344 NATURAL SCIENCE. Nov.. 1895. 



quality taken from a group of individuals will, therefore, be a test of 

 interbreeding, and we shall be able to say, after the inspection of 

 such a curve, whether or not the individuals measured belong to one 

 or more interbreeding groups; this method of inquiry has already been 

 put in practice and is yielding very valuable results. (See Natural 

 Science, vol. vi., pp. 217-221.) Now interbreeding is essentially a 

 result attainable by sexual intercourse alone, for the products of 

 asexual reproduction are offspring which start on deviating lines, and 

 never mix their qualities with their mates, so long as asexual multipli- 

 cation continues. Only in those groups of individuals which inter- 

 breed by sexual union do we find that the mass of the progeny tends 

 towards the mean or average, and as Galton in his later work, 

 " Natural Inheritance," has insisted, the progeny of a sexual union 

 approaches even nearer to the mean type or mid-species than does the 

 mid-parent itself. 



B B^ 



C 



E E' 



X 

 G G' 



(i) (ii) 



Fig. 5. — Diagrams to illustrate (i) asexual and (ii) sexual reproduction : (i) An 

 individual, A, divides into two, these into four, and these into eight individuals. No 

 interaction between individuals occurs, (ii) Two individuals, B and B^, unite and 

 produce C and CV C^ unites with another individual, D, to produce E and E^, 

 E unites with F to produce G and G^. Constant interaction occurs. 



We find, then, that as an actual fact sexual union between 

 members of a group of individuals leads to a convergence towards a 

 mean or average type, and that under constant surrounding conditions 

 this type is preserved. It is curious that those writers who have 

 discussed the utility of sex should have overlooked the results of 

 Quetelet's and Galton's work, for here we find an answer to many of 

 their inquiries. It is true that Quetelet and Galton did not interest 

 themselves in the question from the same point of view that we have 

 taken up : they were more concerned in determining the actual mean, 

 and the law of deviation from that mean. Nevertheless, the facts 

 they gleaned were ready at hand, and obviously bear on this and 

 many other biological problems, 



The convergence to the mean is, then, a result of sexual reproduc- 

 tion ; it maybe termed the Role of Sex, and one, indeed, of no second 

 order. The tendency constantly to vary is a property inherent in 

 protoplasm, yet often for long periods of time the environment may 

 be the same. In order that a species may continue to live in such a 

 constant environment, the effects of variation must be checked. 

 Sexual multiplication, a conservative function, antagonises the pro- 

 gressive tendency of variation. ^ ^^^^^ Haycraft. 



