In the last paper in this series a Fourier projection down the  axis of horse haemoglobin was given (Bragg & Perutz 1954). This projection was centrosymmetric. As a first step towards the three-dimensional analysis, the projection down  has now been attacked. This projection is non-centrosymmetric, and arbitrary phase angles have had to be determined. All the fundamental problems of a three-dimensional study are met, but only a small number of reflexions need be dealt with. The isomorphous replacement method has been used successfully with three mercury derivatives of haemoglobin. This provided a test of new methods for finding the vectors relating heavy atoms. Particular attention has been given to estimation of errors, and to their effect on the results. Further information about the phases has been derived from anomalous scattering by the mercury atoms, using CrK$\alpha $ and CuK$\alpha $ radiation. By combining these results, the phases of most reflexions out to a spacing of about 6 angstrom have been determined with a standard error of about 25 degrees. Ambiguous results are obtained for a few reflexions. The resulting electron density projection shows peaks up to four times the estimated standard error. The prospects for three-dimensional structure analysis at 6 angstrom resolution are favourable. If the polypeptide chain is coiled in the $\alpha $-form, the contrast should be sufficient for it to show up throughout its length.