[edwardbernays]

Wouldn't there necessarily be more lead pipes at the peak and post-peak? Assuming that pipe-building was some non-linear function of dominance, which seems a fair assumption, we would start with 0% pipes at 0% rome and asymptotically close to 100% pipes at the asymptotic 100% peak rome. Is this a bad assumption, or is it basically just pedantry?

[wredcoll]

It would be more about lead pipes per capita, possibly as rome itself grew wealthier from conquests they added more and more piping, but it would be hard to relate this to any specific moment in time.

Presumably the wealthy elites had their pipes installed first anyways.