318 NATURAL SCIENCE [November 
correlation between morphological characters and fertility of the 
specimens of a species as the theory requires cannot be denied. It 
is quite conceivable that, for instance, in insects the copulatory 
organs of one or the other species vary correlatively with the size of 
the individuals in a similar way as the horns on the head and 
thorax of Dynastid beetles, or the mandibles of stag-beetles do; 
such a variation in the copulatory organs of the males and a cor- 
responding variation in the females would necessarily have the 
result, that copulation between specimens of different size could be 
less easily effected, and would be less effective than copulation 
between individuals of the same size. Hence the premise of the 
theory, or ‘the first part,’ which ‘can only be verified by experi- 
ment, must readily be accepted, and would be admissible even if 
there were as yet no facts observed which proved that the required 
variation actually occurs. Mr Vernon promises (p. 185) to make 
further experiments in this direction, for which biologists will surely 
be very thankful. 
The second part of the theory, or the statement, that, if the 
above premise is given, a species will necessarily develop into two 
or more varieties or even fresh species, is ‘ demonstrated mathemati- 
cally. Let us examine this mathematical demonstration. Mr 
Vernon divides the 1800 specimens of a hypothetical species, which 
is assumed to vary in size from 64 to 73 inches, into three sets of 
males and females, of 300 specimens each, the sets being designated 
as S, M, and L, and s, m, and 1 respectively ; then, if it is further 
assumed, that on an average of the 300 S, 100 S will copulate 
with s, another 100 with m, and the third 100 with 1, and so also 
in the case of M and L, the total number of offspring will be—the 
total number of individuals is accepted to be constant in each 
generation— 
I. 100 Ss, 200 Sm, 300 Mm, 200 Ml, 100 LI. 
If now “ the comparative fertility of the various sized individuals is 
slightly changed,” so that for instance 100 specimens copulating 
with individuals of the same size will give birth to 120 offspring, 
100 specimens copulating with individuals of slightly different size 
will produce 95 offspring, and 100 individuals copulating with 
specimens of considerably different size will give birth to 80 off- 
spring of either sex, the total number of offspring will be distributed 
as follows :— 
II. 120 Ss, 190 Sm, 280 Mm, 190 MI, 120 LI. 
By a comparison of II. with I. Mr Vernon comes to the two conclu- 
sions (a) that the limits of variation, which originally were 64 and 
73, will be altered to 62°5 and 74°5 ; and (b) that the individuals 
