FIGURES AND TABLES 



Figure 1. Latitude relationships in the auxiliary sphere-spheroid configuration — 13 



2. The great circle track configuration - - 24 



3. Parallels at a given distance from a great circle 26 



4. Spherical triangles for computation of coordinates along 



parallels to great circle tracks — - 27 



5. Spherical rectangular coordinate system with a great 



circle base line as an axis - - 29 



6. Reference for derivation of polar equation of spherical 



hyperbolas with origin at a focus - - - -— 32 



7. Derivation of alternative equation to spherical 



hyperbolas with origin at a focus - 34 



8. Corresponding plane hyperbola equivalents — - - - -- 35 



9. Polar case of plane equivalent — - - 36 



10. Corresponding distances on the reference ellipsoid 



and the auxiliary sphere - - - -- 39 



11. Relationship between arc length, normal section azimuth, chord length, 



angle of depression of the chord below the horizon, maximum 



separation of arc and chord - - - - -- 41 



12. Relationships relative to the pole on the ellipsoid of reference, 



of the geodesic, normal sections, and great elliptic section - 42 



13. The normal section azimuths — - - - 43 



14. The great elliptic section azimuths - - - - 46 



15. Elements of the great elliptic section 50 



16. Elements of polar spherical triangles - 58 



17. Computations for distance (great elliptic section approximation), 



normal section azimuths, chord length, angle of dip, 



maximum separation of chord and arc - - - - 60 



18,19. Computations, great elliptic arc distance, geodetic azimuths - -62,63 



20. Differential triangles, sphere and spheroid 70 



21. Distance computing form, Forsyth-Andoyer-Lambert type 



approximation with second order terms in f - - o" 



22. Distance computing form, Forsyth-Andoyer-Lambert type 



approximation in terms of parametric latitude and 



second order terms in f - -- 89 



23. Computations, Andoyer-Lambert first order approximation, geodetic azimuths, 



normal section azimuths, chord, angle of dip, maximum separation chord and 



arc, geographic coordinates of point of maximum separation 95 



24. Two plane hyperbolas with a common focus - ^^"^ 



25. Intersection of plane hyperbolas. Example 1 — - - - 109 



26. Intersection of plane hyperbolas. Example 2 — 110 



Table 1. Lines computed - — -- 55 



2. Comparison with true distance and azimuths — — 66 



3. Error summary ,... — — — 67 



4. 17 geodetic lines computed from equations (110) and compared 



with known lengths and azimuths - - — - 81 



