M. Beeton and K. Pearson 
73 
We find 
o-itr, 
Thus \{ X = x^ — c we have 
V27r N^irJa-e 
1 
V27r-^a V27r-'5 
Put 
and we have 
, a 1, h , a — c 
a = — , 6 = — , c = 
O", CTo O-Q 
1 I ft' 1 
q"i V27r V27r-/c' 
V 277 .' a' V 27r J b' 
where 
A/Vo-i2 + 0-2^ = -054,629, c' = - 1-397,888, 
a' = - 1-028,396, 6' = - -948,408. 
All parts of the above expression can now be found from tables of the ordinates 
and areas of the normal curve of errors. We find 
IS-Pllo -398,302 X -918,92 4 
~ -848,113 X -828,538 
= 7-107 years. 
Thus the wife has an expectation of a little more thau seven years of widow- 
hood, i.e. this is the mean period of widowhood of wives of her class. This is 
nearly six times the period found for the difference between the probable ages at 
death of husband and wife and three times the difference between their expecta- 
tions of life. The whole problem of the expectation of widowhood seems deserving 
of treatment on general lines. 
(8) We may now return to the bearing of our results on the problem of 
evolution. A very considerable series of investigations on a variety of organs and 
characters in man have given quite definite results as to both parental and 
fraternal inheritance. Whether we take mental or physical characters, the 
parental correlation lies between "3 and '5, some of our best results tending nearer 
to the latter limit ; for fraternal correlation the limits appear to be closer, from 
-4 to -5. We may take as typical numbers -4 for parents and -45 for brothers. 
Now it is at once obvious that for duration of life treated as an inheritable 
character we have got results which fall far below these values. The direct 
explanation of this lies in the existence of a non-selective death-rate. Hence 
