In endeavoring to illustrate how this question actually affects research I will offer two illustrative cases, one of which may indicate the fruitfulness of the mechanistic conception in the analysis of complex and apparently mysterious phenomena, the other the nature of the difficulties that have in recent years led to attempts to re-establish the vitalistic view. The first example is given by the so-called law or principle of Mendel in heredity. The principle revealed by Mendel's wonderful discovery is not shown in all the phenomena of heredity and is probably of more or less limited application. It possesses however a profound significance because it gives almost a demonstration that a definite, and perhaps a relatively simple, mechanism must lie behind the phenomena of heredity in general. Hereditary characters that conform to this law undergo combinations, disassociations and recombinations which in certain way suggest those that take place in chemical reactions; and like the latter they conform to definite quantitative rules that are capable of arithmetical formulation. This analogy must not be pressed too far; for chemical reactions are individually definite and fixed, while those of the hereditary characters involve a fortuitous element of such a nature that the numerical result is not fixed or constant in the individual case but follows the law of probability in the aggregate of individuals. Nevertheless, it is possible, and has already become the custom, to designate the hereditary organization by symbols or formulas that resemble those of the chemist in that they imply the _quantitative_ results of heredity that follow the union of compounds of known composition. Quantitative prediction--not precisely accurate, but in accordance with the law of probability--has thus become possible to the biological experimenter on heredity. I will give one example of such a prediction made by Professor Cuenot in experimenting on the heredity of color in mice (see the following table). The experiment extended through three generations. Of the four grandparents three were pure white albinos, identical in outward appearance, but of different hereditary capacity, while the fourth was a pure black mouse. The first pair of grandparents consisted of an albino of gray ancestry, AG, and one of black ancestry, AB. The second pair consisted of an albino of yellow ancestry, AY, and a black mouse, CB. The result of the first union, AG x AB is to produce again pure white mice of the composition AGAB. The second union, AY x CB is to produce mice that appear pure _yellow_, and have the formula AYCB. What, now, will be the result of uniting the two forms thus produced--_i.e._ AGAB x AYCB? Cuenot'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