B very beautiful experiments, Lamb and Retherford1 have shown that the fine structure of the second quantum state of hydrogen does not agree with the prediction of the Dirac theory. The 2s level, which according to Dirac’s theory should coincide with the 2p 1 2 level, is actually higher than the latter by an amount of about 0.033 cm−1 or 1000 megacycles. This discrepancy had long been suspected from spectroscopic measurements.23 However, so far no satisfactory theoretical explanation has been given. Kemble and Present, and Pasternack4 have shown that the shift of the Is level cannot be explained by a nuclear interaction of reasonable magnitude, and Uehling5 has investigated the effect of the “polarization of the vacuum” in the Dirac hole theory, and has found that this effect also is much too small and has, in addition, the wrong sign. Schwinger and Weisskopf, and Oppenheimer have suggested that a possible explanation might be the shift of energy levels by the interaction of the