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A NATIONAL REFERENCE SYSTEM AND ITS RELATIONSHIP TO MAPPING

Alden P. Colvocoresses

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Abstract

SINCE THE EARTH IS A NEAR-SPHERICAL FIGURE, THE USE OF SPHERICAL (OR ELLIPSOIDAL) COORDINATES IN TERMS OF LATITUDE AND LONGITUDE IS THE RECOGNIZED BASIC SYSTEM OF REFERENCE FOR THE EARTH'S SURFACE. HOWEVER, WHEN SMALL SECTIONS OF THE EARTH'S SURFACE ARE MAPPED OR SURVEYED, THERE ARE OBVIOUS ADVANTAGES IN TREATING THIS SURFACE AS A PLANE. THUS, LARGE-SCALE MAPPING AND DETAILED SURVEYING INVOLVE THE USE OF PLANE COORDINATES WHICH IS THE DEFINED SUBJECT OF THIS PANEL DISCUSSION. AS WE ALL KNOW, PLANE COORDINATES RESULT FROM THE (NEAR) SPHERICAL EARTH BEING PROJECTED, OR MAPPED, ONTO SURFACES THAT IN TURN CAN BE DEVELOPED INTO PLANES. THE MAPPING SURFACES USED ARE EITHER AN ACTUAL PLANE, A CONE, OR A CYLINDER. THE CONSENSUS OF THOSE WHO HAVE SERIOUSLY CONSIDERED THE FIUNDAMENTAL MAPPING PROBLEM IS THAT, FOR LARGE-SCALE DEPICTION OF THE EARTH'S SURFACE, A SERIES OF CYLINDERS TRANSVERSE TO THE EQUATOR ARE THE BEST SURFACES TO USE AND THAT THE PROJECTION SHOULD BE CONFORMAL. CONFORMALITY PLUS THE TRANSVERSE CYLINDER EQUALS THE TRANSVERSE MERCATOR PROJECTION. WITH ONLY A FEW EXCEPTIONS (OF WHICH THE U. S. IS THE MOST NOTABLE) LARGE-SCALE MAPPING THROUGHOUT THE WORLD IS NOW BASED ON THIS PROJECTION. /AUTHOR/

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What this paper is about

SINCE THE EARTH IS A NEAR-SPHERICAL FIGURE, THE USE OF SPHERICAL (OR ELLIPSOIDAL) COORDINATES IN TERMS OF LATITUDE AND LONGITUDE IS THE RECOGNIZED BASIC SYSTEM OF REFERENCE FOR THE EARTH'S SURFACE. HOWEVER, WHEN SMALL SECTIONS OF THE EARTH'S SURFACE ARE MAPPED OR SURVEYED, THERE ARE OBVIOUS ADVANTAGES IN TREATING THIS SURFACE AS A PLANE. THUS, LARGE-SCALE MAPPING AND DETAILED SURVEYING INVOLVE THE USE OF PLANE COORDINATES WHICH IS THE DEFINED SUBJECT OF THIS PANEL DISCUSSION. AS WE ALL KNOW, PLANE COORDINATES RESULT FROM THE (NEAR) SPHERICAL EARTH BEING PROJECTED, OR MAPPED, ONTO SURFACES THAT IN TURN CAN BE DEVELOPED INTO PLANES. THE MAPPING SURFACES USED ARE EITHER AN ACTUAL PLANE, A CONE, OR A CYLINDER. THE CONSENSUS OF THOSE WHO HAVE SERIOUSLY CONSIDERED THE FIUNDAMENTAL MAPPING PROBLEM IS THAT, FOR LARGE-SCALE DEPICTION OF THE EARTH'S SURFACE, A SERIES OF CYLINDERS TRANSVERSE TO THE EQUATOR ARE THE BEST SURFACES TO USE AND THAT THE PROJECTION SHOULD BE CONFORMAL. CONFORMALITY PLUS THE TRANSVERSE CYLINDER EQUALS THE TRANSVERSE MERCATOR PROJECTION. WITH ONLY A FEW EXCEPTIONS (OF WHICH THE U. S. IS THE MOST NOTABLE) LARGE-SCALE MAPPING THROUGHOUT THE WORLD IS NOW BASED ON THIS PROJECTION. /AUTHOR/

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Available abstract

SINCE THE EARTH IS A NEAR-SPHERICAL FIGURE, THE USE OF SPHERICAL (OR ELLIPSOIDAL) COORDINATES IN TERMS OF LATITUDE AND LONGITUDE IS THE RECOGNIZED BASIC SYSTEM OF REFERENCE FOR THE EARTH'S SURFACE. HOWEVER, WHEN SMALL SECTIONS OF THE EARTH'S SURFACE ARE MAPPED OR SURVEYED, THERE ARE OBVIOUS ADVANTAGES IN TREATING THIS SURFACE AS A PLANE. THUS, LARGE-SCALE MAPPING AND DETAILED SURVEYING INVOLVE THE USE OF PLANE COORDINATES WHICH IS THE DEFINED SUBJECT OF THIS PANEL DISCUSSION. AS WE ALL KNOW, PLANE COORDINATES RESULT FROM THE (NEAR) SPHERICAL EARTH BEING PROJECTED, OR MAPPED, ONTO SURFACES THAT IN TURN CAN BE DEVELOPED INTO PLANES. THE MAPPING SURFACES USED ARE EITHER AN ACTUAL PLANE, A CONE, OR A CYLINDER. THE CONSENSUS OF THOSE WHO HAVE SERIOUSLY CONSIDERED THE FIUNDAMENTAL MAPPING PROBLEM IS THAT, FOR LARGE-SCALE DEPICTION OF THE EARTH'S SURFACE, A SERIES OF CYLINDERS TRANSVERSE TO THE EQUATOR ARE THE BEST SURFACES TO USE AND THAT THE PROJECTION SHOULD BE CONFORMAL. CONFORMALITY PLUS THE TRANSVERSE CYLINDER EQUALS THE TRANSVERSE MERCATOR PROJECTION. WITH ONLY A FEW EXCEPTIONS (OF WHICH THE U. S. IS THE MOST NOTABLE) LARGE-SCALE MAPPING THROUGHOUT THE WORLD IS NOW BASED ON THIS PROJECTION. /AUTHOR/

Key concepts: Map projection, Figure of the Earth, Mercator projection, Projection (relational algebra), Surface (topology), Geometry, Plane (geometry), Projection plane

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