M. Beeton and K. Pearson 
63 
is expressed by o-y = 19'5706 years, and of adult sons of mothers by o-y = 19"1254' 
years. Now to obtain our data we had to take such material as was available and 
we could not select only those sons whose parents' ages at death were both 
recorded. Accordingly our series of sons is not the same in the case of mothers 
as it is in that of fathers, and we have taken in our regression equation the mean 
a-y as determined from both series. Again, in judging of the probable age at death 
of a man from those of his brother and sister, we find that the variability of age at 
death of a man with an adult brother is given by a-r^^ 19'4302 j^ears, but of a man 
with an adult sister as 18'9472 years. Furthei-, the mean age at death of a man 
with an adult brother is 5G"568 years, but with an adult sister is .58'804 years. 
These are sensible differences, and there can hardly be a doubt that men with 
sisters live slightly but sensibly longer than those with brothers, and are slightly 
but sensibly less variable in their age at death. Now our data do not provide 
the constants for the specially differentiated class of men with hotli brothers and 
sisters. Accordingly we have been compelled to take the mean of the two classes 
— men with brothers and men with sisters — to represent both in age at death and 
variability the special class of men with both a brother and a sister. Other similar 
cases will occur to the reader, and there are some in which the assumptions made 
are less justifiable than the above. For example take the case of a minor having 
two minor brothers dying. We have only been able to use the mean age at death 
of a minor having at least one minor brother dying, but this is certainly greater 
than the mean age at death of a minor having at least two minor brothers dying. 
We were only able to obtain altogether 517 cases of minor brothers dying out of 
all the records of the Society of Friends accessible to us. It would have been 
idle to have attempted the differentiation of this small number into sub-classes of 
minors with one or with more than one brother dying as minoi', or with one 
brother and with one sister dying as minor, and so on. Our equations do not 
pretend to give more than a rough appreciation, such as is compatible with the 
comparative paucity of oui' material, of the influence of the death of relatives on 
the probable age at death of any individual. Just because we consider the record 
of the deaths of minors to be very incomplete even in the case of Friends' family 
histoz'ies, while that of adults is fairly complete, we have purposely avoided the 
important problem which lies at the root of much of the practical use of equa- 
tions (.37) to (52), namely : What are the chances in the material we are working 
on that an individual will die as a minor or survive to be an adult ? These 
chances can be determined for the general population from the Registrar-General's 
returns, but our material is considerably differentiated from the general population 
and we have felt bound to leave this problem unanswered. 
(6) Before we proceed to illustrate these equations for the probable ages at 
death, it may be as well to compare, as far as is possible, our present data with 
what we gave in our first study of the inheritance of longevity*. We were then 
working solely with male inheritance and from different classes, those of the 
* R. S. Proc, Vol. 05, pp. 297, 299. 
