From all astro‐geodetic material available at present, geoidal heights were computed on the 1927 North American Datum for the western hemisphere from Canada to Chile, and on the European Datum for the eastern hemisphere from Great Britain to Japan and from Scandinavia to South Africa. Improved reference ellipsoids were determined under various conditions for each hemisphere by the least squares method. Triaxiality is refuted. The Columbus Geoid, gravimetrically derived by W. A. Heiskanen, was used to connect the astro‐geodetic systems of the two hemispheres. By minimizing the differences between the astro‐geodetic and gravimetric geoid elevations at 75 points in the western hemisphere and 127 points in the eastern hemisphere, a theoretically absolute orientation based on the Hough ellipsoid was determined, leading to a tentative World