INTENSIVE SEGHtEQ-ATION". 341 



proportions, they will break over their barriers and interfere 

 with each other in precisely the same way in each section. 

 Amalgamational Intension relates only to the last point. The 

 other two points have been discussed under the principle that 

 Separation always involves more or less Segregation (see the third 

 paragraph of this paper). 



Taking up again the supposed case considered under Elimina- 

 tional Intension, if the different kinds of new food were so 

 situated as to make it more or less difficult for those feeding on 

 one kind to cross with those feeding on other kinds, the repre- 

 sentatives of the species in each of the completely separated 

 districts would be divided into minor segregations of a partial 

 kind J and the difterent degrees of intercrossing between the 

 minor segregations in the separate districts would be an addi- 

 tional cause of divergence, which we may appropriately class as a 

 form of Amalgamational Intension. Occasional interchange of 

 stations by the varieties in one district would produce a degree 

 of homogeneity in the forms of one district that would not be 

 found when comparing those of different districts ; but as the 

 degrees of intercrossing between any two or more identical 

 varieties that might happen to be preserved in both districts 

 would, in all probability, differ in the different districts, the cor- 

 respondence that at first existed between certain portions of the 

 two sections would gradually disappear. "We shall find that in 

 order to ascertain with facility the number of different sets of 

 combinations in which any given number of varieties may be 

 combined while all are propagating, and the probability that 

 any given degree of correspondence will present itself in any two 

 sets of combinations that may be taken at random, we need a 

 table by which the number of permutations that may be made 

 with given numbers of things may be analyzed. I have con- 

 structed such a table, which I call the Permutational Triangle *, 

 with the aid of which the solutions of problems that would 

 otherwise require much time are easily reached. 



Returning to the above calculation, we observe that in 1024 

 experiments, under the circumstances there assumed, there would 

 probably be but one occasion in which, out of the ten identical 

 varieties which were assumed to occur in each district, the same 

 varieties would succeed in propagating in each district. We 



* I give in an Appendix this Permutational Triangle, calculated to the 

 tenth line, with au explanation of how it was formed. 



