68 
Inheritance of the Duration of Life 
this statement, however, must be confined to the parental relationship, for even in 
deaths in middle life we find a fairly continuous and unbroken slope for the regres- 
sion line in the case of brothers or sisters : see for example Figs. 7 and 8. 
The problem is, of course, immensely complex and probably rendered especially so 
by a mixture of different classes of causes, i.e. inheritance of tendencies to develop 
one or more mortal diseases at definite ages in life, and inheritance of general 
physical weakness or physical robustness tending merely to shorten or lengthen 
life as a whole, and largely influenced by environment as far as the definite age at 
death is concerned. All we can do, in default of special statistics stating the 
cause of death for each individual, is to examine in broad outline the general 
influence on the duration of life of an individual of the ages at death of his or her 
nearest relatives. 
(7) To illustrate the use of equations like (1) to (52) the following problems 
may be considered. 
Illustration (i). — A's age is 44, his father and mother are alive at the ages of 79 
and 74. His paternal grandfather died aged 6!) and his paternal grandmother at 
82 ; his maternal grandfather and grandmother lived to be 81 and 59 respectively. 
What are the expectations of life of his parents, and what is his own expectation 
of life based on theirs ? 
Now this is by no means so straightforward a problem as it might appear at 
first sight, and there is more than one way of looking at it which will give a fairly 
reasonable solution. We cannot apply equations (8) and (6) straight off, because 
the M and W there are a man and woman of the general population, but our man 
and woman belong to a select class, namely those who live to have adult sons. 
The average ages of such according to our Table A are : for father 68'370 years 
and for mother 67 947 years. Hence the probable age at death of J.'s father and 
mother would be given by the equations : 
^'s father's age = 68 :370 + -1802 (69 - 68-370) + -1486 (82 - 67-947) 
= 70-571 years. 
^'s mother's age = 67-947 + -2057 (81 - 69-547) + -1914 (59 - 68-702) 
= 68-446 years. 
Thus while A's father gains about 2 2 years by his ancestry, J.'s mother gains 
only "5 years because her mother died comparatively early. 
Again, we must not in calculating S for the selected class take the a of sons in 
general, but rather the value 14-6974 years of fathers of adult sons, and similarly 
we must take 16-9033 years for the a from which we calculate the 2 of A's, 
mother's class. This leads us to the values 14-4339 and 16-5677. Or, A's father 
belongs in an array of men, whose mean age at death is 70-571 years, and whose 
standard deviation is 14 4339 years. Similarly, J.'s mother belongs to an array of 
women whose mean age at death is 68-446 years, and whose standard deviation 
is 16-5677, 
