Ethel M. Elderton and Karl Pearson 
503 
We should need a far longer period than 50 years to determine certainly even the 
signs of these correlations, and their real magnitudes would require still ampler 
data. It would appear impossible to assert on the basis of the above values of 
the correlations at three and four years' intervals more than the insignificance 
of the associations between deathrates of the same groups at intervals of more 
than two years*. In other words the effect of intense selection appears to be 
exhausted after an interval of two years. The word "appears" is used purposely 
because there must be some spurious weakening of the effect due to our not being 
able to follow absolutely the same individuals. 
(8) We have further studied to some extent the relationship between the 
male and female deathrates. There is almost perfect correlation between male 
and female deathrates in any given year of life after we annul the time-factor. 
Thus, if we represent female deathrates by m, we have as illustrations : 
'•5„-4.56»u' = + "9^00. 
Of course the sole significance of these values lies in the fact that years of 
stress, whether due to climatic or epidemic causes, affect equally infants or 
children of both sexes of the same age. But these very high values in our 
opinion cast considerable doubt on the partial correlations derived from them. 
We have in fact 
V(l-n/)(l-7-J) D' 
and if we suppose i\2 and ?'23 nearly equal, then if be of the above high value 
N will be extremely small, but D is also, owing to the presence of the factor 
Vl — ri3^, very small. Thus :j?'i2 although it may be very considerable is the ratio 
* Actually the partial correlations of the sixth differences at three years' interval based on the above 
values are : 
Correlation of 
For constant 
6 
? 
5(i)»i and S^m^ 
S0W2 s-nd SiiWio 
Squio, and h^in^ 
S(,m^ and Sqihh 
+ •,•526 
+ •251 
+ •181 
+ ^485 
These are certainly all positive, but they are irregular as between the sexes and probably quite 
unreliable for the reasons already given. Should a more extended experience show that there is a 
real if slight positive correlation between deathrates at three years' interval, while there is con- 
siderable negative correlation at one and two years' intervals, we should be compelled to discuss 
whether there may not be something periodic in the nature of the heavy and light deathrates of 
infancy and childhood. We have been unable to trace any sign of such periodicity either in the 
deathrates or in the graphs drawn, but we do not believe that a very short periodicity would be elimi- 
nated by the variate difference method using any^moderate number of differences. We cannot on 
this point accept Dr Anderson's view. See BinmetriJcn , Vol. x. p. 279. 
