produced—i.e. AGAB × AYCB? Cuénot's prediction was that they should yield eight different kinds of mice, of which four should be white, two yellow, one black and one gray. The actual aggregate result of such unions, repeatedly performed, compared with the theoretic expectation, is shown in the foregoing table. As will be seen, the correspondence, though close, is not absolutely exact, yet is near enough to prove the validity of the principle on which the prediction was based, and we may be certain that had a much larger number of these mice been reared the correspondence would have been still closer. I have purposely selected a somewhat complicated example, and time will not admit of a full explanation of the manner in which this particular result was reached. I will however attempt to give an indication of the general Mendelian principle by means of which predictions of this kind are made. This principle appears in its simplest form in the behavior of two contrasting characters of the same general type—for instance two colors, such as gray and white in mice. If two animals, which show respectively two such characters are bred together, only one of the characters (known as the "dominant") appears in the offspring, while the other (known as the "recessive") disappears from view. In the next generation, obtained by breeding these hybrids together, both characters appear separately and in a definite ratio, there being in the long run three individuals that show the dominant character to one that shows the recessive. Thus, in the case of gray and white mice, the first cross is always gray, while the next generation includes three grays to one white. This is the fundamental Mendelian ratio for a single pair of characters; and from it may readily be deduced the more complicated combinations that appear when two or more pairs of characters are considered together. Such combinations appear in definite series, the nature of which may be worked out by a simple method of binomial expansion. By the use of this principle astonishingly accurate numerical predictions may be made, even of rather complex combinations; and furthermore, new combinations may be, and have been, artificially produced, the number, character and hereditary capacity of which are known in advance. The fundamental ratio for a single pair of characters is explained by a very simple assumption. When a dominant and a recessive character are associated in a hybrid, the two must undergo in some sense a disjunction or separation in the formation of the germ-cells of the hybrid. This takes place in a quite definite way, exactly half the germ-cells in each sex receiving the potentiality of the dominant character, the other half the potentiality of the recessive. This is roughly expressed by saying that the germ-cells are no longer hybrid, like the body in which they arise, but bear one character or the other; and although in a technical sense this is probably not precisely accurate, it will sufficiently answer our purpose. If, now, it be assumed that fertilization takes place fortuitously—that is that union is equally probable between germ-cells bearing the same character and those bearing opposite characters,—the observed numerical ratio in the following generation follows according to the law of probability. Thus is explained both the fortuitous element that differentiates these cases from exact chemical combinations, and the definite numerical relations that appear in the aggregate of individuals.

Now, the point that I desire to emphasize is that one or two very simple mechanistic assumptions give a luminously clear explanation of the behavior of the hereditary characters according to Mendel's law, and at one stroke bring order out of the chaos in which facts of this kind at first sight seem to be. Not less significant is the fact that direct microscopical investigation is actually revealing in the germ-cells a physical mechanism that seems adequate to explain the disjunction of characters on which Mendel's law depends; and this mechanism probably gives us also at least a key to the long standing riddle of the determination and heredity of sex. These phenomena are therefore becoming intelligible from the mechanistic point of view. From any other they appear as an insoluble enigma. When such progress as this is being made, have we not a right to believe that we are employing a useful working hypothesis?

But let us now turn to a second example that will illustrate a class of phenomena which have thus far almost wholly eluded all attempts to explain them. The one that I select is at