196 G. Udny Yule. 
referring generally to all phenonema covered by the aphorism 
“ like begets like.” In this sense it denotes inter alia the phe¬ 
nomenon of the constancy of specific or racial types and of 
sexual characters; a character may be said to be inherited 
when it always, in one generation after another, is one of 
the characters of the species, of the race, or of the one sex of the 
race, as distinct from the other. The species, race or sex, so to 
speak, “ begets its like ” as a whole. But then a further question 
remains; even if the type of the race is constant, do individual 
types within the race beget their like ? In so far as any individual 
diverges in character from the mean of the race do his offspring 
tend to diverge in the same direction, or not? It is to this question 
that statisticians have confined themselves, and they speak of a 
character being “ inherited ” or not according as the answer to the 
question is yes or no—they deal solely with what we may term 
“ individual heredity.” 
The quantitative procedure is in its essence extremely simple, 
though the actual work may often be rather lengthy. A series of 
measurements is made of some one variable character, e.g. a 
length, in parents and in their offspring, noting the individual 
families (the more the better) and not merely measuring the first 
generation as a whole and then their offspring as a whole. From 
these measurements an equation is derived, giving, as nearly as 
may be, the mean character of the offspring in terms of the 
character of the parent. Supposing X to be the character in the 
parent, Y the mean character in the offspring, then the simplest 
form of such equation is:— 
Y = A + B. X. ( 1 ) 
Where A is a dimension of the same order as X or Y, and B is a 
number that will vary from case to case. We have for instance 
from the data collected by Mr. Galton for inheritance of stature in 
man, reduced by Professor Pearson, the equation relating mean 
stature of sons and stature of father :— 
Y = 3M0 + -45 X. * ( 2 ) 
i.e. the mean stature of sons is 31T inches, together with nine- 
twentieths of the stature of the father (also in inches of course). 
The father’s stature is thus some guide to the stature of his 
offspring ; it enables us to form a closer estimate of their stature 
than we could from a mere knowledge of the mean characters of 
the race, and we may therefore say that stature is an inherited 
character. The sons do diverge from the race-mean in the same 
