Directory of Map Projections

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quartic authalic




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-pole quartic projection.

Similar projections

Several pseudocylindrics, such as the sinusoidal.
Eckert-Greifendorff has slightly curved parallels.


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.

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.