Atomic Energy Relations. I

A simple method for the calculation of approximate energies of atomic levels is presented in this paper. It is based on the derivation of linear relations which express the unknown energy in terms of observed energy values of the atom and its ions. It is shown that the degree of approximation increases with the amount of experimental data available for use in the calculation and also how the best formulas can be obtained for each case. Several tables are given containing formulas for configurations involving $s$ and $p$ electrons. They are applied to the spectra of carbon, nitrogen and oxygen and the energy values so determined are compared with those known from observations. In an appendix the method of approximation is compared with the quantum mechanical perturbation method.