356 ON THE NUMBEB OP POLAR BODIES AND 



demanded by our hypothesis is that there should be complete or 

 approximate equality between the quantities of hereditary sub- 

 stance derived from either parent. If then the germ-cells of the 

 offspring contain the united germ-plasms of both parents, it follows 

 that such cells can only contain half as much paternal germ-plasm 

 as was contained in the germ-cells of the father, and half as much 

 maternal germ-plasm as was contained in the germ-cells of the 

 mother. This principle is affirmed in a well-known calculation 

 made by breeders of animals, who 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 homo- 

 geneous ; the hereditary substance must, in each individual, con- 

 sist 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 con- 

 tain four different ancestral germ-plasms, each of which would 

 constitute a quarter of the total quantity. In each succeeding 

 generation the number of the ancestral germ-plasms is doubled, 

 while their quantities are reduced by one half. Thus in the fifth 



