56 CALIFORNIA ACADEMY OF SCIENCES. 



smallest individual of the species, and 550 in the largest. 

 There could be, then, no variation due to sexual admix- 

 ture which fell below 500 or rose above 550, and hence 

 no progress would be possible. 



Another difficulty in Weismann's theory of variation 

 has been recently communicated to Nature., by Prof. 

 Marcus Hartog."^ He argues from the assumption that 

 Weismann's theory is proved, and the result is, as he 

 says, indeed a startling one. He first presents five theses 

 expressing the main assumptions of Weismann's theory, 

 which Poulton has since admitted to be an impartial and 

 correct statement of the case. They are as follows: 



" I. Each primitive germ-cell of either sex, contains 

 a number of ancestral germ-units, the ahnenplasmas; 

 and this number is constant, for the species at least. 



II. These ancestral germ-units are far more con- 

 stant and unchangeable in character than the species 

 itself. 



III. They lie associated together in the germ-cell 

 without loss or alteration of their individual peculiar- 

 ities. 



IV. The number contained in the mature ovum 

 and spermatzoon is reduced by one-half, and in the 

 fertilized ovum or oosperm the number is restored to the 

 normal by the summation of the ahnenplasmas of the 

 two fusing cells. This process is comparable to the 

 shuffling of two packs of cards by taking half from each 

 and joining the talons or remainders to form a new 

 pack. 



V. The possible combinations under this process 

 are so numerous as to explain the variations among the 

 offspring of sexual union. 



Accepting these statements, we next inquire, How 



* Nature, October 29, 1891, p. 613. 



