M.F. Dacey, 'Analysis of Central Place and Point Patterns by a Nearest Neighbour Method', Proceedings of the I.G.U. Symposium in Urban Geography, Lund1960; edited by K. Norborg, Gleerups, Lund, 1962, pp. 55-75.
2.
B.J.L. Berry and W.L. Garrison, 'The Functional Bases of the Central Place Hierarchy', Ecomomic Geography, Vol. 34 (1958).
3.
' W.K.D. Davies, 'The Ranking of Service Centres: A Critical Review', Unpublished Discussion Group Paper, Department of Geography, University of Southampton, January 1965.
4.
This analysis of central place patterns is only concerned with the hierarchy of retail central places, all other functions are excluded. Moreover, the study is made at the establishment level of generalisation. W.K.D. Davies, 'Some Considerations of Scale in Central Place Analysis', Tijdschrift voor Economische en Sociale Geografie. Vol. 56, No. 6 [Nov. 1965]. Although central place theory has been formulated in terms of goods, not combinations of goods as represented by the establishment, it proved impossible to consider the spatial distribution of individual goods for an area containing a total population of approximately 145,000. Consequently information was collected for each type of establishment, a term used interchangeably with 'outlet' or 'functional type'. Where an establishment contained two different types of function the number of assistants was divided into two and allocated to each type.
5.
L. Jay and P. Hirsch, 'The Comparative Analysis of Settlements', Sociologia Ruralis, Vol. 1, No. 1 (Spring 1960), pp. 51-65.
6.
A ratio of 1:3 between shops and other property was used by the Board of Trade (Census of Retail Distribution, 1961, H.M.S.O. 1964), to define the edge of a shopping centre. A slightly broader definition was used in the study area. A shop was considered to be a part of a central place if it lay within a distance equivalent to the frontage of four terrace houses, otherwise it was considered to be an isolated central place.
7.
These were the central places containing over three different kinds of establishments.
8.
P.J. Clark, 'Grouping in Spatial Distributions', Science, Vol. 123 (1956), pp. 373-4-
9.
Subsidiary centres are allocated to the higher order places purely on the basis of road proximity. It must also be stressed that the A system is not complete since the case study area does not include all the hinterland of Pontypridd. The fifth order is excluded from Fig. 6 simply to aid clarity in the diagram.
10.
'O.W. Christaller, in C. Baskin, A.Critique and Translation of Christaller's Die Zentralen Orte in Suddeutschland ', Ph.D. thesis, University of Virginia, 1956.
11.
ibid, p. 189.
12.
There are three ways in which a service industry can accommodate itself to a change in city size or an increase in its trade area: (I) Duplication of outlet; (2) Increase in the size of the outlet; (3) Specialisation of the outlet into several distinct functional types. Both (1) and (2) are built into the analysis since the calculation of centrality values takes into account the numbers of any type of establishment and also the various sizes instead of simply the presence or absence of a function. The third form of accommodation is also incorporated, since specialised types of establishment are recognised in the initial defunction of types.
13.
B.J.L. Berry and A. Pred, 'Central Place Studies', Regional Science Research Institute Bibliography Series, No. I, Philadelphia, U.S.A., p. 3.
14.
H. Carol, 'The Hierarchy of Central Functions within the City', Annals of the Association of American Geographers, Vol. 5o, No. 4 (December 1960).
15.
W. Christaller in C. Baskinop. cit, p. 419.
16.
ibid., p. 420.
17.
Empirical evidence for this conclusion may be found in: B.J.L. Berry and H. Mayer, 'Comparative Studies of Central Place Systems' Mimeographed Report N.O.N.R. 2121-18. N.R. 389-126 Geography Branch of the U.S. Office of Naval Research, Department of Geography, University of Chicago , 1963.
18.
Comparative study of three rural areas in the American Mid West each with a different agricultural economic base and settlement pattern revealed that three groups of centres could be recognised in all areas. However the functions associated with each grade of centre varied. Almost all the town level functions of Iowa moved to city level in the Dakotas and many of the village level functions shifted to the town level. Towns and cities in the Dakotas perform simple functions and enter at lower thresholds.
19.
L. Wittgenstein , 'Handeln vom Netz, nicht von dem, was das Netz beschreibt', Tractatus Logico-Philosophicus, Harcourt Brace & Co., New York, 1922, 6.35.