Manchester Memoirs, Vol. I. {igo6), No. 11. 5 



parents contribute between them on the average one-half, 

 or (o'5) of the total heritage of the offspring ; the four 

 grandparents, one-quarter, or (o"5)" ; the eight great-grand- 

 parents, one-eighth, or (o'5)^ and so on. Thus the sum of 

 the ancestral contributions is expressed by the series 

 {(o'5)+(o"5/-f(o'5)^ &c.}, which, being equal to i, accounts 

 for the whole heritage." * 



2 {c). The Difference between Pearson's and Galton's Laiv. 



It will be seen how profoundly Galton's differs from 

 Pearson's Law. Yet the belief that the two are much the 

 same is not rare, and the statement that the latter is 

 merely an extension of the former is often made. A clear 

 appreciation of the difference between the two is necessary 

 to anyone who wishes to be conversant with modern 

 theories of heredity. 



One feature the two have in common ; both of them 

 are true only of masses, and do not pretend to apply to 

 individuals. This is so obvious to the careful thinker that 

 Pearson only refers to it in a footnote if yet it is often 

 forgotten. The difference between the two lies in this : 

 Pearson's Law measures the degree of correlation between 

 a character or characters in a given generation, and 

 some similar (or dissimilar) character or characters in 

 the preceding generation. Galton's Law states the 

 amount which a given generation contributes^ to the 

 generation which it produces. It definitely states that 

 on the average a half of the filial generation are like the 

 parental, a quarter like the grandparental,and an eighth like 

 the great-grandparental, and so on. From the knowledge 

 that the parents of a given generation of cats are tabbies, 



• Galton, '97, p. 402. 

 t Pearson, :04, p. 161. 

 + See Appendix B. 



