Karl Pearson 2G3 
Let 71)1 be the number of the population, N, of pairs of parents who exceed the 
value h of the character x ; then : 
v27ro-^. i/i 
2-77 J hja^ 
This equation determines h/a_c from Sheppard's Tables, since 'iik/N' is known. 
Further if f,^ be the mean fertility of those over grade h : 
iitjh = / -iL- e ' i'^'l"'^ y dx, 
'■'IT (7^ 
1 ]e- 
2 o-Q" + 
" dx' (xiv). 
where H' 
Now nhfhlNf is clearly known, therefore H' can be found from the tables. 
We will suppose two grades of the character to be and h., and the corre- 
sponding average fertilities and y^,^, then and H.^ will be known ; and 
there results 
= /(i — — 
7-7- / O^a; 0"o 7 k<^x' 
Further: ^'-~r''^-K = -k 
