274 PROF. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 
frustrated by the obvious fact that size of adult families does not follow any approach to 
a normal distribution. Thus, I find in 205 adult families the following frequency:—• 
This Table shows the number of those families in which (1) the number of sons and 
daughters, (2) the number of sons only, (3) the number of daughters only correspond, 
with the title in the top line. 
Now, although, as I propose to show later, the quantity, r = S [xy)l{;n<j x (T^), is really 
a significant characteristic of correlation, just as oq and oq are significant for variation 
even in the case of skew frequency, still there is little to be gained by working it out 
in this particular case, where, the statistics being insufficient to accurately determine 
the skew law of frequency, we shall not be able to find what we want—the law r of 
regression.* 
But several points as to paternal reproductivity may be learnt from these families. 
In the first place, of the 25 families with no sons, the father in 5 cases only was below 
the mean, in 20 cases above the mean height. The mean height of fathers in general 
is 5' 9"*17, but of sonless fathers is 5' 11"'03. Of the 25 daughterless fathers, 14 are 
below and 11 above the mean height; the mean height of the daughterless father 
being 5' 8 ,/- 71. Or, the same point may be emphasised in this way : If short fathers 
be taken as those below 5' 6"’5, and tall fathers as those above 5' 11"*5, short fathers 
have 65 sons and tall fathers 67 sons. We should accordingly, with our proportion 
of sons and daughters, expect 61 daughters to short fathers and 63 to tall fathers, 
but we find short fathers with 73 and tall fathers with 81. This point in reproduc¬ 
tive selection, that mediocre fathers have more tendency to sons and exceptional 
fathers to daughters, seems of considerable importance in relation to the prepotency of 
paternal inheritance. A similar point, but less emphatically significant, may be noted 
in the case of mothers. Mothers of daughters are less variable than mothers of sons. 
Without laying too great stress on statistics of so small a range and of one charac¬ 
teristic only, we may still suggest that it might be worth while to investigate whether 
the offspring of a mediocre parent and an abnormal parent do not tend to follow the 
sex of the mediocre parent. 
* Much more complete statistics of size in families have recently been sent to me by Mr. F. Howard 
Collins. They give a remarkably smooth skew frequency distribution, thus demonstrating the need of 
the theory of skew correlation when we are dealing with reproductive selection. I propose to illustrate 
this in a memoir on skew correlation. 
