POPULATION, increase of. ( Bridge. ) 



Of the method of finding the increase of population in any country,, 

 under given circumstances of births and mortality. 

 Let P represent the population of a country at any given period j 



the fractional part of the population which die in a year (or ratio 



of mortality j) -j- the proportion of births in a year ; then, if A repre- 

 sent the state of the population at the end of n years, 



Or Log. A = Log. P -f n X log. 1 + 



Of the quantities A, P, m, b, n, any four being given, the fifth may be 

 found. 



Ex. I. Suppose the population of Great Britain, in the year 1800, to have 

 been ten millions ; that th part die annually ; and the number of births 



are ^ , and that no emigration takes place during the present century j 



What will be the state of its population in the year 1900 ? 

 Here A = 22930000. 



Ex. 2. Suppose the population of France in the year 1792 to have been 

 27000000 ; the ratio of mortality, during the 18th century, to have been 



th, and the number of births th j What was the state of its popula- 

 tion in the year 1700 ? 



Here P = 16864396. 



Ex. 3. Suppose the population of North America to have, been five 

 millions in the year 1800 j in how many years will it amount to 16 mil- 

 lions, taking the ratio of mortality at -Uh, and the annual proportion of 



births at ^th ? 



Here n = 60.3 years. 



Ex. 4. The population of a province, in the year 1760, was estimated 

 at 500000 persons j in the year 1800 it amounted to 720000 persons ; from 



the bills of mortality it appeared, that, upon an average, p^th part of 

 209 



