324 STATISTICAL STUDY OF INHERITANCE 



one-quarter, or each of them one-sixteenth ; and so on, the 

 sum of the series i + J + i + tV + • • • •> being equal to i, as it 

 should be. It is a property of this infinite series that each term 

 is equal to the sum of all those that follow : thus 2 == i + ¥ + iV 

 + ••••, i = I + tV + ••• •' a-nd so on. The prepotencies or 

 sub-potencies of particular ancestors, in any given pedigree, are 

 eliminated by a law that deals only with average contributions, 

 and the varying prepotencies of sex in respect to different quali- 

 ties are also presumably eliminated." Thus an inheritance is 

 not merely dual, but through the parents it is multiple, and 

 the average contributions made by grandparents, great-grand- 

 parents, etc., are definite, and diminish in a precise ratio according 

 to the remoteness of the ancestors. 



Diagrammatic Expression. — ^The proportions contributed on 

 an average by the parents, grandparents, great-grandparents, etc., 

 may be seen at a glance from a diagram (on the opposite page) 

 which we have borrowed from one of Mr. Galton's papers. 



Pearson's Statement of Galton's Law. — Prof. Karl Pearson 

 states Galton's law in the following form : " Each parent con- 

 tributes on an average one-quarter or (o'5)", each grandparent 

 one-sixteenth or (o'5)*, and so on ; the occupier of each ancestral 

 place in the wth degree, whatever be the value of n, contributes 

 (o'5)2" of the heritage." He calls attention to the extreme 

 importance of the law, for " if Darwinism be the true view of 

 evolution — i.e. if we are to describe evolution by natural selection 

 combined with heredity — then the law which gives us definitely 

 and concisely the type of the offspring in terms of the ancestral 

 peculiarities is at once the foundation-stone of biology and the 

 basis upon which heredity becomes an exact branch of science " 

 {(grammar of Science, 1900, p. 479). Elsewhere he says : " The 

 law of ancestral heredity is likely to prove one of the most brilliant 

 of Mr. Galton's discoveries ; it is highly probable that it is the 

 simple descriptive statement which brings into a single focus all 

 the complex lines of hereditary influence. If Darwinian evolution 



