The falling-head lined borehole permeameter consists of a snugly fitting tube extending to the base of a vertical borehole in unsaturated soil. Water is suddenly introduced into the tube to standard depth, and the subsequent time course of water depth is observed. Soil-water data in the Amazon basin has been secured with this instrument. We develop an approximate analysis based on a Green-Ampt model, with the flow treated as a gravity-perturbed spherically symmetrically pressure-capillarity-driven flow.