CONTENTS 



FOREWORD iii 



PREFACE V 



FIGURES AND TABLES.. viii 



OVERALL SUMMARY OF INVESTIGATIONS 1 



COLLECTED FORMULAE 4 



DEVELOPMENT 



Section 1. Latitude Formulae 



New formulae 12,4 



Standard formulae 22,5 



For Clarke 1866 spheroid 22,5 



References 22 



Section 2. Spherical Rectangular Coordinate System; Loci 



Great circle track formulae 23,5 



Parallels to the great circle 27,6 



Coordinate system with a great circle as axis 28,6 



Spherical hyperbolas and plane equivalents 37,7 



References 37 



Section 3. Distance Formulae; Azimuths; Associated Quantities 



Normal section azimuths 40,7 



Great elliptic section azimuths 45,7 



Great elliptic arc distance 48,8 



Geodesic in terms of great elliptic arc and geodetic latitude 



with second order terms in f 68,8 



Geodesic in terms of great elliptic arc and parametric latitude 



with second order terms in f ^.-. 79,9 



Form transformations: Geodetic to Parametric — Parametric to Geodetic 90,10 



Difference formulae to second order in f 91,11 



Chord distance 53 11 



Angle of dip 54,11 



Maximum separation — chord and arc — -55,11 



Geographic coordinates of point of maximum separation. 55,11 



References 96 97 



APPENDICES 



No. 1. Computations for intersections of Loran lines of 



position-plane approximation — 99 



No. 2. Computations using Andoyer-Lambert first order approximation 



without conversion to parametric latitude Ill 



No. 3. Computations using Forsyth-Andoyer-Lambert type second 



order formulae without conversion to parametric latitude — 125 



