PROF. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 273 
when statistics of this kind are collected, and more than one son in a family is 
included. There is a more significant difference in the variation of wives and 
daughters. It is, however, in the opposite sense to what we may suppose would 
be produced by natural selection, or by the fact that we have drawn daughters from 
a less general population than wives. There is no definite evidence as to natural 
selection to be drawn from these results accordingly. 
(ii.) Sexual Selection. — (a.) Preferential Mating. — We have no general populations 
to compare with those of husbands and wives. If we suppose the population stable, 
and treat sons and daughters as characteristic of the general unmarried population, 
husbands are not a significant selection from sons. Possibly the difference between 
the variation in daughters and wives might be accounted for by a distaste for very tall 
or very short wives in the middle classes. The difference is, however, not very signifi¬ 
cant, but it should be borne in mind in dealing with a larger range of statistics. 
( b .) Assortative Mating , —Although the probable error (Table II.) is about half the 
coefficient of correlation, it is unlikely that the latter can be really zero, and although 
we must not lay very great stress on the actual value of r, still we are justified in 
considering that there is a definite amount of assortative mating with regard to height 
going on in the middle classes. It may be expressed by saying that wives l" taller than 
the mean will have on an average husbands 'll" taller than the mean, and husbands 1” 
taller than the mean, wives on an average ’OS' 7 taller than the mean (Table III.). 
Table IV. shows us that the variation in matages would hardly be discoverable directly 
from our present range of statistics. # 
(iii.) Reproductive Selection. —Although in the matter of means we cannot assert 
significance between the heights of males in general and fathers in particular, it is 
quite possible that such will reveal itself in more ample data. On the other hand, we 
see at once that fathers are definitely less variable than husbands, and fathers of sons 
remarkably less variable than fathers of daughters. Thus, while the height of a 
father is less closely related to his chances of having a daughter, any tendency to 
normality is of service in the chances of having a son. Peproductivity in males 
seems to be thus essentially correlated to height, and again, height to be potential 
in the question of male or female offspring. 
An endeavour to directly calculate the correlation of reproductivity and height is 
* Of course 200 couples give graphically nothing like a surface of correlation, nor can any section of 
it be taken as a fair normal curve. We assume a priori that 1000 couples would give a fair surface. This 
is practically what I have found for skull-measurements, 900 give an excellent curve, 50 a doubly, or even 
trebly, peaked polygon. None the less, sets of 50 skulls give means and S.D.’s in close accord. For 
example, in Professor Flinders Petrie’s newly discovered race, 50 male crania from T. and Q. graves give 
for cephalic index : Mean, 72‘96, S.D., 2’82; while 53 male crania from General and B. graves give : 
Mean, 72 - 92, S.D., 2‘95. The 103 crania together give : Mean, 72 938, S.D., 2’885, with a probable error of 
S.D. = -29. The variation curves would not suggest any such close agreement at all. The constants, 
however, suffice to show the homogeneous character of the two sets of excavations. 
MDCCCXCVI.—A. 2 N 
