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Thomas's differential equation for the average field inside a heavy atom is analogous to Emden's equation for the polytropic equilibrium of a star. Emden's result that the total gravitational potential energy of a star is calculable once the differential equation has been solved is adapted to give the total electrostatic energy, and hence the total energy of binding, of an atom built on Thomas's model. This should be equal to the sum of the successive ionisation potentials. The total energy is found to be proportional to N , where N is the atomic number. The values found agree with Hartree's calculations of the successive ionisation potentials of certain atoms.
E. A. Milne (Fri,) studied this question.
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