HfTENSIYE SEGREGATION. 339 



of accessible forms of food, ou eacli kind of which one in a million 

 of the individuals of each district might feed it' driven by 

 necessity. 



5. Now suppose the same necessity should occur in eacli district 

 through the destruction of the leaves on which they habitually 

 feed ; and that there are accordiugiy in each district a hundred 

 survivors able to maintain themselves on other kinds of food. 



Under such circumstances (the corres])ondences of which we 

 have in our supposition made much more exact than the actual 

 deviations from a mean ever present) — but even under such cir- 

 cumstances of completely parallel variation — what is the proba- 

 bility that in each of the separate districts the few that would 

 meet with other individuals and have an opportunity to propa- 

 gate the species would be similarly endowed and similarly related 

 to the environment ? 



In order to still further simplify the problem, let us assume 

 that in the case of each kind in each district the probability that 

 it will succeed in propagating is exactly balanced by the proba- 

 bility that it will fail. The probability, then, that any given 

 number of the ten kinds in a given district will succeed is found 

 by estimating the number of combinations that can be secured 

 by taking that number of things out of ten things in different 

 ways. This is completely parallel to the number of ways in 

 which ten pennies can be arranged as to head and tail, each penny 

 representing one form of variation, and its lying head-up indicating 

 success in propagating. In 1024 experiments the probability is 



That will succeed 1 time 



,, Y =10 times 



10x9 _ .K 



1UX9XS _ .^.v 

 1x2x3 ~ " 



1 0x9x8x 7 — o-\o 



1x2x3x4 -■''' " 



„ 252 „ 



„ 210 „ 



„ 120 „ 



45 „ 



„ 10 „ 



