102 ANALYSIS OF THE FOUR PRINCIPLES. 
pure-breeds, which in my tables is represented by M, is 40; and the 
multiplier for the half-breeds is also 40, 2. e., m = 40. And once more, 
let us assume that of the cross-breeds which have their homes on 
the ground with the original stock only 1 in 40 reaches maturity; 
that is, on account of the number of their enemies and the severity of 
the competition for food, their real multiplier, after all the conditions 
of survival have had a chance to operate, is 40 x yy =1. In other 
words, the original stock and the half-breeds mingled with them are 
simply able to hold their own, without any continuous increase. On 
the other hand, the arboreal group are so free from enemies and so 
" well provided with food that three-fourths of them come to maturity, 
and their multiplier when corrected is 4o x #= 30. 
Let us assume that the other half of these rats feeding on the trees 
are of the variation 6, with instincts leading them to spend one-third 
of their time on the ground, and accordingly one-third of them mate 
with the original stock and have their nests on the ground. Asin the 
case of variation a, the multiplier for pure arboreal breeds is 30 and 
for cross-breeds is 1. 
Let us now suppose that there is an arboreal colony of 60 individ- 
uals occupying a forest on one of these islands, and that 30 of them 
belong to the variation a, and 30 of them to variation b. What will 
be the number of pure-breed arboreal ratsin the next generation, and 
of these how many will be the offspring of variation a and how many 
the offspring of variation b? 
Of variation a one-half cross with the original stock and we have— 
Cross-breeding offspring, 15 x I = 15. 
Pure-breed offspring, 15 x 30 = 450. 
Of variation b, one-third cross, and we have— 
Cross-breed offspring, 10 x 1 = 10. 
Pure-breed offspring, 20 x 30 = 600. 
. Therefore, in the next generation of the pure-breed colony in the 
trees there will be 1,050, of which three-sevenths are offspring of varia- 
tion a and four-sevenths are offspring of variation b. It follows 
that through hereditary influences the average instinct for arboreal 
life will be increased; and we may expect it to continue to increase 
in the same way in successive generations. 
But there is a psychological influence that will come in to exaggerate 
the segregative tendency. ‘The 1,050 rats of the generation we have 
now reached have been reared on the trees of the dense forest or jungle, 
where they may travel over a considerable area without descending 
to the ground, and have formed the habit of spending their whole time 
in the trees, so that not 1 in 100 will mate with the ground rats; and 
