IV] STATISTICAL STUDY 41 



obtain a measure of the amount contributed to the 

 offspring by the two parents together, but even now 

 we do not find the correlation complete (I'O) because 

 the contributions from previous ancestors have also 

 to be taken into account. 



Galton was the first to introduce the idea of the 

 * mid-parent,' and he went on to attempt to estimate 

 the average contribution to the children from each 

 generation of ancestors. Since the correlation be- 

 tween offspring and mid-parent is not complete, 

 part of the heritage, which is not visibly present in 

 the parents, must be contributed from more distant 

 ancestors. Galton concluded from the data he collected 

 that on the average half the heritage of an individual 

 may be taken as derived from the two parents, one 

 quarter from the four grandparents, one eighth from 

 the great grandparents, and so on, the whole series 

 (I? h h tV — ) adding up to unity. Pearson estimates 

 the average correlation between offspring and one 

 parent, as about '5, of offspring with a grandparent 

 as '33, with a great grandparent as '22, the correlation 

 coefficient with an ancestor of each generation being 

 I of that of the next below ; these numbers, however, 

 are not in any way comparable with Galton's series 

 •5, "25, '125, etc. Galton attempted to estimate the 

 amount of the heritage received from the 'mid- 

 ancestor ' of each generation independently of what 

 was received from other generations ; but in the 



