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VAN DER GRINTEN PROJECTIONM.HerreraHISTORYIn a 1904 issue of a German geographical journal, Alphons J. van der Grinten(1852-?) of Chicago presented four projections showing the entire Earth.

Aside from having a straight Equator and central meridian, three of the projections consist of arcs of circles for meridians and parallels; the other projection has straight-line parallels.3The best-known Vander Grinten projection, his first (fig. 52), shows the world in a circle and was invented in 1898.

It is not conformal because conformal maps preserve angles but not shapesVan der gritten favors shapes than angles at the expense of area.4FeaturesThere are no special features to preserve in an ellipsoidal form. The meridians are equally spaced along the Equator, out the spacing between the parallels increases with latitude, so that the 75th parallels are shown about halfway between the Equator and the respective poles.5UsageIt is designed for use in the spherical form only. It has been used by the National Geographic Society for their standard world map since 1943,printed at various scales and with the central meridian either through America or along the Greenwich meridian; this use has prompted others to employ the projection.The U.S. Department of Agriculture adopted the projection as the base map for economic data in the 1940's, and this led to frequent use in geography textbooks(Wong, 1965, p. 117). The USGS has used one of the National Geographic maps as a base for a four-sheet set of maps of World Subsea Mineral Resources, 1970, one at a scale of 1:60,000,000 and three at 1:39,283,200 (a scale used by the National Geographic), and for three smaller maps in the National Atlas (USGS,1970, p. 150-151, 332-335). All the USGS maps have a central meridian of long.85 W., passing through the United States.6This projection has an obvious strong resemblance to the Mercator. Thus, while it is intended to moderate, slightly, the exaggeration of areas of the Mercator, and to provide a pleasing appearance with curved meridians and parallels, it definitely favors shapes at the expense of areas. Equator is divided into 360 degrees

For the parallels, a simple geometrical construction determines where each parallel cuts the surrounding circle and the central meridian.

Divide the height of the projection uniformly to indicate latitude, as shown by the blue lines. The height at which the parallel for that latitude intersects the bounding circle is found in a similar fashion. Here, however, instead of the bounding circle, one uses a diagonal line (shown in green) between a pole of the projection and a point where the bounding circle crosses the equator. Then, where a line (shown as red in the diagram) drawn from the bounding circle at the height corresponding to a given latitude to the point where the other side of the bounding circle intersects the equator intersects the central meridian is where the parallel for that latitude crosses the central meridian.A line (shown as purple) is drawn from the point on this diagonal line at the height determined by the uniform division of the height of the projection and corresponding to the desired latitude, again to the point where the bounding circle crosses the equator at the other side. The height of the point where this line crosses the central meridian is the height at which the parallel, as drawn on the actual map, intersects the bounding circle.

10SUMMARYNeither equal-area nor conformal. Not pseudocylindrical. Shows entire globe enclosed in a circle. Central meridian and Equator are straight lines.All other meridians and parallels are arcs of circles.A curved modification of the Mercator projection,.Equator is true to scale.Used for world maps.Used only in the spherical form.Presented by van der Grinten in 1904.It is not pseudocylindrical because pseudocylindrical projections are straight horizontal parallels, not necessarily equidistant andarbitrary curves for meridians, equidistant along every parallel

11Formulas