504 Further Evidence of Natural Selection in Man 
of two small quantities and any disturbing cause which but slightly modifies the 
value of either r-^o or may even change the sign of N and so swing over from 
a considerable positive to a considerable negative value*. 
We can consider the correlations between the female deathrate in one year and 
the male deathrate in a second year, supposing of course time influence annulled. 
We have 
5(jH)] .5(;)Ho' 
•6674 
.5«,».,=--6879), 
•7337 
5f,)Hi' 
.5,,../ = --7188), 
•7313 
.6,,., =--7032), 
5o'"3'-5(i"'4 ~ ~ 
•7278 
Thus we see that the same remarkably high negative correlations exist between 
the male and female deathrates of successive years of groups born in the same year 
as exist between male and male or female and female deathrates within the same 
group in successive years. In fact in two out of the four correlations the cross 
relationships are higher than the direct, although the differences are scarcely 
significant. Here again there is nothing noteworthy, considering the very high 
correlations just noted to exist between the male and female deathrates of groups 
born in the same year. We can, however, endeavour to correct such values by 
finding the relationship between the deathrate in females in the first year of life 
and males bora in the same year in their second year of life for a constant death- 
rate of males in the first year of life. Or still more stringently between the 
deathrates of females in the first year of life with males in the second year of life 
for constant male deathrate in the first year of life and constant female deathrate 
in the second year of life. We should anticipate that such values would come 
out small or insignificant, if our interpretation of the high negative correlations 
between deathrates of the same group in successive years of life be a correct one, 
i e. that the high deathrate leaves a stronger population. For a heavy deathrate 
in the females of one year should not leave a stronger population of males for the 
following year after correction by partial correlation. 
We obtained the following correlations : 
5e,.,''W.5e«.2 = - -5240 + -0692, 
Sc<'^5o».,.W = + -4665 + -0746. 
* The reader must note that we say a "disturbing cause"; it is not the mere result of random 
sampling affecting N. The probable error of W^=»'i2 - ''i3'^23 for a sample of size n is given by 
•67449(rjvr= -67449 ^ {C^ - [2 (1 - r^^) + 2 (1 - nj) + 1 - r^^ - 3] }^ 
and is thus quite easy to calculate. We have tested it on a number of cases of partial correlations 
worked out for this paper and find that if •674490-iv^ is of the same order as N, then •67449(rg^j., is 
of much the same order as 3?'i2. In other words, if N is so small relative to its probable error that 
it might easily have a reversed sign, then ^ri2 is insignificant as compared to its probable error also. 
For example, iV^=-0446 and Z> = -0956 leads to 3?-i2 = '4665 with a probable error of •0746. is 
accordingly considerable and significant, but the probable error of N is only -0105, and we can hardly 
suppose the sign of 3ri2 due to a random sampling variation in the sign of 
