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The principal objective of this study was an evaluation of the formulas basic to the geodetic inverse solution for distance computations used by the U. S. Naval Oceanographic Office in loran-type charting. The adequacy of the formulas for past requirements was verified but, in anticipation of future requirements, they were modified to give geodesic distances and azimuths between any two points on the reference ellipsoid to uncertainties of less than a meter and a second respectively. During the study, associated geometrical configurations were developed or studied: latitudes associated with the auxiliary sphere-spheroid configuration; a spherical rectangular coordinate system on the auxiliary sphere with hyperbolic loci referenced to it; and geometrical quantities associated with arc distance, such as chord length, dip of the chord, maximum separation of chord and arc, and the geographical position of the point of maximum separation. The formulas with their derivations are presented.

The principal objective of this study was an evaluation of the formulas basic to the geodetic inverse solution for distance computations used by the U. S. Naval Oceanographic Office in loran-type charting. The adequacy of the formulas for past requirements was verified but, in anticipation of future requirements, they were modified to give geodesic distances and azimuths between any two points on the reference ellipsoid to uncertainties of less than a meter and a second respectively. During the study, associated geometrical configurations were developed or studied: latitudes associated with the auxiliary sphere-spheroid configuration; a spherical rectangular coordinate system on the auxiliary sphere with hyperbolic loci referenced to it; and geometrical quantities associated with arc distance, such as chord length, dip of the chord, maximum separation of chord and arc, and the geographical position of the point of maximum separation. The formulas with their derivations are presented.