The point scale factor is independent of direction. (On the sphere it depends on latitude only.) The scale is true on the equator. Greenland and Africa are both near to the central meridian their shapes are good and the ratio of the areas is a good approximation to actual values. Greenland is almost as large as Africa the actual area is about one fourteenth that of Africa. Distortion is small near the central meridian and the projection (particularly in its ellipsoidal form) is suitable for accurate mapping of narrow regions. The projection is not suited for world maps. Distortion is small near the equator and the projection (particularly in its ellipsoidal form) is suitable for accurate mapping of equatorial regions.Дistortion increases with x. The shapes of small elements are well preserved.Дistortion increases with y. The points on the equator at ninety degrees from the central meridian are projected to infinity. The projection is unbounded in the x direction. The projection is unbounded in the y direction. Projected meridians and parallels intersect at right angles. The equator projects to the straight line yВ =В 0 but all other parallels are complicated closed curves. The equator projects to the straight line yВ =В 0 and parallel circles project to straight lines of constant y. All other meridians project to complicated curves. Meridians 90 degrees east and west of the central meridian project to lines of constant y through the projected poles. The central meridian projects to the straight line xВ =В 0. Other meridians project to straight lines with xВ constant. Spherical transverse Mercator (truncated at xВ =В В± ПЂ in units of Earth radius). Normal and transverse spherical projections The principal properties of the transverse projection are here presented in comparison with the properties of the normal projection. ) Lambert did not name his projections the name transverse Mercator dates from the second half of the nineteenth century. (The text is also available in a modern English translation. The spherical form of the transverse Mercator projection was one of the seven new projections presented, in 1772, by Johann Heinrich Lambert. For maps of smaller regions, an ellipsoidal model must be chosen if greater accuracy is required see next section. In constructing a map on any projection, a sphere is normally chosen to model the Earth when the extent of the mapped region exceeds a few hundred kilometers in length in both dimensions. The secant, ellipsoidal form of the transverse Mercator is the most widely applied of all projections for accurate large-scale maps. Since the central meridian of the transverse Mercator can be chosen at will, it may be used to construct highly accurate maps (of narrow width) anywhere on the globe. Both projections have constant scale on the line of tangency (the equator for the normal Mercator and the central meridian for the transverse).Both projections are conformal, so that the point scale is independent of direction and local shapes are well preserved.Both exist in spherical and ellipsoidal versions.Both projections may be modified to secant forms, which means the scale has been reduced so that the cylinder slices through the model globe.For the transverse Mercator, the axis of the cylinder lies in the equatorial plane, and the line of tangency is any chosen meridian, thereby designated the central meridian. Both projections are cylindrical: for the Normal Mercator, the axis of the cylinder coincides with the polar axis and the line of tangency with the equator.They share the same underlying mathematical construction and consequently the transverse Mercator inherits many traits from the normal Mercator: The transverse Mercator projection is the transverse aspect of the standard (or Normal) Mercator projection. Comparison of tangent and secant forms of normal, oblique and transverse Mercator projections with standard parallels in red

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