340 EEV. J. T. GULICK OS 



These figures are found in the eleventh line of what is known 

 as the "Table of the Binomial Coefficients," or the "Arithmetical 

 Triangle"*. And so in the case of any number of objects, the 

 number of combinations that may be made with n objects is 

 found in the n + lth line of the Arithmetical Triangle classified 

 according as there are 0, 1, 2, 3, or more objects in each combi- 

 nation. The whole number of combinations may also be found 

 by calculating the nth power of 2. 



The possible combinations of the ten varieties in question are 

 1024, which is equal to 2 raised to the 10th power; the proba- 

 bility, therefore, that the combination that succeeds in one 

 district will also succeed in the other district is jjyjl' or 1 in 

 1024 ; while the probability that those that succeed in the one 

 district will not be all the same as in the other will be y^ff, or 

 1023 in 1024, which is more than a thousand times greater than 

 the reverse probability. 



These 1024 different results, any one of which may occur in 

 one section, are calculated on the supposition that all the repre- 

 sentatives of the species in one section that succeed in propa- 

 gating will in time coalesce by intercrossing ; but, as we shall 

 presently see, the number of divergences in the two sections may 

 be vastly increased by the diversity of ways in which the same 

 varieties may be combined through the greater or less influence 

 of minor segregations within the bounds of each district. 



AMALaAMATIONAL InTENSIOj^. 



In my paper on "Divergent Evolution though Cumulative 

 Segregation," p. 233, I have referred to the fact that the vast 

 majority of divergent forms produced by Segregation, after 

 existing for a time, are interfused with competing forms of the 

 same species. Now it is evident that when a permanent Segre- 

 gation arises, if in the separate sections there is a diversity of 

 amalgamations between the slightly divergent forms produced by 

 partial segregations, the results will be divergent in these sepa- 

 rate sections. That there will be diversity in this respect, we 

 may argue : first, from the improbability that all the varieties 

 in one section will occur in each of the other sections ; second, 

 from the improbability that if the same varieties occur in each 

 section, they will occur in the same proportions; and, third, 

 from the improbability that if they are the same and in the same 

 * See ' Principles of Science,' by W. S. Jevons. 



