THROUGH CUMULATIVE SEGREGATION. 
249 
small, the water will in time find a common level in both tanks, 
unless there are additions or subtractions of water that prevent 
such a result. So, in the case under consideration, final fusion 
will take place, unless differentiation progresses more rapidly than 
the fusion, or some other influence comes in to counteract the 
levelling influence of occasional crosses. If, under such condi- 
tions, some branch of the partially Segregated variety becomes 
more fertile when generating with members of the same variety, 
and less fertile when generating with other varieties, a principle 
will be introduced tending to strengthen any form of partial 
Segregation that already exists between the varieties. This 
principle when co-operating with partial Segregation will produce 
pure masses of each variety, when, without the action of this 
principle, all distinctions would be absorbed by the crossing. 
We know that a transition from Integrate Fecundity to Segre- 
gate Fecundity usually takes place at a point in the history of 
evolution intermediate between the formation of an incipient 
variety and a strongly-marked species ; and though the causes 
that produce this transition may be very difficult to trace, I 
believe the results that must follow can be pointed out with 
considerable clearness and certainty. 
Darwin’s investigations have shown that in many cases, if not 
in the majority, the relation of varieties to each other is that 
which I have called Integrate Fecundity and Integrate Vigour; 
that is, the highest fertility is attained when varieties are crossed, 
and the vigour of offspring thus produced is greater than when 
the intergeneration is within the limits of one variety. He, 
however, gives in ‘Variation under Domestication,’ chapter xvi., 
some special cases, in which “ varieties of the same species behave, 
when crossed, like closely allied but distinct species ” ; and re- 
marks that similar cases “ may not be of very rare occurrence ; 
for the subject has not been attended to.” The same cases are 
also mentioned in all the editions of the ‘ Origin of Species.’ * 
The problems that arise in considering the different results 
produced by different degrees of Positive Segregation and Segre- 
gate Fecundity are of a nature suitable for mathematical treat- 
ment. Before, however, computing the effects of Segregate 
Fecundity when co-operating with Positive Segregation, it will be 
in place to show that it is of itself only a negative form of 
* See 1st edition, p. 238 ; 5th edition, p. 259; 6th edition, p. 258. 
