Abstract The work contained in this dissertation began with a 1st of some properties of matter degenerate in the sense FermiDirac statistics (Papers I, II, VII, IX, X) and this was fol1owed by an investigation into the internal structure of cold stel1ar bodies utilizing the theory of pressure ionization (Paper III). As is wellknown, the cold stellar bodies viz. white dwarf' stars and p1anets, have provided one of' the most ferti fields for the application of the new Quantum statistics. It was realised that under certain simplified conditions, the state of' an e1ectron inside a cold stallar mass could be represented by the wavefunctions of a simp1e harmonic oscillator and a further development of this idea led to a discussed (of the usual (i.e., nonrelativistic) and the relatinetic harmonic oscillator subject to artificial boundary conditions (papers IV, V, VI, VIII). In view of the {two alternative derivations  one based on the pressure of degenerate gas and the other using the idea of' a harmonic oscillator  for the fundamental mass radius relation of a white dwarf, it a1so appeared to be of interest to consider the problem of the density distribution of a FermiDirac gas in the presence of a field, from two alternative stanpoints viz. (1.) . Gibb's free energy and (2) Schrodingerâ€™s equation for the motion of particle in the field of force. In the white dwarf theory, several simplifying assumptions become necessary to make the problem amenable to the two alternative treatments, but the ple problem treated in the paper IX, has the merit that it permits of an exact treatment in both the cases. Paper X deals with a general theorem regarding the ratio of the average kinetic and potential energies per particle, and the condensation phenomenon for a BoseEinstein gas in the presence of a uniform field. The specific heat is found to be discontinuous at the critical point. We now proceed to summarize in somewhat greater detail the contents of the papers referred to above, but always confining ourselves to the essential features, and also give a brief account of some recent work which is necessary to provide a background for them.
