produced in two ways, through inheritance from exceptional ancestors, and through normal variations from less exceptional ancestors. And measurements prove that the greater number are produced by the latter method. This should not be interpreted to mean that exceptional parents are not more likely to have exceptional sons than are mediocre parents; they are much more likely to have them. But average parents constitute so great a majority that the few exceptional variations from them count for more. This discovery should be of considerable significance to a theory of heredity and of racial improvement. Inspection of a correlation table, given in statistical texts, will help to make clear the twofold aspects of regression. Since Galton's notable beginnings in the line of biometry, the work of estimating correlations has been greatly extended. While coefficients of correlation are used to measure hereditary resemblance, they are not limited in their applications to problems of heredity alone. A coefficient of correlation is a means of measuring the degree of resemblance between any two variables. The coefficient is a fraction, varying from o to i, i representing perfect correlation and o no resemblance whatsoever. It may also be negative, which would mean that the two factors vary inversely. Galton's original records of 150 families yielded the following coefficients of correlation for stature: Later measurements, however, collected by Pearson, and taken from over 1,000 families, show a much higher degree of correlation between parents and offspring, and these earlier estimates have therefore been abandoned. Pearson found the coefficient of correlation for stature between parents and offspring to be .51, those for span and length of forearm were a little less, but the average for all three was .46. And still later measurements have been made which make it seem probable that the average strength of inheritance between parents and offspring for physical traits could be expressed with a fair degree of accuracy by a coefficient of correlation of .5. Galton's Law of Alternative Inheritance. Mention should be made of Galton's law of alternative inheritance, although it is now displaced by the Mendelian theory. The problem, as he conceived it, was somewhat different from that of blended inheritance. According to alternative inheritance the child received a character entire from one or another ancestor and the problem was to ascertain the degree of probability of his receiving the character from one of his immediate parents, or from a more remote ancestor. Galton concluded that in the case of alternative inheritance ļ the offspring would take after one or the other of the immediate parents, and 1 would revert to previous ancestors. Of the half that reverted, $ would take after the grandparents, f after the great grandparents, etc. It will be observed that this is the same series as that used in the law of ancestral inheritance; but the two should not be confused. In alternative inheritance the series is known as the law of reversion; and it shows the probability of offspring inheriting a character entire from one or another of his ancestors, while the law of ancestral inheritance shows the proportion which the various ancestors contribute to the character of the offspring when that character is a blend. Pearson later worked out the intensity of resemblance of eyecolor in from eight hundred to fifteen hundred cases for each of the degrees of relationship; and also, in horses, the intensity of the resemblance of coat-color, and the results obtained are given in the table. In the third column he added the geometric series which most closely follows the observed results. TABLE XVIII Eye-Color Coat-Color Close in Man in Horses Series Parent and offspring..... -49 .50 Grandparent and offspring...... -32 33 Great grandparent and offspring... .19 .19 Great great grandparent and offspring .15 .15 .22 Inasmuch as the later studies show no marked difference in the strength of heredity of eye-color and for stature, the original distinction between blended and alternative inheritance has been abandoned by biometricians when estimating correlation. They now seek merely to ascertain degrees of resemblance between generations without regard to mode of inheritance. Some slight differences are obtained in the degree of correlation for different physical characters; but in general they range from .42 to .52 and the above series in Column 3 is thought to indicate approximately the degree of hereditary resemblance. Limitations of the Statistical Method. The chief results of the biometricians are given here because they are both interesting and serviceable; but like all statistical material the results must be used with understanding and discretion. Inasmuch as the statistical method in biology has been severely, and sometimes unjustly, criticized, it may be well to explain some of its limitations. Coefficients of correlation merely indicate degree of similarity. They throw no light on the method of heredity and in fact do not prove heredity at all. The dangers in the use of coefficients of correlation are the same as those in the use of concomitant variations explained in Chapter I. They do not necessarily prove cause and effect. However, in case of physical traits which are known to be inherited, the supposition amounts to a certainty that the degree of correlation expresses hereditary relationship. In case of traits whose inheri . tance is uncertain the demonstration of inheritance, through a statistical statement of degree of resemblance between generations, is not always easy and sometimes may be misleading. The criticism of coefficients of correlation has been that they make no distinctions between inherited and acquired variations; and it is undeniable that the original measurements and comparisons do not. This fact, however, is not of sufficient importance to condemn the use of correlations altogether, for in many cases of human inheritance environmental influence is not a complicating factor. In other cases of inheritance of both physical and mental traits environmental influences may be present; and whenever they are, the disentanglement of the two factors of heredity and environment presents intricate problems. In a few instances where modifications and inherited characters might be confused the environmental influence has been pretty successfully eliminated by means of ingenious comparisons with new factors, so that the hereditary factor is left as the only plausible explanation of the correlation; but in other cases such eliminations cannot be made and the results are therefore doubtful. An illustration of an uncertain result may be taken from Pearson's study of tuberculosis. The coefficient of correlation for parent and offspring for this trait was found to be .5, the same as that of the inheritance of physical traits, so that the presumption favors inheritance. But nothing in this correlation proves that the resemblance was due to heredity rather than to infection. An attempt was made to eliminate the factor of infection by a number of new comparisons, one of which was the correlation for tuberculosis between husband and wife. This was found to be .24 for the middle class, but -.01 for the very poor, and .16 for the more prosperous poor. Inasmuch as there was no correlation for the disease between husband and wife in poor quarters where the danger of infection is supposed to be greatest, the similarity between parents and offspring was assumed to be the result of heredity. This conclusion could be accepted provided all persons, young and old, were equally subject to infection. But it is now an accepted fact that infection in the case of tuberculosis usually takes place in childhood, and therefore the possibility of environmental action does not seem to be entirely eliminated by comparing the condition of adults in the same household. This study seems to me therefore to furnish an example of doubtful results in the statistical method. It is probable that the correlation between parents and offspring arises partly from heredity and partly from direct infection. The fact that correlations offer no positive proof of inheritance seems to be no reason for discarding them as an aid to science. The fact is that heredity can be demonstrated only by measurements and deductions therefrom; and there is no gain in casting aside a convenient and accurate method of measurement and substituting for it an inaccurate one. The above defect in anthropometry is merely in the nature of a limitation; another defect charged against this method of investigation is more in the nature of an error. Pearson has said that the work of the biometricians makes no assumptions concerning the nature of the gametes, or sex cells, and this is true. But Pearl points out that it does make a biological assumption which is inaccurate. The biometrician tries to show hereditary relationship by somatic or bodily measurements, and the objection is that bodily conditions do not always represent the character of the germ plasm, and therefore somatic characters in one generation may bear no resemblance to somatic characters in the preceding generation. An illustration is color in fowls, where sometimes the offspring resemble neither parent. In such cases certainly the experimental method, or the intensive study of a single line for several generations, is the best, perhaps the only, method to be pursued. But cases in which somatic characters are not indicative of the character of the germ cells are much rarer in human heredity than they are among the lower animals. They are confined for the most part to certain abnormalities which skip a generation, or are sexlimited. With the great majority of human traits it must be admitted that somatic characters of offspring do bear a resemblance to those of one or the other parent. In the few exceptional cases where they do not, the irregularity would be anticipated from the correlations obtained, and the error could be rectified by intensive study of the inheritance of that particular character. It is safe to say that the statistical method will continue to be employed as a useful adjunct in the solution of biological problems. The present prejudice against it arises largely from misconceptions as to its proper place and its limitations. When better understood, the method will be employed with greater discrimination; but it cannot be entirely superseded. In some kinds of problems it is indispensable, for it is the only method by which the characteristics of groups of individuals may be presented. Evidence of the Inheritance of Mental Traits. The inheritance of mental traits is still questioned by a few skeptics who do accept the principle of inheritance of physical traits; but, |