SEX-CHARACTERS IJJ EVOLUTION 125 



direct effect of the stimulation. We may express 

 the process mathematically in this way. Suppose 

 the amount of hypertrophy in such a case as the 

 antlers to be x, and that some fraction of this is 

 inherited. Then in the second generation the same 

 amount of stimulation together with the inherited 



/y* 



effect would produce a result equal to x+-. The 



n 



latter fraction being already hereditary, a new 



fraction - would be added to the heredity in each 



n 



generation, so that after m generations the amount 

 of hereditary development would be #+ . If n 



were 1000, then after 1000 generations the inherited 

 effect would be equal to x. This, it is true, would not 

 be a very rapid increase. But it is possible that the 



/y 



fraction - would itself increase, for the heredity 

 7i 



might very well consist not only in a growth in- 

 dependent of stimulation, but in an increasing 

 response to stimulation, so that x itself might be 



/y 



increasing, and the fraction - would become larger 



in each generation. The death and loss of the skin 

 over the antler, originally due to the laceration of 

 the skin in fighting, has also become hereditary, and 

 it is certainly difficult to conceive the action of 

 hormones in this part of the process. All we can 

 suggest is that the hormone from the rapidly growing 

 antler, including the covering skin, is acting on the 

 corresponding factor in the gametocytes for a 

 certain part of every year, and then, when the skin 

 is stripped off, the hormone disappears. The factor 

 then may be said to be stimulated for a time and then 



