Ch. xi. On the Fruitfulness of Marriages. 473 



has been produced by all the marriages included 

 in the period cut off. It is evident, that with 

 the marriages at the beginning of the period will 

 be arranged a number of births proceeding from 

 marriages not included in the period ; and at the 

 end, a number of births produced by the mar- 

 riages included in the period will be found ar- 

 ranged with the marriages of a succeeding period. 

 Now, if we could subtract the former number, 

 and add the latter, we should obtain exactly all 

 the births produced by the marriages of the 

 period, and of course the real prolifickness of those 

 marriages. If the population be stationary, the 

 number of births to be added would exactly equal 

 the number to be subtracted, and the proportion 

 of births to marriages, as found in the registers, 

 would exactly represent the real prolifickness of 

 marriages. But if the population be either in- 

 creasing or decreasing, the number to be added 

 would never be equal to the number to be sub- 

 tracted, and the proportion of births to marriages 

 in the registers would never truly represent the 

 prolifickness of marriages. In an increasing po- 

 pulation the number to be added would evidently 

 be greater than the number to be subtracted, 

 and of course the proportion of births to mar- 

 riages as found in the registers would always be 

 too small to represent the true prolifickness of 

 marriages. And the contrary effect would take 

 place in a decreasing population. The question 

 therefore is, what we are to add, and what to 



