Rank Size Rule by G. K. Zipf

 

 

The concept “Rank-Size Rule” was first propounded during the first quarter of the present century. Though as Rosing (1966) has said, Zipf was not the first person to point towards the regularity of city sizes. The empirical existence of a regular relationship between the size of urban centres and their ranks was first presented by Auerback (1913) in a study of German cities. He opined that the population of the n'th city was 1/n'th the size of the largest city.

The rank-size rule was first scientifically put forward by G. K. Zipf (1941) as a theoretical model to express the relationship between observed and empirical regularity in the size of settlement hierarchy either urban or rural. This observed phenomenon is often referred to as Zipf’s Law.

Zipf (1949) observed that the logarithm of population size when plotted against the logarithm of the rank of the city produced points close to a straight line, with negative slope (rank inversely proportional to size). 

The idea that settlement size and rank have a systematic relationship was popularized by Zipf (1949),
expressed it by simple formula as:

Pr =  ^P1_/r^k , r = 1,2,...

This suggest that if the population of the largest city (P1) is divided by any city in the same region, the result will approximately be the population of the city (Pr) whose rank number is used as a divisor.
If the population of the largest city is known, the population of all other cities can be derived from the rank of their size. 

Thus, if the largest city has 100,000,00 population the tenth city will have one-tenth or 100,000 and the hundredth city will have one-hundredth as many or 10,000.