4 CONTENTS. 



ILLUSTRATIONS. 



Page. 

 Frontispiece. — Transverse polyconic projection of the North 



Pacific Ocean facing page. . 7 



Fig. 1 . — Generating ellipse with the radii of curvature of the earth . 8 



Fig. 2. — Differential elements of a polyconic projection 11 



Fig. 3. — Construction of arc of parallel on rectangular polyconic 



projection 18 



Fig. 4. — Entire surface of the sphere on rectangular polyconic 



projection 19 



Fig. 5. — Radius from center on stereographie projection 24 



Fig. 6.— Transformation triangle for meridian stereographie pro- 

 jection 25 



Fig. 7. — Stereographie meridian projection of a hemisphere 29 



Eig, 8. — Construction of stereographie meridian projection 35 



Fig. 9. — Transformation triangle for stereographie horizon pro- 

 jection 37 



Fig. 10. — Stereographie horizon projection of a hemisphere — 



horizon of Paris ^ 41 



Fig. 11. — Proof that circles project into circles on stereographie 



projections 44 



Fig. 12. — Construction of parallels on stereographie horizon pro- 

 jection 49 



Fig. 13. — Construction of meridians on stereographie horizon pro- 

 jection 51 



Fig. 14. — Elements of a small circle on stereographie projection. . . 52 

 Fig. 15. — Determination of the arc distance from the center on 



stereogi'aphic projection 53 



Fig. 16. — Projection of a circle with given projection of pole and 



given polar distance on stereographie projection 54 



Fig. 17. — Projection of circle whose pole projection Ues on the 



primitive circle on stereographie projection 55 



Fig. 18. — ^Projection of a great circle with given pole projection on 



stereographie projection 56 



Fig. 19. — Locus of centers of great circles through a given point on 



stereographie projection 57 



Fig. 20. — Projection of a great circle through the projections of 



two given points on stereographie projection 59 



Fig. 21. — Plane through the poles of two great circles - . 60 



Fig. 22. — Great circle arc between two points on stereographie 



projection 61 



Fig. 23. — Sphere showing intersection of given lines 63 



Fig. 24. — Projection of great circle through two points and length 



of arc between them on stereographie projection 64 



Fig. 25. — Projection of great circle through two points on stereo- 

 graphic projection, second method 65 



Fig. 26. — Projection of great circle with given inclination to the 



primitive plane on stereographie projection 67 



Fig. 27. — Determination of the inclination of the planes of two 



great circles on stereographie projection 68 



Fig. 28. — Projection of the meridian and parallel through a given 



point on stereographie projection 70 



Fig. 29. — Projection of circles parallel to given circle on stereo- 

 graphic projection 71 



Fig. 30. — Geometrical relations between orthogonal circular 



meridians and parallels, first figure 97 



Fig. 31. — Geometrical relations between orthogonal circular 



meridians and parallels, second figure 99 



