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 Ml, 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 02*5 and 74"5 ; and (b) that the individuals 



