308 
PHYSICS: E. H. HALL 
Proc. N. a. S. 
plied to a metal from without. This proposition seems to be in general 
accord with I^angmuir's conception of atomic shells. See no. 991 in 
Science Abstracts for 1919. 
3. The behavior of these ions in an electric field is somewhat like that 
of magnetic particles in a magnetic field, as set forth in Langevin's theory^ 
of paramagnetism, or that of electric dipoles as described by Sir J. J. Thom- 
son.^ But in one vital particular, indicated in the next paragraph, the 
formula used by Langevin and by Thomson must be modified to suit the 
present case. 
4. When and where the equipartition law of energy holds, the Boltz- 
mann-Maxwell distribution law can be written with the factor e~ ^^^^^ 
where V is the mean potential energy of a particle with respect to any 
coordinate, either of position or of direction, in the field of force, and 
RT is twice the mean kinetic energy of the particles with respect to any 
degree of freedom whatever. But when and where the equipartition 
law fails, we must, if we can use the Boltzmann-Maxwell formula at all, 
use it with regard to the particular coordinate or degree of freedom that we 
are dealing with. Kinetic energy along one coordinate may in this case 
have nothing to do with the distribution of particles along another co- 
ordinate. For example, if all the kinetic energy of air particles became ro- 
tary energy, the atomosphere would fall. So, too, if we are dealing with 
particles that have no rotary energy, the translatory energy of these 
particles will have nothing to do with their orientation in a directing field 
of force. 
5. The atoms and the ions have a mean kinetic energy of rotation 
proportional to the absolute temperature but of a much smaller order of 
magnitude than that of the energy of translatory vibration.^ Accordingly 
we should, in the Boltzmann-Maxwell formula, use a very much smaller 
value than Langevin and Thomson have used in the denominator of the 
exponent of e, thus getting a much greater orientation, in a given field of 
force, than their formula would lead us to expect. This orientation will, 
through a great range of electric field strength, be proportional to the 
strength of the field and inversely proportional to the absolute tempera- 
ture. 
6. The time required for the orientation of an ion to reach its final 
value is large compared with the period of the translatory vibrations of the 
ion. See (21). 
7. An ion has on its surface a fairly definite scar or pit from which an 
electron has been dislodged, and the ion can capture an approaching elec- 
tron, thereby recovering the status of an atom, only when the electron 
strikes, not too violently, within this pit. 
8. A free electron, approaching an ion with the kinetic energy of a gas 
molecule, may, though attracted toward the pit, shoot by, failing to make 
