Conical Equal Area Projection with One Standard Parallel

The German Heinrich C. Albers published his equal-area conic projection in 1805. As usual, there is little distortion along the central parallel and none on the standard ones. The standard parallels may lie on different hemispheres, but if equidistant from the Equator, the projection degenerates into an equal-area cylindrical. This projection was commonly applied to official American maps after usage of the polyconic projection declined. In a particular case of Albers's conic projection, either 90°N or 90°S is chosen as a standard parallel, and therefore meridians converge at a pole. Published by Lambert in 1772, this projection preserves areas, thus parallels are farther apart near the vertex, getting closer together towards the non-standard pole. When 0° is chosen as the other standard parallel, the result is a cone constant of 1/2 and a semicircular map. Lambert himself chose a constant of 7/8 for his map of Europe: the resulting standard parallel, roughly 48°35'N, lies between Paris and Munich. This projection was employed much less frequently than Albers's. In fact, it is probably the least known of Lambert's projections.






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