486 On the Fruitfulness of Marriages. Bk. ii. 



of the prolifickness of marriages, and the propor- 

 tion of the born which lives to marry ; but it must 

 still be remembered that they are only approxi- 

 mations, and intended rather to explain apparent 

 difficulties, than to obtain results which can be 

 depended upon as correct. 



It will be observed how very important the 

 correction for second and third marriages is. 

 Supposing each marriage to yield four births, and 

 the births and deaths to be equal, it would at first 

 appear necessary that, in order to produce this 

 effect, exactly half of the born should live to 

 marry ; but if, on account of the second and third 

 marriages, we subtract \ from the marriages, and 

 then compare them with the deaths, the propor- 

 tion will be as 1 to 44- ; and it will appear that, 

 instead of one half, it will only be necessary that 

 2 children out of 4± should live to marry. Upon 

 the same principle, if the births were to the mar- 

 riages as 4 to 1, and exactly half of the born live 

 to marry, it might be supposed at first that the 

 population would be stationary ; but if we sub- 

 tract -£- fr° m the marriages; and then take the 

 proportion of deaths to marriages as 4 to 1, we 

 shall find that the deaths in the registers, com- 

 pared with the marriages, would only be as 34. 

 to 1 ; and the births would be to the deaths as 4 

 to 34y, or 12 to 10, which is a tolerably fast rate 

 of increase. 



It should be further observed, that as a much 

 greater number of widowers marry again than of 



