282 
PBOFESSOR KARL PEARSOX AND MISS ALICE LEE, 
evolution in tlie real fertility sensible in the one generation, then Mj would equal 
M.,. Hence to a first approximation we should have : 
M, = M, = = 3-494. 
To obtain a second approximation we may substitute this in the small terms of 
(vii.). Here cr'f must be found from (ii.) ; neglecting the cubic term we have : 
ct'Vo-I = 1 - o-i/M- = -2628. 
Hence : 
Ml = Mo = 3-494 
= 3-494 
= 3-494 
f ) 
*\li \ 1/0/2/ 
•0418 X 2-5759 X 1-1513 
-124 = 3-370. 
AYe can now substitute this value of Mi in (viii.), and we find ; 
M"i = 3-370 -f 2-980 = 6-350. 
Tins differs comparatively little from the actually observed value, 6-225, and is 
satisfactory evidence of the validity of our theory. The fact that the elder generation 
was in no way limited like the younger, and that we have neglected the third 
moment—although fertility distributions are never normal—as well as made other 
approximations, is quite sufficient to account for the difference observed. 
We may take it that 3-4 is practically the fertility of the elder generation, and 
that this is raised to about 3-5 by reproductive selection in the younger generation. 
The result 6-2 for the elder generation is thus purely a result of weighting due to the 
nature of the record. 
(ii.) Table II. gives the result of 1000 cases taken from the Peerage. Here the 
conditions of extraction were as follows :— 
One member only was taken out of each family, or no weight was given to the 
fertilit}^ of mothers. 
The daughters’ marriages had all been completed by the death of one parent or had 
lasted at least 15 3 mars. 
Tliere was no limitation with regard to the parents’ marriages. We found : 
M, 
o-d 
The coefficient of regression is sensibl\" equal to that of correlation. The probable 
error of = -0204, or not a tenth of the value of itself. Again we conclude 
= 3-923, 
= 2-758, (7 
r.u. = -2096. 
M„i = 5-856, 
— o 
2-751, 
