Nevertheless a definite assumption is implicitly made regarding the gametes. It is not in question that differences between these gametes may occur in respect of the heritage they bear; yet it is assumed that these differences will be distributed among the gametes of any individual zygote in such a way that each gamete remains capable, on fertilisation, of transmitting all the characters (both of the parent-zygote and of its progenitors) to the zygote which it then contributes to form (and to the posterity of that zygote) in the intensity indicated by the law. Hence the gametes of any individual are taken as collectively a fair sample of all the racial characters in their appropriate intensities, and this theory demands that there shall have been no qualitative redistribution of characters among the gametes of any zygote in such a way that some gametes shall be finally excluded from partaking of and transmitting any specific part of the heritage. The theory further demands—and by the analogy of what we know otherwise not only of animals and plants, but of physical or chemical laws, perhaps this is the most serious assumption of all—that the structure of the gametes shall admit of their being capable of transmitting any character in any intensity varying from zero to totality with equal ease; and that gametes of each intensity are all equally likely to occur, given a pedigree of appropriate arithmetical composition.
Such an assumption appears so improbable that even in cases where the facts seem as yet to point to this conclusion with exceptional clearness, as in the case of human stature, I cannot but feel there is still room for reserve of judgment.
However this may be, the Law of Ancestral Heredity, and all modifications of it yet proposed, falls short in the respect specified above, that it does not directly attempt to give any account of the distribution of the heritage among the gametes of any one individual.
Mendel’s conception differs fundamentally from that involved in the Law of Ancestral Heredity. The relation of his hypothesis to the foregoing may be most easily shown if we consider it first in application to the phenomena resulting from the cross-breeding of two pure varieties.
Let us again consider the case of two varieties each displaying the same character, but in the respective intensities A and a. Each gamete of the A variety bears A, and each gamete of the a variety bears a. When they unite in fertilisation they form the zygote Aa. What will be its characters? The Mendelian teaching would reply that this can only be known by direct experiment with the two forms A and a, and that the characters A and a perceived in those two forms or varieties need not give any indication as to the character of the zygote Aa. It may display the character A, or a, or a character half way between the two, or a character beyond A or below a. The character of Aa is not regarded as a heritage transmitted to it by A and by a, but as a character special and peculiar to Aa, just as NaCl is not a body half way between sodium and chlorine, or such that its properties can be predicted from or easily stated in terms of theirs.
If a concrete case may help, a tall pea A crossed with a dwarf a often produces, not a plant having the height of either A or a, but something taller than the pure tall variety A.
But if the case obeys the Mendelian principles—as does that here quoted—then it can be declared first that the gametes of Aa will not be bearers of the character proper to Aa; but, generally speaking, each gamete will either bear the pure A character or the pure a character. There will in fact be a redistribution of the characters brought in by the gametes which united to form the zygote Aa, such that each gamete of Aa is pure, as the parental gametes were. Secondly this redistribution will occur in such a way that, of the gametes produced by such Aa’s, on an average there will be equal numbers of A gametes and of a gametes.
Consequently if Aa’s breed together, the new A gametes may meet each other in fertilisation, forming a zygote AA, namely, the pure A variety again; similarly two a gametes may meet and form aa, or the pure a variety again. But if an A gamete meets an a it will once more form Aa, with its special character. This Aa is the hybrid, or “mule” form, or as I have elsewhere called it, the heterozygote, as distinguished from AA or aa the homozygotes.
Similarly if the two gametes of two varieties distinguished by characters, A and B, which cannot be described in terms of any common scale (such as for example the “rose” and “single” combs of fowls) unite in fertilisation, again the character of the mule form cannot be predicted. Before the experiment is made the “mule” may present any form. Its character or properties can as yet be no more predicted than could those of the compounds of unknown elements before the discovery of the periodic law.
But again—if the case be Mendelian—the gametes borne by AB will be either A’s or B’s[18], and the cross-bred AB’s breeding together will form AA’s, AB’s and BB’s. Moreover, if as in the normal Mendelian case, AB’s bear on an average equal numbers of A gametes and B gametes, the numerical ratio of these resulting zygotes to each other will be