Quantisation & Energy - The second section provides a detailed justification of the orbital quantisation criteria for the principal quantum number, by relating the single valuedness of the orbiting electron's matter wave wavelength, to the requirement that, for a stable orbit, its bound energy must remain constant over one complete orbit. This provides a direct proof of the veracity of permitted and non-permitted orbits. The process also leads to the justification of Bohr's original orbital angular momentum quantum rule. Based on Einstein's energy/momentum relationship, a generalised relativistic orbital energy equation is also developed, for the later use in the quantisation of the orbital energies of four sample orbits.

Quantisation of Simple Orbits - In this Section the results of the previous Section are used to generate quantised orbital energy equations for simple circular and elliptic orbits.

Quantisation of Relativistically Corrected Orbits - The fourth Section generates quantised orbital energy equations, in which account is taken of the effects of the relativistic increase in mass of the electron due to its high orbital velocity. Both a circular and an elliptic orbit are considered. The latter is shown to result in the expanded version of Sommerfeld's quantised orbital energy equation.

Conclusions - Concluding remarks on all aspects of this first paper, including a brief comparison of the resurrected theory, (as so far developed), with Bohr's original theory and the modern quantum theory.

Appendix A - This Appendix uses the solution to the genaralised orbital equation of motion, (see Reference 2), to generate three subsiduary equations needed in the derivation of the generalised orbital energy equation in the Section 2. In addition, from the earlier results, for interest, this Appendix also provides a derivation of the full version of Sommerfeld's quantised energy equation for a relativistically mass corrected elliptic orbit.