Ethel M. Eldbrton and Karl Pearson 
501 
It is easy to see how those who contented themselves with crude deathrates, 
making no allowance for the betterment of deathrates with the time, interpreted 
a higher deathrate in one year to mean a higher deathrate in the next year of life, 
and so questioned whether natural selection applied to civilised man. As a 
matter of fact we see that the true organic relationship of deathrates is much 
more probably summed up in the statement that a decrease or an increase of 
deathrate in one year of infancy or childhood is in each case followed by an 
increase or a decrease in the deathrate of the survivors of the same group in the 
following year. Disregarding the time-factor we have a result quite incompatible 
with natural selection ; annulling the time-factor, we have a result not only 
compatible with natural selection, but very difficult of any other interpretation 
than that of a selective deathrate, i.e. a heavy mortality means a selection of the 
weaker members, and the exposure to risk in the following year of a selected 
or stronger population, which has accordingly a lesser deathrate. 
(6) We now turn to the problem of how far this influence extends, or 
probably it would be better to phrase it : how far this influence can be traced. 
It is not only that the age group we follow does not absolutely consist of the 
same individuals but even with those members that are the same there is very 
often change of environment due not to time but to a change of locality or 
of economic condition affecting individuals. Added to this there is a continuous 
immigration and emigration. But beyond these causes weakening the association, 
there is another difficulty of great importance arising from what has happened 
in the intervening years. We wish to find out how an increase of deathrate 
in the sth year of life affects the deathrate in the (s + 2)th year of life, but 
the events in the (s + l)th year will largely dominate and, perhaps, screen the 
results we are seeking. Such problems are always arising in statistical research. 
For example, a child may resemble its grandfather simply because both grand- 
father and child are like the child's father. We know that the problem is 
answered statistically by inquiring what is the relation between a character in 
the child and the grandparent for a constant value of the character in the parent. 
In precisely the same manner we must in the present problem inquire : What 
is the correlation between the deathrates in the sth and (s + 2)th year of life 
for constant deathrate in the (s-f l)th year of life? 
TABLE IX. 
Influence of Natural Selection at Interval of Two Years. 
Partial Correlation of 
For constant 
6 
? 
Sgmi and d^m^ 
- -4307 
- -5242 
S(jOT2 and B^nii 
- -2555 
- -2058 
and Sowij 
56«i4 
- -1798 
- -3129 
04— 2 
