Threedimensional system of coordinates used at CERN

This report is a complete account of the transformations and corrections necessary for geodetic quantities, whether directly measured or derived, before they can be entered into calculations involving the basic reference system used at CERN. A special type of projection (orthographic projection) has been developed, with the aim that it be the best possible for the geodetic system employed for the Super Proton Synchrotron (SPS) whilst retaining the basic possibilities provided for the Proton Synchrotron (PS) and the Intersecting Storage Rings (ISR). The coordinate system in which the geometry of particle beams is defined is necessarily Cartesian. This feature, although mathematically simple, has a number of consequences for the treatment of measurements which are physically connected with the shape of the Earth. Details of the orthographic projection, the planimetry, and the altimetry are given. (Author)