THE LAW OF ANCESTRAL INHERITANCE 129 



existence in the germ-plasm of definite units carrying definite 

 characters, and the regular halving in the average strength or 

 amount of such characters during the reducing division of the 

 nuclear matter of the sex-cells which precedes each act of 

 reproduction." 1 



215. Apparently, then, each ancestor is supposed to contribute 

 a unit to the germ-plasm, which, since the contributions taken 

 together amount to unity, is thus totally compounded of ancestral 

 units two large units from the parents, four units each a quarter as 

 large from the grandparents, and so on. But each ancestor's unit is 

 also totally compounded of units from his ancestors, whose units in 

 turn are totally compounded of units from their ancestors, and so on 

 in endless recession. Now, imagine a line of individuals, A,B, . . . 

 Y,Z. Then Z will have a unit from A. He will also have one 

 from B (which will contain a contribution from A). Likewise, he 

 will have one from C (which will contain a contribution from A 

 and one from B [which will contain one from A]). Yet again Z 

 will have a unit from D (which will contain a contribution from 

 A and one from B [which will contain one from A] and another 

 from C [which will contain a contribution from A and one from B 

 {which will contain a contribution from A}]) and so on. Obviously 

 A's unit will be repeated many times over, in almost infinite sub- 

 division, in all the contributions of his descendants. So, also, as 

 regards B's unit and the units of the other ancestors, especially the 

 more remote. Really, however, ancestral contributions have not 

 this ideal simplicity of composition ; for every individual is of 

 almost infinitely long descent, and if of a sexually dimorphic species, 

 has two parents, four grandparents, eight great-grandparents, and 

 so on. 



216. At first sight a law of ancestral contributions seems simple : 

 we suppose merely that each ancestor adds something representing 

 himself to the germ-plasm. If, however, we make the necessary 

 rigorous deductive inference of consequences, it becomes almost 

 unthinkable. It is opposed, in language at any rate, to the notion 

 that the ancestors of the germ-cells are, not ' individuals,' but the 

 cells of the germ-tract, which merely dwell within the individuals. 

 Notwithstanding all its appearance of mathematical precision, it is 

 so vaguely expressed that I doubt if any two people understand it 

 alike. 2 I describe it as I understand it, or as far as I am able to 



1 Vernon, Variations in Animals and Plants, pp. 134-5. 



2 " This law, that the mean Characters of the offspring can be calculated with 

 the more exactness, the more extensive our knowledge of the corresponding characters 



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