Kinematic Corrections to Atomic Beam Experiments

We have calculated and measured the effective velocity distribution for metastable hydrogen atoms produced in a typical beam apparatus. The distribution is characterized by $U^n\exp (-U^2)$, where $n\simeq 4$ rather than $n=2\mathrm{}$. We discuss modifications of velocity-dependent corrections to beams measurements of the Lamb shift in the first excited state of atomic hydrogen.