1- The "ordinary" formula for the minimum electron pressure P corresponding to an electron density σ is of form P = Kσ. It has been generally accepted that this is a non-relativistic approximation, applying only to slow-moving electrons; and a "relativistic" formula has been given, intended to take account of change of mass with velocity. In a recent paper I have contended that the "ordinary" formula is the exact relativistic solution of the problem, and that the "relativistic" formula rests on a misconception. Since a decision on this point has far-reaching consequences in the theory of dense stars, and, moreover, has a fundamental bearing on the union of quantum theory with relativity theory, it has seemed desirable to supplement my earlier paper. I think the earlier paper makes it clear that whether the "relativistic" formula is right or wrong, existing proofs of it cannot be accepted. Briefly, the fallacy lies in the fact that the cell-divison of phase space is obtained by
standing waves
, but these are assigned an energy which has been derived for
progressive waves
. If this is not simply a mistake, it is a step which requires careful justification; and up to the present no one seems to have given any reason why one should assume that the energy or hamiltonian of standing waves is the same as that of pro-gressive waves. We may recall that the energy of plane progressive waves is easily calculated, because by a Lorentz transformation they are converted into waves advancing along the time-axis, and the energy is then the rest-energy of the particle; if the Lorentz transformation is applied to standing waves no such simplification results, and the reduction of the particle to rest involves an involves an altogether different type of transformation.