474 On tlic Fruitfultiess of Marriages. Bk. ii. 



subtract, when the births and deaths are not 

 equal. 



The average proportion of births to marriages 

 in Europe is about 4 to 1. Let us suppose, for 

 the sake of illustration, that each marriage yields 

 four children, one every other year.* In this 

 case it is evident that, wherever we begin the 

 period in the registers, the marriages of the pre- 

 ceding eight years will only have produced half 

 of their births, and the other half will be arranged 

 with the marriages included in the period, and 

 ought to be subtracted from them. In the same 

 manner the marriages of the last eight years of 

 the period will only have produced half of their 

 births, and the other half ought to be added. 

 But half of the births of any eight years may be 

 considered as nearly equal to all the births of the 

 succeeding 3-| years. In instances of the most 

 rapid increase it will rather exceed the births of 

 the next 3^- years, and, in cases of slow increase, 

 approach towards the births of the next 4 years. 

 The mean therefore may be taken at 3f years.f 

 Consequently, if we subtract the births of the first 

 3^ years of the period, and add the births of the 

 3f years subsequent to the period, we shall have 



* In the statistical account of Scotland it is said, that the ave- 

 rage distance between the children of the same family has been 

 calculated to be about two years. 



f According to the rate of increase which has lately been 

 taking place in England (1802,) the period by calculation would, 

 be about 3f years. 



