Developing the approximate theory of CFE from metals above is comparatively easy, for the following reasons. (1) Sommerfeld's free-electron theory, with its particular assumptions about the distribution of internal electron states in energy, applies adequately to many metals as a first approximation. (2) Most of the time, metals have no surface states and (in many cases) metal wave-functions have no significant " surface resonances ". (3) Metals have a high density of states at the Fermi level, so the charge that generates/screens external electric fields lies mainly on the outside of the top atomic layer, and no meaningful "field penetration" occurs. (4) Metals have high electrical conductivity : no significant voltage drops occur inside metal emitters: this means that there are no factors obstructing the supply of electrons to the emitting surface, and that the electrons in this region can be both in effective local thermodynamic equilibrium and in effective thermodynamic equilibrium with the electrons in the metal support structure on which the emitter is mounted. (5) Atomic-level effects are disregarded.