64 
The Intensity of Natural Selection in Man 
then probably come in later years. The tendency of the partial standard devia- 
tions for the Prussian data is opposite to that for the English, viz. for males ^a-j 
is greater than l)3 a 1 and M o- 2 is less than 03 cr 2 . For females, however, these are 
reversed, except for the 1882 cohort in the ten-year period. Another feature of 
the Prussian results is that the regressions for males are smaller by the new 
method of measuring environment, but for females the reverse is the case. This 
is also true for four out of the six examples from English data, and arises chiefly 
from the differences in the male and female variability in mortality in the second 
period compared with the first. In the first two years of life the (partial) standard 
deviation for males is always greater than for females, but for the second period 
the female (partial) standard deviation is in some cases the larger, the mean 
mortality in this second period being about the same for the two sexes. 
In the memoir (§ xxiv) a short discussion is given to the question of what 
amount of correlation between the mortalities should be expected if selection were 
entirely absent. This has been referred to as 03 e 12 and oi e u in the present paper. 
These values are only intended as approximations, and it would undoubtedly be an 
advantage if by direct correlations we could obviate the use of such corrections. 
These direct values could be obtained by correlating the mortality rate of the first 
two years of life (based on the number of births) of the cohort with the mortality 
rate in the 3rd, 4th and 5th (or 3rd to 10th) years of life (based on the number of 
survivors to the age of two), correction being made in some manner for a constant 
environment rate. This would entail a correlation between such variables as - 
y 
and and in my opinion might involve an element of 'spurious' correlation, 
x — y 
and for this reason alone rates were not used in the memoir. So far as I can 
understand, however, the critics of the memoir do not hold this opinion, so that to 
them the corrected correlation between two variates of the above type is probably 
as satisfactory as a partial correlation of the third order. The employment of such 
correlations saves considerable labour and requires no discussion of the question 
of ' expected ' correlation if selection were inoperative. Accordingly, for a few 
cases, the following new variables have been taken : 
z 0 = Male or Female Deaths in the first two years of life divided by Male or Female 
Births, 
z l = Male or Female Deaths in next three (or eight) years of life divided by number 
of survivors to the age of two, 
z., = Total Female or Male (i.e. of opposite sex to z 0 and z x ) Deaths in the whole 
five (or ten) years divided by Female or Male Births, 
and the values of z r 01 worked out. The statistical constants on which they are 
based are given below : 
