Ratios
1ab class produce only ab’s.
31aB class may produce either all aB’s,
2or both aB’s and ab’s.
31Ab class may produce either all Ab’s,
2or both Ab’s and ab’s.
91AB class may produce either all AB’s,
2or both AB’s and Ab’s,
2or both AB’s and aB’s,
4or all four possible classes again, namely,
AB’s, Ab’s, aB’s, and ab’s,

and the average number of members of each class will approach the ratio 1 : 3 : 3 : 9 as indicated above.

The details of these experiments and of others like them made with three pairs of differentiating characters are all set out in Mendel’s memoir.

Professor de Vries has worked at the same problem in some dozen species belonging to several genera, using pairs of varieties characterised by a great number of characters: for instance, colour of flowers, stems, or fruits, hairiness, length of style, and so forth. He states that in all these cases Mendel’s principles are followed.

The numbers with which Mendel worked, though large, were not large enough to give really smooth results[10]; but with a few rather marked exceptions the observations are remarkably consistent, and the approximation to the numbers demanded by the law is greatest in those cases where the largest numbers were used. When we consider, besides, that Tschermak and Correns announce definite confirmation in the case of Pisum, and de Vries adds the evidence of his long series of observations on other species and orders, there can be no doubt that Mendel’s law is a substantial reality; though whether some of the cases that depart most widely from it can be brought within the terms of the same principle or not, can only be decided by further experiments.

One may naturally ask, How can these results be brought into harmony with the facts of hybridisation hitherto known; and, if all this is true, how is it that others who have carefully studied the phenomena of hybridisation have not long ago perceived this law? The answer to this question is given by Mendel at some length, and it is, I think, satisfactory. He admits from the first that there are undoubtedly cases of hybrids and cross-breds which maintain themselves pure and do not break up. Such examples are plainly outside the scope of his law. Next he points out, what to anyone who has rightly comprehended the nature of discontinuity in variation is well known, that the variations in each character must be separately regarded. In most experiments in crossing, forms are taken which differ from each other in a multitude of characters—some continuous, others discontinuous, some capable of blending with their contraries, while others are not. The observer on attempting to perceive any regularity is confused by the complications thus introduced. Mendel’s law, as he fairly says, could only appear in such cases by the use of overwhelming numbers, which are beyond the possibilities of practical experiment. Lastly, no previous observer had applied a strict statistical method.

Both these answers should be acceptable to those who have studied the facts of variation and have appreciated the nature of Species in the light of those facts. That different species should follow different laws, and that the same law should not apply to all characters alike, is exactly what we have every right to expect. It will also be remembered that the principle is only explicitly declared to apply to discontinuous characters[11]. As stated also it can only be true where reciprocal crossings lead to the same result. Moreover, it can only be tested when there is no sensible diminution in fertility on crossing.

Upon the appearance of de Vries’ paper announcing the “rediscovery” and confirmation of Mendel’s law and its extension to a great number of cases two other observers came forward almost simultaneously and independently described series of experiments fully confirming Mendel’s work. Of these papers the first is that of Correns, who repeated Mendel’s original experiment with Peas having seeds of different colours. The second is a long and very valuable memoir of Tschermak, which gives an account of elaborate researches into the results of crossing a number of varieties of Pisum sativum. These experiments were in many cases carried out on a large scale, and prove the main fact enuntiated by Mendel beyond any possibility of contradiction. The more exhaustive of these researches are those of Tschermak on Peas and Correns on several varieties of Maize. Both these elaborate investigations have abundantly proved the general applicability of Mendel’s law to the character of the plants studied, though both indicate some few exceptions. The details of de Vries’ experiments are promised in the second volume of his most valuable Mutationstheorie. Correns in regard to Maize and Tschermak in the case of P. sativum have obtained further proof that Mendel’s law holds as well in the case of varieties differing from each other in two pairs of characters, one of each pair being dominant, though of course a more complicated expression is needed in such cases[12].

That we are in the presence of a new principle of the highest importance is manifest. To what further conclusions it may lead us cannot yet be foretold. But both Mendel and the authors who have followed him lay stress on one conclusion, which will at once suggest itself to anyone who reflects on the facts. For it will be seen that the results are such as we might expect if it be imagined that the cross-bred plant produced pollen grains and egg-cells, each of which bears only one of the alternative varietal characters and not both. If this were so, and if on an average the same number of pollen grains and egg-cells transmit each of the two characters, it is clear that on a random assortment of pollen grains and egg-cells Mendel’s law would be obeyed. For 25 per cent. of “dominant” pollen grains would unite with 25 per cent. “dominant” egg-cells; 25 per cent. “recessive” pollen grains would similarly unite with 25 per cent. “recessive” egg-cells; while the remaining 50 per cent. of each kind would unite together. It is this consideration which leads both Mendel and those who have followed him to assert that these facts of crossing prove that each egg-cell and each pollen grain is pure in respect of each character to which the law applies. It is highly desirable that varieties differing in the form of their pollen should be made the subject of these experiments, for it is quite possible that in such a case strong confirmation of this deduction might be obtained. [Preliminary trials made with reference to this point have so far given negative results. Remembering that a pollen grain is not a germ-cell, but only a bearer of a germ-cell, the hope of seeing pollen grains differentiated according to the characters they bear is probably remote. Better hopes may perhaps be entertained in regard to spermatozoa, or possibly female cells.]

As an objection to the deduction of purity of germ-cells, however, it is to be noted that though true intermediates did not generally occur, yet the intensity in which the characters appeared did vary in degree, and it is not easy to see how the hypothesis of perfect purity in the reproductive cells can be supported in such cases. Be this, however, as it may, there is no doubt we are beginning to get new lights of a most valuable kind on the nature of heredity and the laws which it obeys. It is to be hoped that these indications will be at once followed up by independent workers. Enough has been said to show how necessary it is that the subjects of experiment should be chosen in such a way as to bring the laws of heredity to a real test. For this purpose the first essential is that the differentiating characters should be few, and that all avoidable complications should be got rid of. Each experiment should be reduced to its simplest possible limits. The results obtained by Galton, and also the new ones especially described in this paper, have each been reached by restricting the range of observation to one character or group of characters, and it is certain that by similar treatment our knowledge of heredity may be rapidly extended.