560 Proceedings of the Royal Society 
exact, is got by dividing the number of married women of child- 
bearing age by the number of legitimate children born, all in the 
same year. It is thus found that every 3*55 wives, aged from fifteen 
to forty-five, add one to the population annually. 
The fertility of all marriages in Edinburgh and Grlasgow that 
were fertile in 1855 is found to be 3*7 children to a marriage. 
The fertility of fertile marriages enduring for the whole child- 
bearing period of life is shown to be on an average ten children to 
a marriage ; and as the average interval between successive births 
is about twenty months, fertile women, living in wedlock, from fif- 
teen to forty-five, are fecund for about seventeen years. 
The fertility of persistently fertile marriages, lasting during the 
whole child-bearing period of life, is shown to be at least fifteen 
children to a marriage. Persistently fertile wives, taken at any 
duration of marriage, are found to have born at the rate of a child 
very nearly every two years. 
It is shown that, at any epoch in married life, the average num- 
ber of a fertile woman’s family is one-third of the number of years 
elapsed since her marriage, and that the number of a persistently 
fertile woman’s family is one-half of the number of years elapsed 
since her marriage. These numbers vary according to the age of 
the wives at marriage — a circumstance which is subsequently 
explained. 
The average interval between marriage and the birth of a first 
child is shown to be seventeen months. Inclusive of this period, 
the interval between the births of successive children is twenty 
months. In average families, the first four children succeed one 
another more rapidly than the next six — that is, on to the tenth. 
But in large families, or those above ten, the children, from the 
first, do comparatively hurry after one another with brief intervals. 
Fertile women, married at different ages, have an amount of fer- 
tility which decreases as the age at marriage increases ; and this 
greater total fertility arises from the greater continuance or per- 
sistence in fertility of the younger married. Women married at 
higher and higher ages have a shorter career of fertility. This per- 
severance in fertility explains why the women married from fifteen 
to twenty years of age have a greater fertility than those married 
from twenty to twenty-five, who have the highest fecundity or like- 
