Correlation and Application of Statistics to Problems of Heredity 1 1 



maintain stability for two successive generations in somatic characters. This 

 stability Galton achieved by aid of reversion. 



In dealing with the problem of Natural Selection, Galton takes only the 

 case of selection round type and assumes that those selected to live, not 

 those selected to die, will follow a normal distribution. This limits to some 

 extent its general applicability, but he illustrates his idea by a second 

 ingenious Quincunx (see Fig. 3), in which the middle stage is formed by a 

 vertical normal-curve diaphragm which cuts off from the descending pellets, 

 uniformly distributed over the horizontal bases of their compartments in the 

 top stage, the "selected pellets," which again are on the removal of the sliding 

 floor allowed to run down into the third stage compartments where they 

 form a normal distribution of much reduced variability. 



Speaking of the principles of " reversion " and reduced variability in 

 the offspring of a given parentage, Galton says : 



"The typical laws are those which most nearly express what takes place in nature generally; 

 they may never be exactly correct in any one case, but at the same time they will always be 

 approximately true and always serviceable for explanation. We estimate through their means 

 the effects of the laws of sexual selection, of productiveness and of survival, in aiding that of re- 

 version in bridling the dispersive effect of family variability. They show us that natural selection 

 does not act by carving out each new generation according to a definite pattern on a Procrustean 

 bed, irrespective of waste. They also explain howsmall a contribution is made to future generations 

 by those who deviate widely from the mean, either in excess or deficiency, and they enable us 

 to discover the precise sources whence the deficiencies in the produce of exceptional types are 

 supplied, and their relative contributions. We see by them that the ordinary genealogical course 

 of a race consists in a constant outgrowth from its centre, a constant dying away at its margins, 

 and a tendency of the scanty remnants of all exceptional stock to revert to that mediocrity, 

 whence the majority of their ancestors originally sprang." (loc. cit. p. 17.) 



Thus Galton stated his law of reversion originally ; we see that it really 

 covers the most marked features of bivariate normal correlation, we have 

 even the now-familiar symbol r. Whether, however, he was at that time 

 justified in asserting reversion as a typical law of heredity on the basis of 

 his sweet-pea results may be open to question. Is the weight or diameter of 

 a single seed a fair representation of a parental somatic character? Was 

 Galton justified in considering the variability of his offspring constant ? These 

 are points which have much bearing on later work and on what correlation 

 the r really signified in the case of Galton's actual experimental data. 



C. Heredity in Stature of Man. Development of the Conception of 

 Regression. That Galton had some doubts himself is, I think, clear from the 

 fact that for eight years he published nothing further on the subject of 

 regression, but started by aid of his family records to collect data bearing on 

 inheritance in man: see Vol. n, pp. 363 et seq. As soon as he had obtained 

 enough data to deal with the inheritance of stature in man he returned to 

 the subject, and in 1885 and 1886 published a number of papers dealing with 

 the topic. The first of these is his Presidential Address to the Section of 

 Anthropology of the British Association, Aberdeen Meeting, 1885*. He next 

 published a more detailed paper in the Miscellanea of the Journal of the 



* B. A. Transactions, 1885, pp. 1206-1214; Nature, Vol. xxxn, pp. 507-510. 



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