472 On the Fruitfulness of Marriages. Bk. ii. 



If we suppose a country where the population 

 is stationary, where there are no emigrations, 

 immigrations, or illegitimate children, and where 

 the registers of births deaths and marriages are 

 accurate, and continue always in the same pro- 

 portion to the population, then the proportion of 

 the annual births to the annual marriages will 

 express the number of children born to each mar- 

 riage, including second and third marriages, and 

 when corrected for second and third marriages, 

 it will also express the proportion of the born 

 which lives to marry, once or oftener ; while the 

 annual mortality will accurately express the ex- 

 pectation of life. 



But if the population be either increasing or 

 decreasing, and the births, deaths and marriages 

 increasing or decreasing in the same ratio, such 

 a movement will necessarily disturb all the pro- 

 portions, because the events which are contem- 

 porary in the registers are not contemporary in 

 the order of nature, and an increase or decrease 

 must have been taking place in the interval. 



In the first place, the births of any year cannot 

 in the order of nature have come from the con- 

 temporary marriages, but must have been derived 

 principally from the marriages of preceding years. 



To form a judgment then of the prolifickness of 

 marriages taken as they occur, including second 

 and third marriages, let uscutoffacertain period of 

 the registers of any country (30 years for instance) 

 and inquire what is the number of births which 



