A scheme for displaying the Earth’s curved surface on a plane surface. Some of the more common projections are shown in Figure M-4. Distortions of one sort or another are inevitable. Equivalence is the projection property wherein the product of orthogonal scale factors is maintained constant so that areas are preserved. Conformality is the property wherein angles are preserved. Standard lines are great or small circles along which the scale is uniform and constant. (a) Tangent projections are projections onto a surface (plane, cylinder, or cone) that is tangent to the Earth; (b) secant projections are those made onto a surface that intersects the Earth. (c) A transverse projection has its axis perpendicular to the Earth’s axis (sometimes merely at any angle to the Earth’s axis). (d) An azimuthal projection is onto a tangent plane; distortions increase as the distance from the point of tangency. (e) A stereographic projection is both azimuthal and conformal. (f) A polyconic has a straight central meridian and each parallel is the arc of a circle and is standard; the scale along meridians is therefore variable and the map is neither equivalent nor conformal. (g) Transverse Mercator projections (onto a cylinder at right angles to the Earth’s axis) and Lambert conic projections (q.v.) form many official coordinate systems; the Universal Transverse Mercator (q.v.) is one standard system in widespread use. (h) A Robinson projection permits some distortion in size at high latitudes to maintain shapes at middle and low latitudes.