NATURAL SELECTION SINCE DARWIN 73 



of a species and by A+l, A + 2, etc., the variations 

 differing in degree from the point of view of a cer- 

 tain character which they all possess. Let us suppose 

 that in the course of every generation each individual 

 gives birth to n similar individuals and to 2 indi- 

 viduals differing slightly, one in a negative and one 

 in a positive direction. After the second generation 

 we shall find : 



«A+1 (A+l) + l (A— 1) 



Now if we figure out the descendants of A + 1, we 

 will find in the third generation : 



n (A+l) + l (A + 2) + l A 



Whatever the number of generations considered 

 may be, variations will always outnumber constant in- 

 dividuals. The ratio of variations to constant types 

 is at the beginning 2/n; if the two variations (A+l) 

 and the n constant types produced only individuals 

 identical to them, the ratio would remain the same; 

 but such is not the case. 



Let us consider separately the descendants of the 

 variations and of the constant types. If for a gen- 

 eration the number of constant types is n and the 

 number of variations 2, the n constant types will, 

 according to Delboeuf, produce n z similar individuals 

 and 2Xn dissimilar individuals, which will then in- 

 crease the number of variations. On the other hand, 



