The Rank Size Rule

• The relationships between city rank and city population size was first noticed by F. Auerbach in 1913, that when the rank numbers (from largest to smallest towns) are plotted against their respective population, a regular relationship generally emerges.
• The “rank-size rule”, proposed by G. K. Zipf in 1949, states that if all urban settlements in an area are ranked in descending order of population, the population of the ‘nth’ town will be 1/n^th that of the largest town.
• Zipf’s rank-size rule can mathematically be expressed as P_n = P₁/n where Pn is the population of the town of rank n in the descending order and P1 is the population of the largest city. Thus, if the largest city has a population of 50 lakhs, the tenth ranking town should, as per the rule, have a population of 5 lakh people.

Concept Note
The ‘exploded city’ view was postulated in the book Social Geography of the United States by J. Wreford Watson. The theoretical position of the margin of an urban field can be calculated by using a technique known as breaking point theory.

A. E. Smailes divided a city region into Core Area, Outer Area and Fringe Area. The ‘law of Retail Trade Gravitation’ predicts the proportion of retail trade that two towns will derive from a settlement (k) lying between them. This is relevant to the question of the theoretical delimitation of urban fields.

Theories of Urban Structure

Concentric Zone Theory
This theory based on hypothetical pattern of urban growth was first postulated in 1923 by an urban sociologist, E.W. Burgess, while studying the urban morphology of the city of Chicago, the USA. Through this model, Burgess stated that the development of a city place from its central commercial core takes place in a series of concentric circles. He identified five zones in concentric pattern expanding outward from the city core. Let’s know what are these zones.
Zone No. 1: This is the C.B.D. (Central Business District), the heart of the City. It has shops, offices, banks, theaters and hotels. It has multi-story skyscrapers, transport lines, converge in this zone. The CBD draws its business from all other encircling zones.
Zone No. 2: Surrounding the CBD, lies a traditional area, a zone of residential deterioration, marked also by the encroachment of business and light manufacturing. This is a zone of urban plight of tenements and slums and inadequate services.
Zone No. 3: This is the Zone of working men’s houses.
Zone No. 4: This consists of middle class residence, a suburban area that is characterized by greater affluence and spaciousness.
Zone No. 5: This is the Urban Fringe consisting of communities that are in effete dormitories of the CBD, where most of the economically active residents go to work. Here lies some of the highest quality residential houses.

Concentric Zone Theory as Propounded by Prof. E.W. Burgess

Indian City of Muzaffarpur Somewhat Conforming to The Concentric Theory

The Sector Theory
This theory was proposed by Homer Hoyt and M. R. Davie in 1939. According to this theory, patterns of urban land use are conditioned by the arranged routes radiating from the city Center creating a sectoral pattern of land and rental value influencing the urban land use pattern.

Sectors: –

1. The CBD
2. Wholesaling and Light Manufacturing
3. Low-Class Residential Area
4. Medium Class Residential Area.
5. High Class Residential Area.

Colby’s Dynamic Theory
According to this theory the patterns of any city at any given point is the result of forces at work, i.e., centripetal and centrifugal. Centripetal forces are of two types: (i) residents and business class people seeking the comforts of life in urban centers get lured into a city; (ii) within the city residents and business are drawn towards C.B.D from the fringe area, a C.B.D provides better access to both the consumers and the laborers. It is main hub of the city with stores, banks, libraries, theaters and clubs. Centrifugal forces just act in a reverse manner and drive people away from the C.B.D into suburbs. Even congested slums force people and business activities to move out of the city center.

The Multiple Nuclei Theory
In 1945, this theory was proposed by C. D. Harris and E. L. Ullman.  It was suggested that land use pattern in most large cities develop around a number of discrete centers or nuclei rather than a single center as described in the concentric and sector models.

Von Thunen’s Model
Von Thunen conceived the idea of a land use model in both urban and rural landscape around a city on an isotropic landscape. His idea is basically how economic rent decreases from center of a city to its periphery. His system of land use around a city with no trade alliance with any other country is ring shaped. Near the city, he envisages rings of forest, crop rotation, horticulture and dairying. His theory stresses more on agricultural land use around a city rather than the land use within the city.

Sinclair’s Model
Sinclair propounded a ring type model in 1967. The progression of intensity of his ring’s is directly proportional to the degree of urban influence in form of high urban taxes, constrained zoning and disturbances in the vicinity of urban areas. This theory is also supported by two British writers, Best and Gosson. They believe there is a shift supported by cause i.e. increasing competition from distant areas with better production facilities, and loss of casual labour to city jobs by rural-urban fringe farmers.

Sinclair’s Pattern of Land use around an expanding metropolitan area are as follows: –

1. Urban Farming close to the city
2. Vacant and grazing land
3. Field crop and grazing land
4. Dairying and field crop land
5. Specialised food grain-livestock

Concept Note
A pioneer study of the CBD was done by American geographers R. E. Murphy and J.E. Vance Jr. In 1951, based on a study of 36 cities, the economist C. Clark describe the pattern of population density in any city.Hypermarkets are carefully planned out-of-town shopping centers.

The Central Place Theory
The theory of central place is associated with the economically optimum location of services of different variety and range both for the town as service provider and the countryside as the service getter. The term ‘central place’ was first used by Mark Jefferson in 1931, while defining a settlement which is necessarily a focus of various economic and social activities for the surrounding hinterland.

Walter Christaller analyzed the ‘centrality’ in detail in 1931, in West Germany, on the basis of number of telephone connections at a place as the prime criterion for determining the hierarchy. Later A. Losch did some modification on it.

Christaller proposed that settlements with the lowest order specialization would be equally spaced and surrounded by hexagonal-shaped service areas or hinterlands. He assumed a stable price of the land, equal land surface and isotropic characteristics of the land.According to him, the smallest centers would lie approximately 7 km. apart. He also outlined hierarchy according to K value:K=3 represents Marketing Principle. It favors the development of symmetrical nested hierarchy of central places. This principle postulates that rural produce comes to the higher order centers through lower order centers and the goods produced in urban areas move through higher order centers to the lower order centers.K = 4 represents Traffic Principle.

In this principle, the number of centers followed the geometrical progression as 1,4,16,64, and so on. At this level one big center serves 4 lower order centers.K-7 represents Administrative Principle. At this level one bigger central place serves seven second order centers.In 1940, the economist A. Losch presented an important modification of Christaller’s Model. Like Christaller, he again used hexagonal service areas, but allowed various hexagonal systems to co-exist. He developed a more sophisticated form of economic landscape by superimposing all the various hexagonal systems.

Nested Hierarchy Theory
A. K. Philberk, an American geographer based his nested hierarchy theory on the following: –

• Inter-connection between different occupations viz. agriculture, cattle rearing, mining, manufacturing, industry and trade are found between uniform areas which are homogenous in terms of occupance.
• Origin of nodal areas — in one nodal area different uniform areas are found which are connected with the focal point. The example of a nodal region could be one town, which is made of different mohallas.
• Nested hierarchy of nodal organization — this is the third postulate of nested hierarchy theory, which is related with the occupant units arrangement. This hierarchy turns from uniform relationship to nodal organization.