An experiment to study the $\overline{p}$ annihilation process at 1.05 Bev/c was performed with the Lawrence Radiation Laboratory 30-in. propane bubble chamber. It was observed that the $K$-meson production in annihilation events rises sharply with the increase in energy, namely from 4\ifmmode\pm\else\textpm\fi{}1% for annihilations at or near "rest" to 8\ifmmode\pm\else\textpm\fi{}1%. On the other hand, the pion multiplicity was not observed to increase appreciably with the increase of available energy. We have found a pion multiplicity of 5.0\ifmmode\pm\else\textpm\fi{}0.2. These numbers are discussed in this paper and compared with existing models for the $\overline{p}$ annihilation process. It is pointed out that with further increase in bombarding energy different models may differ appreciably in the above quantities.We have observed a $\overline{p}$-H annihilation cross section of 51\ifmmode\pm\else\textpm\fi{}10 mb and a $\overline{p}$-C annihilation cross section of 368\ifmmode\pm\else\textpm\fi{}60 mb at a $\overline{p}$ momentum of 1.05 Bev/c. Crude determinations of the $\overline{p}$ charge-exchange process---which turns out to be forward peaked--- and of $\overline{p}$ inelastic-scattering events leading to pion production are also discussed.