406 NATURAL SCIENCE [December 



parents give rise to the same numbers of children in each group as 

 do medium parents. 



If we now take the case of 900 parents of either sex and divide 

 them into three groups of 300 short, medium and tall individuals, it 

 will be found that, as- the result of their chance intermarrying, they 

 will give rise to the following numbers of offspring of each sex : 



293 short. 314 medium. 293 tall. 



These numbers thus differ slightly from the 300 of each group 

 which were started with, but it is not possible to arrange the numbers 

 resulting from the various intermarryings so as to give quite identical 

 figures. This, in fact, is not necessary, as it is only sought to 

 compare two different cases, in one of which a correlation between 

 fertility and stature is absent, and in the other of which it is present. 

 This latter case we will now proceed to discuss. 



Let it be granted that, in pursuance of this principle, 100 

 parents intermarrying with parents of similar stature now give rise 

 to 120, and not 100 offspring of each sex. When on the other 

 hand they marry with moderately taller or shorter individuals, let 

 the number of offspring remain unchanged, and when tall or short 

 parents marry with short or tall, let only 80 offspring instead of 

 100 arise. If now the same 900 parents of either sex intermarry 

 according to the laws of chance, it will be found, on calculating out 

 the numbers in accordance with the data given above, that the 

 following numbers of offspring will be produced : 



Short. Medium. Tall. 



300-6 318-8 300-6 



instead of 293 3,14 293. 



That is to say, the numbers of short and tall individuals will have 

 increased by 2 - 59 per cent., but those of the intermediate ones by 

 only 1-52 per cent. There is thus a gain of about 1*07 per cent, 

 in favour of the extreme individuals over the intermediate ones, or 

 supposing the original 3,00 medium individuals had again been 

 produced, there would now be 303-2 instead of 3,00 tall and short 

 ones. This seems a very small amount in comparison with the 

 fairly large differences of fertility we assumed to be present. It is, 

 however, none the less genuine, in spite of its smallness, and it will 

 of course become increasingly larger in succeeding generations. 

 Thus supposing that in the next generation respectively 3,03-2, 300, 

 and 303-2 short, medium and tall individuals of each sex inter- 

 marry, the short and tall offspring will be increased by slightly 

 more than 1-07 per cent. ; by in fact about 1/08 per cent. There 

 will now, therefore, be 300 + 3-2 1 + 3'24 = 306*45 short and tall 

 offspring, instead of 300. In succeeding generations the increase 

 will gradually become more and more marked, and the divergence 



