24 O. H. KNIBBS. 



that is that any increment to the rates of infantile mortality 

 will cause a sensibly constant proportional increase to the 

 birth-rate, but this increase must in any case be very small- 

 One may consequently suppose that a birth-rate fi n may 

 be deduced which would be free from the effects of infant ile 

 mortality. This last equation may be put in the form 



(7) ft, = 0(1 - fc /t ) 



in which ft is the actual birth-rate, k a constant for a par- 

 ticular community at a particular epoch, and ft, the rate 

 freed from the influence of infantile mortality. This 

 equation is the same as (9) on p. 241 of the paper quoted, 

 illustrated on p. 243, and tabulated on p. 244. It gives for 

 Europe the average result 



ft n - 22*8 + 0-033 ik 

 the value of ft ranging from 12'9 to 38*9 and of k from 

 - 0'07 to +0*19. Theoretically it should always be positive. 

 Further refinement in the theory so as to take account of 

 the influence of change of population, is, in the light of the 

 plotted results shewn on p. 243 in vol. xlii, referred to, 



