  Quantifying the population density of an urban area is a fraught issue.
Measures of density are often defined differently from place to place or
applied inconsistently, and arguments abound over just how much of the land
surrounding a city should and should not be classified as `urban'. The prime
candidates for a consistent density measure are overall density OD (also known
as average density) and population-weighted density PWD (as recently adopted by
the US Census Bureau). In this note some less intuitive aspects of PWD are
explored, so that the consequences of adopting PWD as a density measure are
better understood relative to OD. It will also be seen that one cannot entirely
dispense with the need to define urban boundaries, to work preferentially with
the smallest parcels of land for which one has data, and to pay careful
attention to the delineation of boundaries to ensure high-density and
low-density developments are allocated to separate parcels where possible.
