The beam-foil excitation method has been used to measure the radiative mean lives of the $2p$ and $3p$ states of atomic hydrogen. The results obtained were (1.60\ifmmode\pm\else\textpm\fi{}0.01)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}9}$ sec and (5.5\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}9}$ sec, respectively. A study of the results of this experiment has led to the following conclusions: (a) the Lyman-$\ensuremath{\alpha}$ decay curves are best fitted by the sum of two exponential terms whose characteristic decay times correspond to spontaneous decay of the $2p$ state and repopulation of this state by higher states, (b) the shapes of the Lyman-$\ensuremath{\alpha}$ decay curves vary with foil thickness, and (c) the ion energy loss in the foils used in this experiment changes with the age of the foil. A review of previous measurements on atomic-hydrogen radiative mean lives is also made and compared with theory.