M. Beeton and K. Pearson 
69 
Now A's father has already lived 79— 70'571 years = 8-429 years beyond the 
mean age, and A's mother 74 — 68'446 years = 5'554 years beyond the mean age. 
We require their expectations of life. In default of better hypotheses we take the 
distribution of the array to be represented by the normal curve of errors. Then if 
Xi be A's father's further expectation of life, and a'l = 8*429 years, o-i=14'4339 
years, 
8-429 +X, = ^^'^ 
1 
/27rix/ 
These values are to be found from the usual tables, and lead to 
X, = 17-364 - 8-429, 
= 8-935. 
Thus A's father will probably live to be 87-935 years. Working- out the case of 
^'s mother in the same manner we find for her probable further length of life 
11-388 years, or her probable age at death is 85-388 years. 
If we turn to Ogle's expectation of life table we find the expectation of life of a 
man of 79 to be 5-07 years, and of a woman of 74 to be 7-25 years, or they will 
probably reach ages of 84-07 and 81-25 years respectivelx'. In other words A's 
parents appear to have 4 years' greater duration of life than is deducible from 
Ogle's results. How is this to be accounted for ? I think in the following way. 
The mean age of all our series of fathers is 66-334 years, but the mean age of 
fathers with an adult son is 68-370 years. Hence if we consider that the majority 
of men who live to be 79 are either fathers or in general quite equal to fathers in 
physique, it follows that ^'s father increases his expectation of life by 4 years 
over Ogle's estimate in two nearly equal parts, 2 years because he has an adult 
son and 2 years on account of the longevity of his ancestry. Treating the case of 
the mother in the same way we find the mean age at death of mothers of any kind 
to be 63-225 years, but tlie age of mothers with adult sons is 67-947 years ; in 
other words about 4-7 years' difference in the duration of life. As A 's mother only 
gains about '5 years from ancestry, we might expect a total gain of about 5 years 
on Ogle's estimate. There is actually a gain of a little over four years*. Thus, 
allowing for the fact that we are selecting special classes, our results are not 
widely divergent from what we might expect from Ogle's general mortality table. 
* The average age at death of our Friends series is 59-97 for adult males and 58-78 for adult females. 
Ogle's results give about 59-5 for adult males and 62 for adult females. So that our males are 
longer and not shorter lived than the females. 
