CALCULATION. 367 



tlio ivsult would be a chaos of male forms gradually passing into 

 each other and all belonging to a single female form. And he 

 adds that this result, mathematically calculated, stands in tren- 

 chant contrast to the facts, for it Ls kno^n on the contrary that 

 the secondary sexual characters of male beetles, in by far the 

 greater number of cases, are extremely constant. 



FIG. 97. ChaJcotoma allot, from the Philippines ; the upper one to the left is the horned 

 form of male (('. Atlas, Linn.), the upper one to the right is the almost hornless form 

 (C. Phidias, Blain.). Below is the female. Half natural size. 



But Kramer has not taken one element into his calculation 

 which ought, under the circumstances, to have been, duly con- 

 sidered ; he calculates only the results of an unlimited capacity 

 for variation in the males, while it is precisely this variability 

 which, according to Darwin's views, will be limited by sexual 



