We present precise and reproducible mean pressure measurements at the botto
m of a cylindrical granular column. if a constant overload is added, the pr
essure is linear in overload and nonmonotonic in the column height. The res
ults are quantitatively consistent with a local, linear relation between st
ress components, as was recently proposed by some of us. They contradict th
e simplest classical (Janssen) approximation, and may rather severely test
competing models.