1894.] The Numerical Intensity of Faunas. 753 
On the other hand a more recondite suggestion is made in 
this inquiry. Favorable conditions for the multiplication of a 
species, such as temperature, food-supply, freedom from 
enemies, habitability of station, etc., naturally assist numerical 
increase. But the speculation suggests differences in the time 
required for a species to attain momentum, the time required 
for it to reach the maximum rate of increase, when its vitality 
has attained such force as to most effectually overcome hamper- 
ing conditions, and is recorded in the number of individuals 
produced at one period. This question touches the surmises 
made as to the manner of specific introductions. Does a 
species make its appearance in one example—as an individual 
—on the world's stage or, if dicecious, in pairs, and then pro- 
ceed to establish its currency, and so in geometrical ratio of in- 
crease engage itself in subjugating its environment and dispers- 
ing or suppressing its competitors? Or do species appear in 
numbers, and from separated points of occupation begin spread- 
ing, until their divided areas coalesce, and their geographical 
coincides with their numerical maximum? Or finally does 
the manner of their entrance into life vary for different species, 
or the species of different groups in both these ways?  Itseems 
probable that the higher orders of animals—especially the 
vertebrates—are sporadic in their appearance, viz., differentiate 
as individuals, while the lower are massive, viz., differentiate 
in hosts. 
Conditions being equal the invertebrates should reach their 
numerical maxima quicker than the higher vertebrates, and 
their maxima should, comparatively, reach enormously higher 
figures. What the functional activity of procreation in 
a new species is, cannot be determined. It would seem prob- 
able that if specific variation were a process of insensible or 
slightly sensible changes in forms or external physical features, 
the correlated disturbances of function would be imperceptible 
and the new species would earry on the work of self-propaga- 
tion with the same energy as the allied species amongst whom 
it makes its appearance. The actual numerical results would 
be at first low, because of the smaller number of individuals of 
the new species and would increase as that number enlarged, 
