| P + 0 | giving uniform pairs with the active mark, |
| P + 0' | P + 0' giving unequal pairs, |
| P' + 0 | P' + 0 giving unequal pairs, |
| P' + 0' | P' + 0' giving uniform pairs with the latent mark. |
In this combination the four groups are obviously of the same size, each containing one-fourth of the offspring. Manifestly they correspond exactly to the direct results of the experiments, P + O representing the individuals which reverted to the specific mark, P' + O' those who reassumed the varietal quality and P + O' and P + O' those who hybridized [298] for the second time. These considerations lead us to the following form of Mendel's,
| P + O | = 1/4 Active | or 1A, |
| P + O' P' + O | = 1/2 Hybrid | or 2 H, |
| P' + O' | = 1/4 Latent | or 1 L |
Which is evidently the same as Mendel's empirical law given above.
To give the proof of these assumptions Mendel has devised a very simple crossing experiment, [299] which he has effected with his varieties of peas. I have repeated it with the sugar-corn, which gives far better material for demonstration. It starts from the inference that if dissimilarity among the pollen grains is excluded, the diversity of the ovules must at once became manifest and vice versa. In other terms, if a hybrid of the first generation is not allowed to fertilize itself, but is pollinated by one of its parents, the result will be in accordance with the Mendelian formula.
In order to see an effect on the spikes produced in this way, it is of course necessary to fertilize them with the pollen of the variety, and not with that of the specific type. The latter would give partly pure starchy grains and partly hybrid kernels, but these would assume the same type. But if we pollinate the hybrid with pollen of a pure sugar-corn, we may predict the result as follows.
If the spike of the hybrid contains dormant paternal marks in one-half of its flowers and in the other half maternal latent qualities, the sugar-corn pollen will combine with one-half of the ovules to give hybrids, and with the other half so as to give pure sugar-grains. Hence we see that it will be possible to count out directly the two groups of ovules on inspecting the ripe and dry spikes. Experience teaches us [298] that both are present, and in nearly equal numbers; one-half of the grains remaining smooth, and the other half becoming wrinkled.
The corresponding experiment could be made with plants of a pure sugar-race by pollination with hybrid pollen. The spikes would show exactly the same mixture as in the above case, but now this may be considered as conclusive proof that half the pollen-grains represent the quality of one parent and the other half the quality of the other.
Another corollary of Mendel's law is the following. In each generation two groups return to purity, and one-half remains hybrid. These last will repeat the same phenomenon of splitting in their progeny, and it is easily seen that the same rule will hold good for all succeeding generations. According to Mendel's principle, in each year there is a new hybridization, differing in no respect from the first and original one. If the hybrids only are propagated, each year will show one-fourth of the offspring returning to the specific character, one-fourth assuming the type of the variety and one-half remaining hybrid. I have tested this with a hybrid between the ordinary nightshade with black berries, and its variety, Solanum nigrum chlorocarpum, with pale yellow fruits. Eight generations of the hybrids were cultivated, [299] disregarding always the reverting offspring. At the end I counted the progeny of the sixth and seventh generations and found figures for their three groups of descendants, which exactly correspond to Mendel's formula.
Until now we have limited ourselves to the consideration of single differentiating units. This discussion gives a clear insight into the fundamental phenomena of hybrid fertilization. It at once shows the correctness of the assumption of unit-characters, and of their pairing in the sexual combinations.
But Mendel's law is not at all restricted to these simple cases. Quite on the contrary, it explains the most intricate questions of hybridization, providing they do not transgress the limits of symmetrical unions. But in this realm nearly all results may be calculated beforehand, on the ground of the principle of probability. Only one more assumption need be discussed. The several pairs of antagonistic characters must be independent from, and uninfluenced by, one another. This premise seems to hold good in the vast majority of cases, though rare exceptions seem to be not entirely wanting. Hence the necessity of taking all predictions from Mendel's law only as probabilities, which will prove true in most, but not necessarily in all cases. [300] But here we will limit ourselves to normal cases.
The first example to be considered is obviously the assumption that the parents of a cross differ from each other in respect to two characters. A good illustrative example is afforded by the thorn-apple. I have crossed the blue flowered thorny form, usually known as Datura Tatula, with the white thornless type, designated as D. Stramonium inermis. Thorns and blue pigment are obviously active qualities, as they are dominant in the hybrids. In the second generation both pairs of characters are resolved into their constituents and paired anew according to Mendel's law. After isolating my hybrids during the period of flowering, I counted among their progeny:
| 128 | individuals with blue flowers and thorns |
| 47 | individuals with blue flowers and thorns |
| 54 | individuals with white flowers and thorns |
| 21 | individuals with white flowers and without thorns |
| —— | |
| 250 |
The significance of these numbers may easily be seen, when we calculate what was to be expected on the assumption that both characters follow Mendel's law, and that both are independent from each other. Then we would have three-fourths blue offspring and one-fourth individuals with white flowers. Each of these [301] two groups would consist of thorn-bearing and thornless plants, in the same numerical relation. Thus, we come to the four groups observed in our experiment, and are able to calculate their relative size in the following way:
| Proportion | ||
| Blue with thorns | 3/4 X 3/4 = 9/16 = 56.25% | 9 |
| Blue, unarmed | 3/4 X 1/4 = 3/16 = 18.75% | 3 |
| White with thorns | 1/4 X 3/4 = 3/16 = 18.75% | 3 |
| White, unarmed | 1/4 X 1/4 = 1/16 = 6.25% | 1 |
In order to compare this inference from Mendel's law and the assumption of independency, with the results of our experiments, we must calculate the figures of the latter in percentages. In this way we find:
| Found | Calculated | |
| Blue with thorns | 128=51% | 56.25% |
| Blue, unarmed | 47=19% | 18.75 |
| White with thorns | 54=22% | 18.75 |
| White, unarmed | 54=22% | 6.25% |
The agreement of the experimental and the theoretical figures is as close as might be expected.
This experiment is to be considered only as an illustrative example of a rule of wide application. The rule obviously will hold good in all such cases as comply with the two conditions already premised, viz.: that each character agrees with Mendel's law, and that both are wholly independent of each other. It is clear that our figures show the numerical composition [302] of the hybrid offspring for any single instance, irrespective of the morphological nature of the qualities involved.
Mendel has proved the correctness of these deductions by his experiments with peas, and by combining their color (yellow or green) with the chemical composition (starch or sugar) and other pairs of characters. I will now give two further illustrations afforded by crosses of the ordinary campion. I used the red-flowered or day-campion, which is a perennial herb, and a smooth variety of the white evening-campion, which flowers as a rule in the first summer. The combination of flower-color and pubescence gave the following composition for the second hybrid generation: