ABSTRACT 



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 re- 

 quirements, 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 coor- 

 dinate system on the auxiliary sphere with hyperbolic loci ref- 

 erenced 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. 



