AVERAGE RADIUS OF DISTRIBUTION. 221 
the other hand, Apex, which for the most part occupies trees and 
shrubs on the ridges which are connected with each other through the 
central ridge of the mountain range, and Amastra and Leptachatina, 
’ which are for the most part found on the ground under dead and de- 
caying leaves, seem to possess better opportunities for migration than 
either the Achatinella or Bulimella. Corresponding with these facts 
we find the species of Achatinella and Bulimella especially limited in 
the areas they occupy, while the species of Apex, Amastra, and Lep- 
tachatina are less so. For example, the area occupied by Amastra 
turritella, A. tristis, and A. ventulus includes the areas occupied by 
many species of Achatinella and Bulimella; and Apex loratus and 
A. pallidus, occupying the mountain ridges, range from Makiki to 
Halawa, exceeding the range attained by any arboreal species occupy- 
ing the valleys of the same region. 
(6) When a group of divergent forms that are fertile with each other ts 
being developed through the influence of local or geographical isolation, 
other conditions remaining constant, the number of forms that will be pro- 
duced within a gen area will vary inversely as the square of the average 
radius of distribution for the different forms. As this average radius of 
distribution may be taken as the measure of the power and opportu- 
nities for migration, we may say that, other powers and opportunities 
remaining constant, the number of species developed within a givenarea 
will vary inversely as the square of the average power and opportunities for 
migration. 
Though migration is in one sense a cause of isolation, it is evident 
that the number of isolated groups of individuals of a given form 
within a given area does not increase with the increase of migration. 
Isolation 1s produced by the great contrast between ordinary and extraor- 
dinary combinations of opportunities for migration; and this contrast is 
liable to be as great in the case of species that have limited powers 
and opportunities as in the case of those that have very great powers 
and opportunities. The number of isolations thus produced that can 
exist within the limits of a given area must vary inversely as the square 
of the power and opportunity for migration. 
The facts of distribution we have been considering seem to corre- 
spond to this law. 
(7) Forms that are most nearly related, and are, therefore, the least 
subject to sexual and impregnational isolation, are distributed in such a 
manner that their divergence 1s directly porportional to their distance 
from each other, which 1s also the measure of the time and degree of their 
geographical tsolation; while those most mantfestly held apart by sexual 
instincts and impregnational incompatibilities do not follow this law. 
