INFLUENCE OF INFANTILE MORTALITY ON BIRTHRATE. 241 
suppose for example that, & = 0°250; q =1, and »=0°100; 
the last rate becoming later »’ = 0°200. Then the term 
(x’ — ») q8/}1-B6(A—»)| is identically 
(0°200—0°100) q.0°250 _ 0°025 _ 
1—0°250 (1-—q°0°100) 1-—0°225 
Thus the original rate 0°250 could become at most (i.e., 
when g = 1) only 0°250 x 1°03226, viz. 0°25806, or say 258 
per 1000 instead of 250; or in other words the doubling of 
the rate of infantile mortality, would on the assumption 
made, affect the birthrate by increasing it the small 
amount of about 34 per cent. 
4, Reverting to equation (6) the result deduced may be 
put in the form IB —, 8 == ON (hia mn) eocewecs (7) 
pee b= 9B2/11—-B(1- qn) } seesseee (8) 
fB/ denoting the birthrate as modified by a change in the 
rate of infantile mortality. The above expression (7) is 
the equation of a straight line making with the angle of 
abscissee an angle whose tangent is b, the abscissee being 
values of » and the ordinates values of #’. This result shews 
that b is essentially positive, a matter to which reference 
will be made later on. 
One may thus suppose that an ultimate birthrate 6, could 
be deduced which would represent that rate when infantile 
mortality was reduced to zero, and that any actual birth- 
rate may be put in the form 
(Gi Be Ae topes sense ks (9) 
in which, as may be seen from (8) above, b must be very 
small and theoretically should always be positive. 
The result deduced may be expressed as follows :— 
(i) When either all mothers of deceased infants, or any 
constant proportion thereof, may be regarded as subject 
to equal risk of fecundity (i.e. equally likely to bear chil- 
P—Oct. 7, 1908. 
