Previous results obtained by the magnetic deflection method of analysis have been extended, using a new but similar apparatus in which ions produced by accelerated electrons are accelerated through a slit into a chamber where a magnetic field bends them around a semi-circle whose radius depends on the speed, field and ratio of mass to charge. Those going into a Faraday cylinder are measured by means of an electrometer. The conclusion that ions produced at 16 volts are diatomic is confirmed, but no evidence of simultaneous ionization and dissociation, which was previously thought to occur for voltages above 20.2, is obtained. However, atomic ions H+ are readily produced by secondary dissociation of molecular ions H2+ even when the maximum electron energy is just above 16 volts. Triatomic ions H3+ also appear in large numbers as secondary products, for any voltage above 16. A mathematical theory of the dependence of the relative numbers of H2+ and H+ ions on pressure, gives curves in general agreement with experiment and leads to the conclusions that the probability of dissociation of H2+ is about 15 times the probability of a collision with a molecule according to the ordinary kinetic theory, and that the probability of the formation of H+ by dissociation is greater for H2+ than for H3+. The processes involved in ionization followed by dissociation are discussed, and it is shown that the apparent discrepancy between the heat of dissociation computed from the ionization potentials and Langmuir's result for the heat of thermal dissociation may perhaps be explained by the energy radiated, which is at present unknown.