Granting these premises, we may now ask as to the results of the fertilization of hybrids, when this is brought about by their own pollen. We assume that numerous pollen grains fertilize numerous egg cells. This assumption at once allows of applying the law of probability, and to infer that of each kind of pollen grains one-half will reach egg-cells with the same quality [297] and the other half ovules with the opposite character. Calling P pollen and O ovules, and representing the active mark by P and O, the latent qualities by P' and O', they would combine as follows: P + 0 giving uniform pairs with the active mark, P + 0' giving unequal pairs, P' + 0 giving unequal pairs, 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' > = 1/2 Hybrid or 2 H, P' + O 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.