46 NATURAL SCIENCE [January 



ones, or supposing the original 300 medium individuals had again 

 been produced, there would now be 303'2 instead of 300 tall and 

 short ones." I have to reply : 



(1) That, as the individuals under II. 5. are not the offspring of 

 those under I. &., but of the individuals II. a., the number of tall and 

 short offspring II. &. is smaller than the number of their tall and 

 short parents under II. a. after the reduction to 900. 



(2) That against every 300 medium individuals three are 

 under II. &. only 282'9 short and tails ones. 



(3) That Mr Vernon changes the 1"07 per cent., which, by the 

 assumption of greater fertility of parents of the same size, the short 

 and tall offspring II. h. gain more than the medium-sized offspring 

 II. &. over the respective numbers of the offspring I. 5., into an 

 excess of the number of small and tall offspring II. h., 

 over the number of medium offspring II. 5., and hence 

 comes to the astonishing conclusion that the 900 parents II. a. pro- 

 duce 303'2 short and 303*2 tall offspring against 300 medium ones. 



(4) That the before-mentioned gain of 1*07 per cent, on the 

 part of the short and tall offspring II. &., means nothing else than 

 that the curve representing the offspring II. h. is not so convex as 

 that representing the individuals I. &. 



Apart from mathem:i,tical details it is evident from Mr Vernon's 

 figures on p. 405, Vol. XI., that the degree of fertility of the three 

 sets of parents of equal size can have no influence upon the propor- 

 tional numbers of tall, medium, and short offspring, as long as the 

 three sets are equally fertile. The difference in the numbers of the 

 three sets of offspring is entirely dependent on the results of the 

 intermarrying of parents of different size. From the lower figures on 

 p. 405, Vol. XI., we see that there will always be more medium than 

 tall and short offspring produced by these marriages, however much 

 less productive these marriages may be than those of parents of the 

 same size. The number of medium offspring produced by the inter- 

 marrying of short with tall parents has certainly decreased by the 

 assumption of lesser fertility of such parents, but so have the num- 

 bers of short and tall offspring. 



A consideration of another kind will perhaps more obviously 

 show that there is an error concealed in Mr Vernon's mathematical 

 demonstration. The above 920 offspring II. h. are produced by 

 300 short, 300 medium, and 300 tall parents; according to Mr 

 Vernon's own calculations the set of 300 short and the set of 300 

 tall parents have 300 offspring each, while the 300 medium parents 

 produce 320 offspring. The medium individuals are, therefore, 

 according to Mr Vernon's figures, the more favoured as regards 

 fertility and hence mtist necessarily gradually replace the tall and 

 small ones, provided (as is assumed by Mr Vernon) that the three 



