526 TRANSMISSION 



between offspring and grandparent, and so on indefinitely ; but 

 it would need to be done for each character separately. This 

 involves immense labor, and, moreover, we do not ordinarily 

 possess sufficiently accurate information about ancestors back 

 of the parent to enable us to make such calculations. We 

 seek, therefore, some expression for this relation, and such 

 an expression when generalized would constitute a law of 

 ancestral heredity. 



How much influence belongs to each separate ancestor ? If 

 inheritance is from the race, or in a more particular sense from 

 the family group, then, in practical breeding affairs, we need a 

 measure of the influence of each ancestor in order to know how 

 much importance to attach to the parent and how much to 

 attach to the several ancestors back of the parent. 



One generation back the total heritage rested in the two 

 immediate parents, and, roughly speaking, is to be regarded as 

 divisible equally between them. Two generations back it rested 

 in four grandparents, and, again waiving considerations of pre- 

 potency, one fourth of the heritage came from each. The third 

 generation back the heritage was divided among eight great- 

 grandparents, presumably, on the average, equally, that is, 

 one eighth coming from each. Still another remove, and no less 

 than sixteen great-great-grandparents contributed to the stream 

 that made the final heritage, and it is fair to assume that each 

 individual contributed its share, namely one sixteenth. 



Now these same sixteen individuals have contributed also to 

 the production of many other lines of descent. If we had all 

 the descendants of these sixteen great-great-grandparents of the 

 particular individual we have in mind, they would constitute a 

 large population, and we have no knowledge as to where, in their 

 frequency distribution with respect to the character in question, 

 our special individual might be found. But of all the descendants 

 of these sixteen great-great-grandparents only eight of the next 

 generation contributed to the production of the individual we 

 have specially in mind ; again, in the next generation, only four 

 have so contributed, and, last of all, out of the large population 

 descended from these sixteen ancestors, two only have produced 

 our individual. Now the law of ancestral heredity is designed 



