HEREDITY 48 1 



parent and in the column representing his personal value as to 

 the character under question. When completed, such a table 

 will show the number of offspring of each particular value, and 

 also the kind of parents from which they sprung. 



In whatever direction its parts are read, such a table consists 

 of frequency distributions whose means and standard deviations 

 may be determined by the methods already given. The horizontals 

 show the distribution of offspring of like parents, the verticals 

 show the range of parents capable of producing like offspring, 

 and the totals represent the respective generations. 



One of the first tables of this kind published, and one of the 

 best for our present purposes, is the one on the preceding 

 page, from Gal ton, based on his studies of the stature of Eng- 

 lish people. 1 



1 See Gallon, Natural Inheritance, p. 208. 



In this table the heights were taken in small fractions, but recorded in i-inch 

 groups. For instance, all measurements falling between 66 and 67 inches he 

 recorded as 66.5. In attempting to do this for the sons, however, he noticed "a 

 strong bias in favor of the integral inches." Hence he adopted for these 

 measurements 66.2, 67.2, etc., instead of 66.5, 67.5, etc. As a matter of fact, 

 it makes little difference what scale is adopted, provided the same plan is always 

 observed in the matter of discarding or of recording fractions. 



One slight inaccuracy for the individual in the long run offsets another, and as 

 a whole such adjustments do not interfere with results. Trial calculations, too, 

 will show that measurements taken an inch apart give substantially the same 

 results as when taken a half inch or a quarter inch apart. 



In this table the heights of the adult children are compared with the heights 

 of the mid-parents ; that is, with the average height of the father and the mother 

 after multiplying the mother's height by 1.08, because women are, on the 

 average, one twelfth shorter than men. All female heights are, therefore, " trans- 

 formed " and recorded as male heights. This custom is observed in all statistical 

 studies involving sex ; that is, the female values are reduced to their " male equiv- 

 alents," so that sex differences are eliminated from the mid-parent, or, more prop- 

 erly speaking, everything is reckoned in terms of males. 



Early in his studies the question arose whether the mid-parental height is a 

 safe basis ; that is to say, whether the child of one tall and one short parent is, in 

 general, the same as the child of two parents whose heights are equal, but whose 

 average height is the same as the average height of the tall and the short parent ; 

 in other words, would the children of a 70- and a 64-inch parent (average 67 inches) 

 be the same as one of two parents each of whom is 67 inches in height ? 



After the study of many cases Galton found no difference. He therefore con- 

 cluded that a perfect blend takes place in respect to stature, and that the mid- 

 parental height, after making due allowance for sex differences, may be safely 

 taken as the true height of the mid-parent for purposes of heredity studies (see 

 Natural Inheritance, pp. 88-90). We have since learned that for extreme accuracy 



