486 TRANSMISSION 



This mediocrity is, therefore, a thing always to be reckoned 

 with by the breeder who hopes to attain uniform success with 

 improved strains. He cannot free himself from its influence. 

 We shall see that its pull is not less than 50 per cent. The fail- 

 ure to know this fact, and the willingness to rest the case with 

 the immediate parents and to assume that " like father like son " 

 is the way of heredity, or to accept purity of blood (pedigree) as 

 synonymous with uniformity of type, this is the one fertile 

 cause of the greatest failures in stock breeding. The only sure 

 basis of uniform success lies in a uniformly excellent ancestry 

 for at least five or six generations back. 1 Then the " drag of 

 the race" will become a friend and not an enemy of improve- 

 ment ; but, no matter how excellent the ancestry, it can never 

 equal the exceptional parent. In order to make the most of him, 

 therefore, this drag should be reduced to a minimum. 



SECTION VI THE MEASURE OF HEREDITY 



Now this regression is the pull of the ancestry back of the 

 parent, and it is the best argument for the fact that inheritance 

 is partly from the race and not exclusively from the immediate 

 parent. Clearly, we need a measure of the degree of resemblance 

 between the offspring and the immediate parent, so that we may 

 know how much to credit to the parent and how much to credit 

 to the back ancestry through regression. Such a measure of 

 resemblance between mid-parent and offspring will be a good 

 measure of heredity, and it is called the coefficient of heredity. 



The coefficient of heredity. Fortunately this involves no new 

 conceptions and no new methods. The regression table is noth- 

 ing more nor less than a special form of correlation table in which, 

 instead of involving two characters in the same set of individuals, 

 we seek the correlation between two sets of related individuals 

 with respect to the same character. 



Thus, in the table of statures, we have in fact a correlation 

 table between mid-parents and sons with respect to stature, and 

 its correlation coefficient (r) 2 is for them a coefficient of heredity. 



1 See Law of Ancestral Heredity, sect, xiv of this chapter. 



2 The coefficient of correlation is everywhere denoted by the letter r. 



