i68 THE FIRST PRINCIPLES OF HEREDITY 



on, the sum of the series i + i + i + TV+ • • • being equal 

 to I, as it should be.* Or, as expressed by Pearson, this 

 series would stand : 



0-5 + (0-5)2+ (0-5)3+ (0-5)4+ .... (o-5)>^=i, 



though, using his own coefficient of correlation, he found 

 slightly different values. 



The diagram on p. 169 illustrates Galton's Law of 

 Ancestral Inheritance. Only four generations are here 

 recorded in the square (the original individual, equal to 

 the whole square, being numbered i, the two parents 

 2 and 3, the four grandparents 4, 5, 6, 7, etc.), but their 

 number could be increased indefinitely. 



Viewed from another standpoint, this law gives us " the 

 average amount of resemblance between an individual and 

 any particular ancestor." 



The above law being based on the Coefficient of Correla- 

 tion, Pearson has shown a most important corollary to 

 flow from it. If we introduce artificial selection at any 

 given point of the ancestry, what will be the result on the 

 progeny ? Pearson has calculated the exact values of any 

 selected character for the successive generations. Thus, 

 if we choose stature in man for selection, and select a 

 mid-parent having a height, h, above the average popula- 

 tion, P, then the offspring (first generation) of this 

 mid-parent will differ only f h, or 0-62, from P. The 

 second generation, having parents and grandparents of 

 the selected type, will differ only by 0-82 h\ the third 

 generation by 0-89 h, and so on up to 0-92 h. So that finally 

 a race could be bred aU the members of which would not 



* This law must not be confused with the statement on p. 75 

 about the " Quantitative Contribution of Ancestors." It was 

 there stated that the contribution of each parent is half, as each 

 parent furnishes half the hereditary substance of the child. This 

 is so, but it'^must be remembered that each parental germ carries 

 within itself the constituents of the whole ancestral line. If we 

 subtract the contributions of all these ancestors, the parents them- 

 selves contribute each only one-quarter to the constitution of the 

 child. 



