Footnote 24: Bateson, in his book on “Mendel’s Principles of Heredity,” has given an admirable presentation of Mendel’s results. I have relied largely on this in my account. The importance of Mendel’s results and their wide application is apparent from the results in recent years of De Vries, Correns, Tschermak, Bateson, Castle, and others. Mendel carried out his experiments on the pea, _Pisum sativum_. Twenty-two varieties were used, which had been proven by experiment to be pure breeds. When crossed they gave perfectly fertile offspring. Whether they all have the value of varieties of a single species, or are different subspecies, or even independent species, is of little consequence so far as Mendel’s experiments are concerned. The flower of the pea is especially suitable for experiments of this kind. It cannot be accidentally fertilized by foreign pollen, because the reproductive organs are inclosed in the keel of the flower, and, as a rule, the anthers burst and cover the stigma of the same flower with its own pollen before the flower opens. In order to cross-fertilize the plants it is necessary to open the young buds before the anthers are mature and carefully remove all the anthers. Foreign pollen may be then, or later, introduced. The principle involved in Mendel’s law may be first stated in a theoretical case, from which a certain complication that appears in the actual results may be removed. If _A_ represent a variety having a certain character, and _B_ another variety in which the same character is different, let us say in color, and if these two individuals, one of each kind, are crossed, the hybrid may be represented by _H_. If a number of these hybrids are bred together, their descendants will be of three kinds; some will be like the grandparent, _A_, in regard to the special character that we are following, some will be like the other grandparent, _B_, and others will be like the hybrid parent, _H_. Moreover, there will be twice as many with the character _H_, as with _A_, or with _B_. A B ↘ ↙ H ↙|↘ A | B ↙ | ↘ A | B H ↙|↘ A | B ↙ | ↘ A | B H ↙|↘ A | B H If now we proceed to let these _A_’s breed together, it will be found that their descendants are all _A_, forever. If the _B_’s are bred together they produce only _B_’s. But when the _H_’s are bred together they give rise to _H_’s, _A_’s, and _B_’s, as shown in the accompanying diagram. In each generation, the _A_’s will also breed true, the _B_’s true, but the _H_’s will give rise to the three kinds again, and always in the same proportion. Thus it is seen that the hybrid individuals continue to give off the pure original forms, in regard to the special character under consideration. The numerical relation between the numbers is also a striking fact. Its explanation is, however, quite simple, and will be given later.