Observations at 21 cIn have hown that the neutral hydrogen layer is exceedingly flat over the region of the Galaxy within 7 kpc from the centre. The mean plane of the hydrogen in this region must have an important dynamical significance, and may be regarded as the principal plane of the Galaxy. The position of this plane has been determined, using data from two extensive surveys of the Milky Way by the Leiden and Sydney groups. A number of least squares solutions have been made for the position of the plane. Besides the main series of solutions incorporating all the points, various partial solutions were made for restricted regions of the Galaxy, to obtain additional information about the flatness of the hydrogen layer and the reliability of the observations. Close agreement was obtained between the best solutions, indicating that the region of the Galaxy within 7 kpc from the centre is indistinguishable from a plane. The finally-adopted solution has the following elements and overall probable errors, expressed in terms of Ohlsson's coordinate system: 1o', the longitude of the north pole of the plane, 3470 + O 0 A, the deviation of this pole from Ohlsson's pole, ,0.50 + 0 12 Z , the height of the Sun above the plane, 4 pc+ 12.