368 ON THE NUMBER OF POLAR BODIES AND [VI. 



plasm contained in a single germ-cell. We know nothing 

 whatever of the length of time over which this process of 

 division of the ancestral germ-plasms may have endured, but 

 even if it had continued to the utmost possible limit — so far 

 indeed that each ancestral germ-plasm was only represented 

 by a single unit — a time would at last come when any further 

 division into halves would cease to be possible ; for the very 

 conception of a unit implies that it cannot be divided without 

 the loss of its essential nature, which in this case constitutes it 

 as the hereditary substance. 



In the diagram represented in Fig. I. I have tried to render 

 these conclusions intelligible. In generation i. each paternal 

 and maternal germ-plasm is still entirely homogeneous, and 

 does not contain any combination of different hereditary 

 qualities, but the germ-plasm of the offspring is made up 

 of equal parts of two kinds of germ-plasm. In the second 

 generation this latter germ-plasm unites with another derived 

 from other parents, which is similarly composed of two an- 

 cestral germ-plasms, and the resulting third generation now 

 contains four different ancestral germ-plasms in its germ-cells, 

 and so on. The diagram only indicates the fusion of ancestral 

 germ-plasms as far as the offspring of the fourth generation, 

 the germ-cells of which contain sixteen different ancestral 

 germ-plasms. If we imagine the germ-plasm units to be so 

 large that there is only room for sixteen of them in the nuclear 

 thread, the limits of division would be reached in the fifth 

 generation, and any further division into halves of the ancestral 

 germ-plasms would be impossible. 



Now however minute the units may be, there is not the least 

 doubt that the limits of possible division have been long since 

 reached by all existing species, for we may safely assume that 

 no one of them has acquired the sexual method of reproduction 

 within a small number of recent generations. All existing 

 species must therefore now contain as many different kinds of 

 ancestral germ-plasms as they are capable of containing ; and 

 the question arises, — How can sexual reproduction now pro- 

 ceed without a doubling of the quantity of germ-plasm in each 

 germ-cell, with every new generation ? 



There is only one possible answer to such a question : — sexual 

 reproduction can proceed by a reduction in the nitjnOer of 



