The previous post suggested that mound shape could be modeled as a spherical cap. I then proposed that the shape of those mounds may change through time, due to weathering and repeated plowing by modern agricultural equipment, but mound volume might remain the same. As illustrated in the following figure, mounds might become shorter but wider as they are weathered and plowed. In the figure, A represents the original mound shape, while B reflects mound shape after weathering and plowing. The height, *h*, has decreased over time, while the radius, *a*, has increased.

Other hypotheses are possible, but I will evaluate this scenario first.

I have compiled museum data on mound condition and mound size for all recorded mounds in my study region. The museum records characterize mound condition as either “whole” or “plowed”. The records did not disclose the basis for this characterization. These records also document mound height and width. For each mound, I calculated a volume, assuming that mound shape resembles a spherical cap. The following two histograms illustrate the distribution of mound volume for plowed mounds and for whole mounds.

As you can see, the distributions of mound size for plowed and whole mounds look very similar. A few outliers may occur at the right tail of both distributions. These outliers represent unusually large mounds. The similarity of the histograms suggest that a single probability distribution could be used to model monument volume. The next post will evaluate monument volume more rigorously.

© Scott Pletka and *Mathematical Tools, Archaeological Problems*, 2013.