An apparatus is described which is suitable for a study of the velocity distribution of ions formed by single electron impact Electrons, confined to a narrow beam by a magnetic field, pass along the axis of two coaxial cylinders, ionize the gas, and are collected by a trap. The thick, inner cylinder, which is slotted, serves to allow only ions moving perpendicularly to the electron beam to pass to the outer collecting cylinder. A retarding voltage is applied between the cylinders. A study of the positive ion current collected as a function of the retarding voltage permits a determination of the velocity distribution of the ions. The above method is employed in a study of hydrogen.Velocity distribution of ${\mathrm{H}}^{+}$ ions formed by electron impact in ${\mathrm{H}}_{2}$. Theory shows that when the ${\mathrm{H}}_{2}$ molecule is ionized by electron impact, it may prove unstable and dissociate into ${\mathrm{H}}^{+}$+H (or H\ensuremath{'}) or into ${\mathrm{H}}^{+}$+${\mathrm{H}}^{+}$ if two electrons have been removed. The ${\mathrm{H}}^{+}$ ions thus formed possess kinetic energy. The ${\mathrm{H}}^{+}$ ions coming from dissociation into ${\mathrm{H}}^{+}$+H should occur at minimum electron velocities of about 27 to 40 volts, possessing roughly 5 to 11 volts velocity; while the ${\mathrm{H}}^{+}$ ions resulting from removal of two electrons occur at minimum electron velocities of 46 to 56 volts, possessing 7.5 to 12.5 volts velocity. In agreement with the predictions of the theory it was found that the velocities of those ions resulting from dissociation into ${\mathrm{H}}^{+}$+H and ${\mathrm{H}}^{+}$+${\mathrm{H}}^{+}$ together with the minimum velocities necessary to produce them satisfy linear relationships.