone. Breeders of Houdans have sought to exaggerate the height of the fold. In both races there is great variability in the degree of "openness" of the nostril, and to indicate this I have adopted a scale of 10 grades (running from 1, the narrowest, to 10, the widest). To get some idea of this variability let us consider the grade of nostril in some families of pure Houdans.

Table 45 shows that the prevailing grade in the offspring of pure Houdans is 9; that grades 8 and 10 are also extremely common; and that lower grades, even down to 1, may occur, but these are much less common.

We have next to consider the grade-distribution of the offspring of the narrow mated with the wide nostril.

Table 46.—Distribution of the frequency of the different grades of "openness" of nostril when one parent has the open nostril and the other the closed.

Table 46 gives us a picture of the nature of the dominance in this case. At first sight the narrow nostril, grades 1 and 2, including 57 per cent of the offspring, appears to be dominant. But, as later evidence shows, it is recessive. The wide nostril is dominant, but so imperfectly that only 10 per cent have a nostril above one-half open.

Let us now consider the distribution of nostril form in families whose parents are hybrids of the first or later generation, crossed respectively on recessives, heterozygotes, and dominants (tables 47-49).

The study of the tables 45 to 54 establishes the following conclusions:

First, high nostril is dominant. This means that there is a factor that inhibits the development of the narial flap. In the absence of such a factor the flap goes on developing normally. This hypothesis is opposed to the conclusion that I reached in my report of 1906 (pp. 68, 69). I there said:

A close agreement exists between the percentage obtained in each generation and the expectation of the Mendelian theory, assuming that narrow nostril is dominant. The statistics do not, however, tell the whole story. In 36 per cent of the cases in the F₁ generation the nostril was wider than in the "narrow" ancestor. Even in the F₂ generation nearly half of the "narrow and intermediate" were of the intermediate sort. This intermediate form is evidence that dominance is imperfect and segregation is incomplete.

These earlier data were not even roughly quantitative, and it is the quantitative data that first give the key to the true relations. However, sufficient evidence for the change in the conclusion is certainly due. The evidence is found in a careful study of table 55, keeping constantly in mind this fundamental principle that the recessive condition alone in the parents can never give rise to the dominant; for the recessive condition implies entire absence of the dominant factor. But the pure dominant condition will vary in the direction of the recessive condition; such a result implies only a partial failure of the factor to develop completely; and we should not be surprised if occasionally the failure were complete. This implies no "reversal of dominance," but rather an arrested development of the factor.