VI.] THEIR SIGNIFICANCE IN HEREDITY. 367 



only differ from us in their use of the term 'blood' instead of 

 the term germ-plasm. Breeders say that half of the ' blood ' of 

 the offspring has been derived from the father and the other 

 half from the mother. The grandchild similarly derives a 

 quarter of its ' blood ' from each of the four grandparents, and 

 so on. 



Let us imagine, for the sake of argument, that sexual repro- 

 duction had not been introduced into the animal kingdom, and 

 that asexual reproduction had hitherto existed alone. In such 

 a case, the germ-plasm of the first generation of a species 

 which enters upon sexual reproduction must still be entirely 

 homogeneous ; the hereditary substance must, in each indi- 

 vidual, consist of many minute units, each of which is exactly 

 like the other, and each of which contains within itself the 

 tendency to transmit, under certain circumstances, the whole 

 of the characters of the parent to a new organism — the offspring. 

 In each of the offspring of such a first generation, the germ- 

 plasms of two parents will be united, and every germ-cell 

 contained in the individuals of this second sexually produced 

 generation will now contain two kinds of germ-plasm — one 

 kind from the father, and the other from the mother. But if 

 the total quantity of germ-plasm present in each cell is to be 

 kept within the pre-determined limits, each of the two ancestral 

 germ-plasms, as I may now call them, must be represented 

 by only half as many units as were contained in the parent 

 germ-cells. 



In the third sexually produced generation, two new ancestral 

 germ-plasms would be added by fertilization to the two already 

 present, and the germ-cells of this generation would therefore 

 contain four different ancestral germ-plasms, each of which 

 would constitute a quarter of the total quantity. In each suc- 

 ceeding generation the number of the ancestral germ-plasms is 

 doubled, while their quantities are reduced by one half. Thus 

 in the fifth sexually produced generation, each of the sixteen an- 

 cestral germ-plasms will only constitute j^^ of the total quantity; 

 in the sixth, each of the thirty-two ancestral germ-plasms, only 

 ^*2j and so on. The germ-plasm of the tenth generation would 

 be composed of 1024 different ancestral germ-plasms, and that 

 of the n*^ of 2»i. By the tenth generation each single ancestral 

 germ-plasm would only form y^V^ of the total quantity of germ- 



