We thus see that the first generation of the hybrid when two such characters are combined contains two kinds of egg-cells and two kinds of sperm-cells, sh far as this one character-pair is concerned.
The third important principle of Mendel's law is what is termed the law of probability, and ex plains what may be expected in plants of the second generation of such a hybrid. Remembering that we have formed in the first-generation hybrid, as explained above, two kinds of egg-cells and two kinds of sperm-cells with reference to the opposed characters, what would happen if the hybrid were bred with its own pollen ; or, in the case of an animal, if it were bred with another hybrid of the same parentage? For the purpose of illustration, suppose that a hybrid of a bald wheat with a bearded wheat be fertilized with its own pollen and that 100 egg-cells be fertilized with 100 pollen grains of the same hybrid. There are two kinds of egg-cells produced, some with potentialities of the bald wheat and some with potentialities of the bearded wheat, and the same is true of the pollen grains. Taking the egg-cells and pollen-grains without selection, therefore, we would expect to have of the egg-cells 50 with bald potentialities and 50 with bearded potentialities. In the pollen grains also we would expect to have 50 with bald potentialities and 50 with bearded potentialities. If these are brought together, allowing the law of chance to govern the union, the probability is that we would have 25 bald uniting with 25 bald; 25 bald uniting with 25 bearded ; 25 bearded uniting with 25 bald, and 25 bearded uniting with 25 bearded. Representing the bald potentialities by B and the bearded potentialities by b, we have the following formula, which explain the probable unions graphically (and this is what is known as Mendel's law):— "This formula for the hybrids," writes Bailey, "is Mendel's law. In words, it may be expressed as follows : Differentiating characters in plants reappear in their purity and in mathematical reg ularity in the second and succeeding hybrid off spring of these plants ; the mathematical law is that each character separates in each of these generations in one-fourth of the progeny and thereafter remains true." The above illustration will explain the law of iegregation, and probable ratio of recombination when hybrids are inbred with their own pollen, and when only one pair of characters is considered.
When an egg-cell with bald potentialities unites with a sperm-cell with bald potentialities, this gives rise to a pure germ-cell containing only bald potentialities, and the progeny in subsequent gen erations will breed true so far as this character is concerned. Also when the egg-cell with bearded potentialities unites with a sperm-cell with bearded potentialities, the result is a pure germ-cell con taining only bearded potentialities, and the progeny would reproduce true, so far as this character is concerned, in subsequent generations. In the other two cases where, in fecundation, germs with bald potentialities unite with germs with bearded poten tialities, giving the combinations Bb and bB, which amount to the same thing, we have in reality hybrids exactly the same as in the first generation, and the progeny from these in the next generation behave exactly the same as did the first-generation hybrids in the second generation. In such a case as this, where one of the characters, as the bald head, is strong and dominant, all combinations that contain the potentialities of this character, whether pure or mixed, show this character only. Thus, in the above table the 25bb would come with bearded heads, while the 75 of other combinations would have bald heads. To determine which of these 75 heads are the combination Bb, that is bald with bearded, and which BB, that is bald with bald, would require the growing of progeny, to deter mine which were reproduced true to type. The ratio of the combinations, it will be noticed, is 1BB to 2Bb to lbb. While in certain hybrids of parents possessing two opposed parental characters this ratio of probabilities is not produced, if large num bers are used the ratio will be found in many cases with little deviation. A sufficiently large number of cases have now been carried out with various plants and animals to place the conclusion beyond question. We do not know, however, how many characters follow Mendel's law, and are not yet entirely certain whether those character-pairs that sometimes follow the law of segregation always follow it.