The name is absent

where l[x] denotes the population density within the city. It is reasonable to assume that Ra is
symmetric and decreasing with |x|, and we will denote the fraction

Ra(D) = а
Ra (0)

as the marginal fraction, which we may think of as a number approximately equal to zero w.r.t. the
problem in question. As a simple device of this sort we will consider

(3.2)

R [ x ] = K ■ — e
a

L₀

After a change of variables, we see that (3.1) implies
(3.3)

K = _r 7 L / ^D

∫ e ^-u 21 ( Du / 7) du

-V

where

7 = √- ln[ а ]

If we consider the case where the population is uniformly distributed within a 2-dimensional disc,
l[x]=C|x| and we get

(3.4)

C (1) =

If on the other hand the population is uniformly distributed along a truly 1-dimensional geography,
l[x]=C and this gives

(3.5)

7

∫ 2 e^{- u} 2 du

0

The point to be made here is that C₇⁽¹⁾ and C?² are never very much different. If the marginal level
αe[0.01,0.50] , then 2 = C( / C7(,²2 = 4. Hence C/ and C7(,²2 always have the same order of
magnitude. Moreover, it follows from (3.3) that any population density satisfying a condition of the
form
(3.6)

C₁IX ≤ lX ≤ C₂D - D ≤ x ≤ D

11

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