Using Heisenberg's theory as developed by Öhman for problems of this kind, it is shown that, for the line Hα , the hydrogen atom acts as a space oscillator for 35 per cent of the incident energy, and as an isotropic scatterer for the remaining 65 per cent. For the D 3 line of neutral helium the figures are 36 and 64 per cent. For the photospheric radiation an approximate value for the coefficient of darkening β1 = 0.67 is derived for the centre of Hα from Abbot's observations and Evans' residual intensities. For the D 3 line a value β1 = β = 1.36 is adopted. The theory, given for a prominence of small total optical depth, predicts for the emission a degree of polarization of 1.6 per cent at the photosphere, and 7.5 per cent at an altitude of 50,000 km., as compared with Lyot's observed values of 0.8 to 1.2 per cent in general. For the D 3 emission the theory gives 2.6 per cent at the photosphere and 8.4 per cent at an altitude of 50,000 km., as compared with the observed 0.9 to 1.2 per cent. The excess of the theoretical above the observational effect may in part be attributed to other processes of excitation like fluorescence and ionization and re-combination. The fact that the plane of vibration is not parallel to the solar limb, but shows deviations lying between 0° and 30° for Hα and 0° and 40° for D 3 , is not explained by the simple theory.