A method is outlined for calculating nonrelativistic eigenvalues and wave functions for a two-electron $P$ state of odd parity, and for evaluating the mass polarization and all of the relativistic corrections, apart from the radiative terms. Calculations have been made for the low-lying $P$ states of He and the $2{}_{}{}^1{}_{}{}^{}P$ state of ${\mathrm{Li}}^{+}$ using up to 560 terms in expansion of the wave function. The nonrelativistic eigenvalues converge to within an accuracy of from ${10}^{-4\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$ to ${10}^{-2\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$. The values of the mass polarization and of the relativistic corrections converge more rapidly than this, so that the total theoretical ionization energy is estimated to be correct to within an error of not more than ${10}^{-2\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$, i.e., considerably less than the experimental error, in the case of all of the states considered. The difference between the theoretical and experimental term values is in no case greater than 0.1 ${\mathrm{cm}}^{-1\mathrm{}}$ in absolute magnitude, and is presumed to be due to the contributions from the radiative terms, which have not been included in the calculation. The term value obtained for the $2{}_{}{}^1{}_{}{}^{}P$ state of ${\mathrm{Li}}^{+}$ confirms the identification of the line at 9581.42 Å in the ${\mathrm{Li}}^{+}$ spectrum as belonging to the $2{}_{}{}^1{}_{}{}^{}S-2\mathrm{}{}_{}{}^1{}_{}{}^{}P$ transition.

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