Abstract
The second-order perturbation energy of the hydrogen molecule ion is recalculated without restoring to the mathematical approximations used by Brooks or by Unsöld. The disagreement between the corrected perturbation calculations and the exact results of Hylleraas is presumably due to the neglect of exchange forces in the initial perturbation formula and cannot be removed by Brooks' proposed scheme of arbitrarily limiting the range of integration in the matrix elements.