INFLUENCE OF INFANTILE MORTALITY ON BIRTHRATE. 239 
two quantities being given by the formulae :— 
Bi BP ssecees: (1) 
fete =" [EV BESS 3.2 020 (2) 
the square brackets merely denoting the sum of the quan- 
tities written within them (as in the notation ordinarily 
used in least squares). 
Repeating this process for a series of small ranges of 
#4, successive mean birthrates are obtained corresponding 
toa series of mean rates of infantile mortality, and, if 
these be plotted as ordinates and abscissae respectively, 
the succession of points will afford some indication whether 
on the whole the birthrates increase with increase of 
infantile mortality. This has been done for a number of 
countries and the results are shewn on Fig. 1 hereinafter. 
3. That a priori some such increase is to be expected 
may be shewn as follows :— 
Let it be supposed that (’ denotes the ratio say of the 
number of births, not to the total population, but to the 
number of women of childbearing age; and p- the ratio of 
the number of infant deaths to the total number of infants 
born: then the ratio of the number of-infant deaths to the 
women of childbearing age is /’p. 
In a community containing n married women of child- 
bearing age, the annual number of births would be nf and 
the annual number of deaths of infants nf'p. If it be 
assumed that all other conditions remain constant, the 
problem resolves itself into ascertaining what would be the 
consequence to the birthrate of the rate of infantile mor- 
tality changing, say from p to p’. 
The only way in which an increase in the rate of infantile 
mortality can be assumed to directly increase the birthrate, 
other circumstances remaining constant, is by increasing 
the number of childbearing women at risk, viz. the number 
likely to give birth to children. It may be assumed there- 
