M. Bbeton and K. Pearson 
53 
diminish so rapidly during the first two years of life. I find 917 children on the 
record under the heading 0, and 774 under the heading 1. Hence we have for the 
917 X •25 + 774 X 1 
centre of the group ^.^^^ ^ = '59. The real value must be something 
less than this owing to the rapid diminution of mortality in the first and second 
years of life. We have accordingly selected 5 as the centre of the group recorded 
under 0 — 1, a value which makes the calculations simpler and cannot be very far 
from the truth. Important as some appreciation of the approximate value of the 
true centering is. tiie reader may note that a slight error does not sensibly alter the 
constants we are investigating. Thus, if we change the centre of the 0 — 1 group 
from '5 to 64 of a year this, for example in the cases of the cori'elation in lengths 
of life of mothers and minor sons, of fathers and infant daughters, only alters the 
value of the coefficients from '0756 to '07(51, and from '0.520 to •0523 respectively. 
In every case the change is far less than the probable error of the coefficient. 
(3) Another point must be referred to here. In forming a correlation table 
for two perfectly homogeneous groups, e.g. adult sisters and adult sisters, the 
table was first formed by taking as one entry the elder sister (i.e. the one born 
first whether she died first or not) and as the other the younger sister. The table 
was then rendered symmetrical by adding corresponding rows and columns, so that 
we finally obtained a table giving the correlation between ages at death of a pair 
of sisters without reference to their relative position in the family. The correla- 
tion coefficient was found to be changed by this procedure by an amount less than 
the probable error. Thus the correlation between the ages at death of pairs of 
adult sisters in general is "3322 + "0185, while that between elder sisters and 
younger sisters is '3464 + '0183. In the case of brothers the coefficients are 
respectively '2853 ± '0194 and '2990 ± '0194. 
But while the correlation remains unchanged by this procedure the means 
differ very widely. Tlie elder adult sister and adult brother live on an average 
four years longer than the younger adult sister or brother. The actual values based 
on 1000 or more cases are as follows : 
Average Life of Brothers and Sisters. 
All Adult 
Elder Adult 
Younger Adult 
Sister 
Brother 
57-795 
56-568 
59-924 
58-560 
55-667 
54-575 
Here an elder brother or sister was one who might have been born one year or 
twenty before the younger brother or sister. This greater expectation of life on 
the part of the first born was so much beyond our anticipations, and as far as we 
are aware so little noticed hitherto, that we determined to make an independent 
investigation of this special point. Accordingly correlation tables were prepared 
