THEIE SIGNIFICANCE IN HEKEDITY. 357 



sexually produced generation, each of the sixteen ancestral germ- 

 plasms will only constitute T V of the total quantity ; in the sixth, 

 each of the thirty-two ancestral germ-plasms, only ^\, and so on. 

 The germ-plasm of the tenth generation would be composed of 

 1024 different ancestral germ-plasms, and that of the n th of 2 B . 

 By the tenth generation each single ancestral germ-plasm would 

 only form Tff Vr f ^ ae total quantity of germ-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 ancestral germ-plasms, and the re- 

 sulting 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 an- 

 cestral 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 genera- 

 tion, 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- 



