An experiment is described which utilizes the Hanle technique for measurement of atomic excited-state lifetimes, with particular application to the3P1state of mercury. The components for the experiment are comparatively inexpensive or readily constructed, and the technique is one of the few which directly illustrate features of the interaction between radiation and free atoms. A simple classical description of the effect is given, followed by a more detailed quantum description, as well as constructional details of an experimental arrangement suitable for an advanced undergraduate or graduate laboratory.