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Correlation and Application of Statistics to Problems of Heredity 85

means, and we might proceed at once to do this without introducing at all the ideas of inheritance and regression. Galton's definition might be of service if we could determine from the regression of the offspring of a single pair of parents, or a few pairs, the typical centre, but this is no more feasible than to determine from a few individuals the population mean ; the very backbone of Galton's conception of parental regression is that the ancestors of the parents cover all' the possible pairs in the community, or are on the average mediocre.

Having defined his races A and B to be those having different centres of regression, which if the races are stable simply connotes different population means, Galton concludes that if A and B are stable then intermediate types are less stable. I think this is only a theory, not necessarily a demonstrable fact. It may be that races A and B have not diverged from a common ancestral race C by continuous variation, but there is nothing in Galton's theory of regression to prevent A, and B arising from C or even A from B by continuous variation. The idea of " stability " as a source of organic evolution is one that Galton was very fond of ; when a race has been largely selected, it topples over, so to speak, into a new form of organic equilibrium with a new centre of regression. In this way Galton would account for "sports" and the prepotency and permanency of certain sports, and he considers that most breeds have arisen from sports. He then refers to various kinds of sports as in peacocks, peaches, and the appearance of remarkable intellectual gifts in man. Under the latter category he cites Sebastian Bach. " Can anybody believe that the modern appearance in a family of a great musician is other than a sport ?" (p. 368). He also refers to Inaudi the mental arithrnetician, who started as an illiterate Piedmontese boy. In the latter case, however, the Inaudi stock may well have possessed similar, if less intense powers which were never called into activity, while in the former case we now possess the pedigree of the Bach family, and their remarkable musical power is certified for five or six generations. All variation is discontinuous when examined in small groups such as families, and the extreme deviations in such small groups may be easily interpreted as sports. Newton again may well have been a sport, but till we know more than we do at present of his mother's ancestry, it is hardly wise to hold that he was such. Nor again if some of these men are to be considered "sports," can we dogmatically assert that they might, like the "japanned" or black-shouldered peacocks, have produced offspring regressing to a new typical centre.

The phrase organic stability must not as yet be taken to connote more than it actually denotes. Thus far it has been merely used to express the well-substantiated fact that a race does sometimes abruptly produce individuals who have a distinctly different typical centre, in the sense in which those words were defined. The inference or connotation is that no variation can establish itself unless it be of the character of a sport, that is, by a leap from one position of organic stability to another, or as we may phrase it, through 'transilient' variation. If there be no such leap the variation is, so to speak, a mere bend or divergence from the parent form, towards which the offspring in the next generation will tend to regress; it may therefore be called a 'divergent' variation.. Thus the unqualified word variation comprises and confuses what I maintain to be two fundamentally different processes, that of transilience and that of divergence, and its use destroys the possibility of reasoning correctly in not a few

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