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 293 314 293. 
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 300 medium individuals had again been 
produced, there would now be 3032 instead of 300 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 sueceeding generations. 
Thus supposing that in the next generation respectively 3032, 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 + 3-21 + 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 
