The limitations imposed by space charges on the separation of ions in the usual magnetic mass spectrograph and the possibility of trapping electrons in the ion beam are described. It is found that high voltages and intense magnetic fields are required for moderate ion currents unless these are neutralized. Calculations are given on velocity modulated or interrupted ion beams and the performance'of a modulated separator is described. The theory of a radial magnetic separator is given in some detail and an experimental arrangement of such a separator proved more successful than the separator employing modulation. Some ion sources and suggested improvements are described.

The problem of the flow of heat through a long tunnel wall in an infinite solid has been treated and the results for the rate of flow and total heat flow have been expressed in a convenient form for numerical computations. This general problem has become of interest in connection with the cooling of deep mines.

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The radial potential distribution in an ionic beam of circular cross section is calculated and the maximum beam current which can be obtained in a beam of given radius and boundary conditions is computed. In the case of ions the maximum beam currents may be quite small. The ions in such beams have a considerable velocity distribution which in turn leads to a greater beam divergence than former calculations indicate. In Section 3 a method is worked out for holding the beam together during the initial accelerations. A disadvantage of cylindrical lenses is pointed out in this connection. The use of electrostatic lenses for holding together a beam composed of high energy particles is discussed in some detail. Calculations show the special arrangements of the lenses necessary for producing convergence of the beam. A few other arrangements to prevent divergence which were tried experimentally are described.

An examination of the positive ion emission from tungsten and molybdenum has been made in which it was sought to determine the following points: (1) The nature of the ions emitted at various temperatures; (2) the temperature variation of the positive ion current; (3) the theory of positive ion emission with regard to where and how the ions are formed; (4) the positive ion work function for these metals; (5) whether the work function, determined by experiment, checks with that calculated by a simple cyclic process involving the thermionic work function, the ionizing potential, and the latent heat of evaporation of the metal.The mass spectrum for tungsten and molybdenum filaments taken at moderate temperatures (1700° to 2000°K) has shown that the emitted ions consist of sodium, the two isotopes of potassium, and aluminum. At high temperatures these impurities disappear and finally both tungsten and molybdenum filaments yield positive ions of their own metal. The latter confirm a report by Wahlin. The temperature variation of the positive ion current at high temperature yields a value of 6.55 volts for the positive ion work function of tungsten and 6.09 volts for that of molybdenum. These values disagree widely from the values 10.88 volts and 9.26 volts calculated from the simple cyclic process mentioned above. This suggests that the ions are formed as a by-product of an irreversible recrystallization of the metal. Theoretical considerations show that the ions are emitted from the metal and are not formed after a neutral atom evaporates.