An Introduction to a Biology 



statistics we know the most probable result of the causes 

 A, B, C, D, E and the frequency of each deviation from this 

 most probable result. The recognition that in the existing 

 state of our knowledge the true method of approaching the 

 problem of heredity is from the statistical side, and that 

 the most that we can hope at present to do is to give the 

 probable character of the offspring of a given ancestry, is 

 one of the great services of Francis Galton to biometry." * 



(b) GALTON'S LAW 



Galton formulated his Law as follows : " The two parents 

 contribute between them on the average one-half, or (0-5) of 

 the total heritage of the offspring ; the four grandparents, 

 one-quarter, or (0-5) ; 2 the eight great-grandparents, one- 

 eighth, or (O5), 3 and so on. Thus the sum of the ancestral 

 contributions is expressed by the series {(0-5) + (0-5) 2 -f (0-5),3 

 etc.}, which, being equal to 1, accounts for the whole heri- 

 tage." 



(c) THE DIFFERENCE BETWEEN PEARSON'S AND GALTON'S 



LAW 



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 apprecia- 

 tion of the difference between the two is necessary to any- 

 one 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 indivi- 

 duals. This is so obvious to the careful thinker that Pearson 

 only refers to it in a footnote ; 3 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 dis- 



i Pearson, :03a, p. 215. 2 Galton, '97, p. 402. 3 Pearson, :04, p. 161. 



170 



