378 BEV. J. T. GULTCK OK 



and divergence. Want of space in'my first essay made it neces- 

 sary to postpone the full discussion of this part of the theory ; 

 but in the present paper I have sought to point out some of the 

 more manifest principles on vphieh this general law of Intension 

 rests. There are undoubtedly other principles of transformation, 

 which, when combined with separate breeding, inevitably produce 

 divergent instead of parallel evolution ; but the principles pointed 

 out in this paper are sufficient to establish the general tendency, 

 and to show that natural selection is by no means the only prin- 

 ciple on which the law rests. If we could obtain sections of a 

 species presenting exactly the same average character, and if we 

 could prevent all the principles of transformation from coming 

 in to aid in the process, separate breeding under such conditions 

 would perhaps never produce divergence ; but, as separation never 

 produces exactly equivalent sections, it always tends to introduce 

 transformation, through changed or unbalanced action in prin- 

 ciples that would otherwise be unchanged and balanced in their 

 action and therefore without transforming influence, and trans- 

 formation in the separated sections inevitably becomes divergence. 

 We thus gain an explanation of the fact that Isolation, even when 

 accompanied by exposure to the same environments, usually in- 

 troduces divergent forms of Selection, natural, sexual, social, or 

 dominational, and often new effects from the action of other 

 principles." Independent G-eneration precedes and determines 

 the possibility of the divergence, and if it is segregative, it also 

 determines in a measure the form of the divergence ; but if it is 

 simply separative, the form of the divergence depends on some 

 other principle or principles. 



APPENDIX. 



Construction of the Permutational Triangle. 

 In the last chapter of my paper on " Divergent Evolution 

 through Cumulative Segregation" (p. 250) I referred to the 

 Permutational Triangle, which I had constructed to facilitate 

 the solution of a problem there raised in regard to the degree 

 of probability of extinction that would, under certain conditions, 

 result from Segregate Fecundity. The first four lines of the 

 table were obtained by direct observation on the permutations 

 of letters arranged to represent the pairing of animals entirely 



