Geocart Projections

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quartic authalic


Equal area


Meridians: Central meridian is a straight line 0.45 as long as the Equator. Other meridians are equally spaced curves fitting a fourth-order (quartic) equation and concave toward the central meridian.
Parallels: Unequally spaced straight parallel lines, farthest apart near the Equator. Spacing changes gradually. Perpendicular to the central meridian.
Poles: Points
Symmetry: About the central meridian or the Equator


True along the equator
Constant along any given latitude; same for the latitude of opposite sign


Distortion is severe near outer meridians at high latitudes but somewhat less than that of the Sinusoidal projection. Distortion can be substantially reduced by interruption. Free of distortion along the Equator.


Basis for McBryde-Thomas Flat-Polar Quartic projection


Presented by Karl Siemon (?-1937) of Germany in 1937. Independently presented by Oscar Sherman Adams (1874-1962) of the U.S. Coast and Geodetic Survey in 1945.

Similar projections

Several pseudocylindricals, such as the Sinusoidal
Eckert-Greifendorff has slightly curved parallels.

Description adapted from J.P. Snyder and P.M. Voxland, An Album of Map Projections, U.S. Geological Survey Professional Paper 1453. United States Government Printing Office: 1989.