The rank size rule was proposed by G. K. Zipf in 1949. RSR is a study in urban hierarchy but unlike the primate city concept which focuses only on the largest city, the RSR discusses the relationship of the largest cities with the other cities & settlements in the entire country.
This again is an empirical observation and does not throw much light on the process of responsible for rank size relationship. Although the theory is based on empirical observations, the conclusions are normative in character.
The cities in any region may be ranked from largest to smallest according to their population size. Thus the largest city is ranked 1, the second largest no. 2, continuing in this way down to the lower ranking towns.
If Pn= population of nth rank settlement in the settlement complex
Then Pn= K P1/n
Mathematically and graphically depicted K is not always a unitary value and the relationship is actually an exponential relationship b/w population and rank depicted as follows:
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What can be concluded from the graph is:
1. That lower ranked settlements have comparable population
2. There are numerous smaller towns & villages which have comparable population
3. Higher rank cities are few and the population is not comparable for the larger cities
2 issues to be understood in this area are:
1. Why large cities are few in numbers
2. How does the relationship establish itself
The mechanism how the rank size relationship develops was not objectively explained by Zipf but he suggested the process of agglomeration and diversification as follows:
According to Zipf, villages and towns are relatively self contained system and therefore they don’t enter into competition with adjoining towns and villages. Hence it is possible for numerous towns and villages to co-exist and therefore can be more in number. On the other hand, urban systems in general are not self contained and depend on hinterland for supporting their economy, hence it is not possible for two large urban centres to co-exist side by side and tend to locate themselves as far as possible for efficient use of space.
Rank Size Rule can also be represented in logarithm relationship:
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Deviation A represents the existence of primate cities i.e. largest city is disproportionally large than compare to 2nd largest city.
Deviation B represents absence of primacy where more than one city are very large and of comparable population e.g. India has 4 megacities of comparable size.
Rank Size Rule in India:
RSR does not exist in India at national level as population of Mumbai, Calcutta and Delhi is comparable. Similarly majority of states do not conform to RSR. 15 out of 28 states have primacy. In another 8, leading city is just larger than 2nd largest city. (Bihar, Keral, MP, Punjab, Orissa, Goa, Arunachal Pradesh and Nagaland)
Rank size relationships appear to hold good in Rajasthan. In brief RSR in India is an exception rather than a rule.