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Correlation and Application of Statistics to Problems of Heredity 65

the population. This is not generally correct; Galton is confusing the regression coefficient with the correlation coefficient. As long as both relatives have equal variability, which we may suppose to be the case with father and son or uncle and nephew, the two coefficients are numerically equal ; but when the two variates have not equal variability, this formula is of course incorrect. In the first entry in the table we have the regression of sons on midparent

given as 3 , and Galton calculates from p s 1- w' the probable deviation of the array of sons to be 1.27. The variability of midparents is, however, not equal to that of sons, but is in the ratio of 1 to 1-2; accordingly r = w/,/2 must be used here instead of w, and the probable deviation of the array of sons is 1.50 and not 1.27.

Further the equality of the regressions of sons on midparents and of brothers on brothers is made by Galton to be 3 in both cases. I think this value is too low in the case of midparents and too high in the case of brothers, the regressions being much more nearly in the ratio of 1.0 to 0.5 than in a ratio of equality. Other regressions entered in this table are very doubtful. We have to look upon the numerical values given as suggestions of the relative degrees of resemblance of various kinsmen, rather than conclusive values founded on observation of adequate numbers (see our pp. 23-4). The main result of Galton's work was to indicate the mechanism by which a population could remain stable notwithstanding variation and inheritance. It was a great direct achievement, and in the indirect light it cast on the general idea of correlation of still greater importance.

Chapter VIII contains the Discussion of the Data of Eye-Colour. This corresponds to the Royal Society paper, which I have already analysed on pp. 34-40 above. The same criticisms must be considered as still valid, and need not be repeated here.

Chapter IX deals with The Artistic Faculty. I do not think the contents of this chapter had been previously discussed by Galton. The data were deduced from the answers in Records of Family Faculties to the questions "Favourite Pursuits and Interests ? " and " Artistic Aptitudes'? "

The object of this chapter is not to give a reply to the simple question, whether or no the Artistic Faculty tends to be inherited. A man must be very crotchety or very ignorant, who nowadays seriously doubts the inheritance either of this or of any other faculty*. The question is whether or no its inheritance follows a similar law to that which has been shown to govern Stature and Eye-Colour, and which has been worked out with some completeness in the foregoing chapters (p. 155). The conclusions

* It may be interesting with regard to these words to cite a few sentences from an obituary notice of Francis Galton which appeared in Nature, February 2, 1911 (Vol. Lxxxv, p. 441).

The writer says

"Only once do I remember on a public occasion a slight severity in his usually gentle tone. A medical man of distinction [Dr Charles Mercier], speaking obviously without any knowledge of the literature of the subject, had asserted that the supposition that the children of parents with certain mental and moral peculiarities would reproduce these features, arose from a totally false conception of what the laws of heredity are. The mental and moral aptitudes were for the speaker outside the purview of hereditary investigation. Galton's reply was very simple : Much of what his critic had said ' might have been appropriately urged forty years ago, before accurate

measurement of the statistical effects of heredity had been commenced, but it was quite obsolete now."'

P G III