52 
Inheritance of the Duration of Life 
death are very frequently not stated. Either the individual is said to be n years 
of age at death, or the years of his birth and death are given. In the former case 
it would be quite reasonable for adults to assume that the average of such 
individuals was n + "5 years, for a man n years old at death may be of any age 
from exactly n to just under n + 1 years. In the latter case since the individual 
may be born any time and die any time between Jan. 1 and Dec. 31, his age may 
lie between p — 1 and p years where m is the given year of his birth and 
m + p oi his death, so that the mere subtraction of the birth and death years 
gives p years for his age, which corresponds to the probable average life of such 
individuals if adult. As the years of birth and death are almost always given 
even when the age is, we obtained the simple rule for classifying : subtract the 
year of birth from that of death and group on the mid-year of the five year 
period. Thus ages so found, 21, 22, 23, 24 and 25 are grouped at 23, which 
denotes exactly 23 years of life and not the mid-point of the 23rd year. 
With regard to minors with one and two year periods our difficulties were 
more serious, p years' difference between the birth and death years still meant 
p years' life and therefore grouping together lives of p and p + \ years, we could 
centre the group at j) + b years, so long as we were not dealing with the first year 
or two of life and their very unequal mortality. It is these early years of life 
which present difficulties. If those we have recorded as dying in the same year 
as they are born, or under the heading 0, were just as likely to be born at any 
time of the year and to die at any later part of it, their mean life in years 
would be 
I {y-x)dxdy \ \ dxdy, 
J 0 J X I J 0 J X 
where x, y are the periods (in fractions of a year) from January 1 to the days of 
their birth and death. This gives a result = \, or the average life would be four 
months. Mr G. U. Yule kindly considered the problem from the actual statistics 
provided in the Report of the Registrar-General for 1S91. This gives the mor- 
tality for each month for the first twelve after birth for the rural counties and 
three selected towns. Taking the former Mr Yule finds 2'34 months instead of 
four months for the mean duration of life. As he observes, 2'34 is probably some- 
what too large for his material, as undoubtedly more children die towards the 
beginning than towards the end of the first month. On the other hand the 
infantile mortality among the Society of Friends is nothing like as great as in the 
general population. After some consideration we determined to centre the group 
dying in the first year of life at three months or "25 years. 
Now turning to the group clubbed together as 0 — 1 in some of our tables, we 
must ask where it is to be centred. The children recorded as 0 years at death we 
have seen are to be centred at "25 years, and those placed under 1 year would be 
anything from 0 to 2, and accordingly have their mean at 1, if mortality did not 
undoubtedly not recorded, and accordingly we have not got infant and adult deaths in their proper 
proportions. As many infants as possible were extracted, only about 1000 adults. 
