PROF. Iv. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 311 
U 1 As + Pi 7.3) 
7i - 72 
p'lfli + Pi (£3 ~ 7i) ^ 
7i - 7 2 
and 
7n j = V {A: d- /3 3 d= V 7 (A — ^ 3 )" + 4r$ 8 fi'. 2 }. 
Since the /3’s for parental inheritance will be < "5, it follows that y l and y 3 are 
proper fractions, hence by taking p sufficiently large, we can make p p and f p as small 
as we please. 
This result is equally true whether the /3’s be those for assortative mating or not. 
Thus we conclude that suspended natural selection, whether accompanied by sexual 
selection or not, would ultimately result in a regression of means to the foci of 
regression of the two sexes. 
(iv.) Panmixia for Human Stature .—It is worth while illustrating this by an 
example. Let us suppose that owing to natural selection, the mean of the male 
human population were pushed up to 4" above its present level, and the mean of the 
female population were pushed up 3" above its present level, and then let us inquire 
how they would regress in p generations of suspended natural selection with and 
without that factor of sexual selection we have termed assortative mating:. 
(a.) Without Assortative Mating .—We must take the values of the /3’s from 
Table III. : 
Further 
We find 
whence 
(3% — ‘4456, /3 3 = '3381, /8' 3 = -309 6, 0' 3 = • 2932. 
Pi — 4 , p 1 — 3 . 
y 1 = 7069, y 3 = '0419, 
A x = 3-9549, A a = *0451, 
j> 
jx p = 3-9549 (7067)^ -1 + ‘0451 (-OILJ)^- 1 , 
fi p = 3-0538 (7067)^ -1 - -0538 (-OTIO)^- 1 . 
Thus, in four generations (p — 5) the males will have sunk to "9876" and the 
females to ‘76-26' from the old means* before natural selection started, while in 
nine generations (p = 10), the mean of the males will have sunk to "2036", and the 
mean of the females to "1816" from the old means; thus the means of the general 
populations of both sexes have been sensibly carried back by panmixia to the focus 
of regression. 
* The smallness of the contributions given by the second terms in the values of ftp, ftp is to be noted. 
