250 REV. J. T. GULICK ON DIVERGENT EVOLUTION 
Segregation, having no power to ensure the propagation of the 
varieties thus characterized, though they are fully adapted to 
the environment. This is most easily brought to light by con- 
sidering the effect of a high degree of this quality when Posi- 
tive Segregation is entirely wanting, or when it is sufficient to 
give simply a chance of Segregate Breeding by bringing each 
individual near to its natural mate. For example, let us suppose, 
1st, that a male and a female each of several allied hut mutually 
sterile species are brought together on one small island, all other 
tendences to Positive Segregation being removed, while mutual 
sterility still remains ; 2nd, that a male and female when 
once mated remain together for the breeding-season ; and 3rd, 
that all find mates. Now, if we have 7 species, each represented 
by one individual of each sex, what is the probability that all the 
species will be propagated ? And what the probability for the 
propagation of none, or of but one, or of but two, or of but three 
of the species ? The answers, as I have computed them, are as 
follows : — The probability that none will be propagated is 4 ; 
that 1 species will be is ; that 2 species ; that 3 species 
; that 4 species ^ ; that 5 species g- that 7 species 
iTffTiJ. These numerators are found in the 7th line of a table of 
figures which I call the Permutational Triangle. If we have 10 
species, the probability that in any one trial no species will 
match truly and be propagated is fiHrolT 5 that 1 species will 
match truly and propagate is 5 that 10 will is 3 ^ 7 ^ uU- 
This means that if 3,628,800 trials are made, one of them will 
probably be a case in which each male pairs with the female of 
the same species, while 1,334,961 will be cases in which none are 
so matched, and 1,334,960 will be cases in which one pair is so 
matched. It therefore appears that more than T 8 T of the proba- 
bilities are against the continuance of more than one of the ten 
species. 
There will perhaps be some hesitation in receiving these 
figures before I have given the method by which the results have 
been reached ; but the necessary length of this paper, even when 
restricted to the briefest discussion of general principles, induces 
me to reserve my computations for another occasion. It is 
not, however, necessary to have a complete solution of this 
problem, in order to reach the conclusion that the origin of 
separate races and species depends not only upon their adap- 
tation to the environment and their mutual sterility when 
