494 Further Evidence of Natural Selection in Man 
very substantial value of about —■7. In other words a rise in the deatbrate of 
one year of life means a fall in the deathrate of the following year of a most 
marked kind. While with the sixth differences we are approaching fairly closely 
steady values it may be doubted whether we have reached them in any case but 
that of i\ ^ . The following are the sixth difference correlations in the case 
of the deathrates of successive years: 
Male. Female. 
%,n,.Sr,m, - 688 ± '090 - -719 ± -081 
- -673 + -092 - -660 + -095 
-•703 + -085 --731 + -078 
' 5o Hi2 ■ 5f, Ills 
' Sums ■ 5on'4 
--695 + -087 --736 ±-077 
Again the male and female results are in excellent agreement, and we grasp 
the startling manner in which the new method reverses a judgment based on 
relations which have been deduced without any regard to secular change. 
(4) The question naturally arises: How far are these the "steady" values of 
the difference correlations measuring the organic relation apart from the time- 
factor of the deathrates in different years of infancy and childhood ? 
There are three fundamental tests: (i) The correlation coefficients of suc- 
cessive differences should have ceased to be markedly rising or falling. Table III 
(p. 497) shows that this is approximately but not absolutely the case, but we have 
reached a stage in which any further changes are certainly of the order of the 
probable errors and thus of little significance. The unsteadiness as will be in- 
dicated later in better tests is greatest in the differences of the deathrates in the 
first and second years of life. Here the correlations were taken to the seventh 
and eighth differences and gave : 
Male. Female. 
^'S:m,.S:m. - -696 ± 090 - -729 + "082 
rs,m,.5,.„ --092 + -094 - -731 + "084 
which appear to have reached practical steadiness. Actually the final correlations 
must be somewhat greater than those obtained from the sixth differences. To 
push the process further, however, would be of small advantage because higher 
differences involve introducing earlier data, and the birthrate data before 1855 
become more and more unreliable. Again in the extremely high differences, the 
additional year required for an additional difference if not appertaining to rela- 
tively smooth data may in itself, when we have only a small total frequency of 50, 
produce a certain amount of unsteadiness. 
(ii) We may consider the mean values of the differences. 
