940 G. H. KNIBBS. 
fore that some definite proportion, q say, of the women 
whose children have died, may be added to the number of 
childbearing age who are equally likely to increase the 
total number of births. 
The maximum value of q is of course 1, that is its value 
when every woman whose infant has died is at risk. This 
proportion may on the whole be supposed characteristic 
of a country, or of a particular period. 
The total number of women at risk will be therefore, 
n — np + ngf'p = nf 1-— £' (1—qp) 
Thus the ratio of births to this number will be 
nB'in , 1- BA -q) } =! {1 -B(1- qu) Lat aa (3) 
If at some other period the rate of infantile mortality is 
found to have changed to the value +’ the total number of 
women at risk will similarly be n} 1-/'(1 -qv’) t sabi (4) 
Since ex hypothesi all other conditions have remained 
unchanged the ratio of births to the total number of women 
at risk will be as before, and the total number of births 
under the changed rate of infantile mortality will con- 
sequently be :— 
n}1—B(1—qr') | era ae (5) 
that is to say, the original birthrate will have to be multi- 
plied by the factor :— 
Lid Gi qh 
Ga = 14+("'—-p) Meise cleat (6) 
Since the difference of the rates of infantile mortality 
must always be a small fraction, and /’ is itself also a small 
fraction, it is obvious that the birthrate cannot be greatly 
modified by infantile mortality. 
Retaining for the present (’ as denoting | B]/[W], in which 
W denotes the number of women of childbearing age, 
