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We need scarcely add that the contemplation in natural science of a wider domain than the actual leads to a far better understanding of the actual.' (p. 267,The, Nature of the Physical World.)x PREFACE evolutionary theory was thus chiefly retrogressive, the mighty body of Mendelian researches throughout the world has evidently out- grown the fallacies with which it was at first fostered.As a pioneer of genetics he has done more than enough to expiate the rash polemics of his early writings.To treat Natural Selection as an agency based independently on its own foundations is not to mimimize its importance in the theory of evolution.On the contrary, as soon as we require to form opinions by other means than by comparison and analogy, such an indepen- dent deductive basis becomes a necessity.This necessity is particu- larly to be noted for mankind ; since we have some knowledge of the structure of society, of human motives, and of the vital statistics of this species, the use of the deductive method can supply a more intimate knowledge of the evolutionary processes than is elsewhere possible.In addition it will be of importance for our subject to call ) attention to several consequences of the principle of Natural Selection!which, since they do not consist in the adaptive modification of specific I forms, have necessarily escaped attention.The genetic phenomena of I dominance and linkage seem to offer examples of this class, the future ' investigation of which may add greatly to the scope of our subject.No efforts of mine could avail to make the book easy reading.I have endeavoured to assist the reader by giving short summaries at the ends of all chapters, except Chapter IV, which is summarized conjointly with Chapter V.Those who prefer to do so may regardChapter IV as a mathematical appendix to the corresponding part of the summary.The deductions respecting Man are strictly in- separable from the more general chapters, but have been placed together in a group commencing with Chapter VIII.I believe no one will be surprised that a large number of the points considered demand a far fuller, more rigorous, and more comprehensive treat- ment.It seems impossible that full justice should be done to the subject in this way, until there is built up a tradition of mathematical work devoted to biological problems, comparable to the researches upon which a mathematical physicist can draw in the resolution of special difficulties.