Some Extensions of Mills's Method for Urban Population Density Gradient Estimation

This paper extends Milk's method for estimating urban population density gradients to general noncircular and asymmetrical urban forms, using Gauss-Legendre quadrature embedded in a Newton-Raphson root finding algorithm. We also examine the sensitivity of the Mills method to measurement errors in the assumptions. Several issues arising from the comparison of analytical, Mills type estimation procedures with statistical procedures are explored, particularly in light of recent work that questions the negative exponential formulation of urban density gradients. We note in particular the influence of secondary population centers as a source of estimation bias.     

Hobbes on political allegiance and obligation

Since he was convinced that men of virtue were the exception rather than the rule, the primary political problem for Hobbes was how best to guarantee the adherence of men in general to the civil law. Hobbes' solution to this problem appears at times to be inconsistent. This was not the case; Hobbes was advancing two separate, though complementary, theories as to why men do in fact obey the civil law. Whether or not there is a similar kind of duality in Hobbes' argument concerning why men ought to obey lawful authority is also discussed.