Geocart Projections

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McBryde-Thomas flat-pole quartic


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. Perpendicular to the central meridian.
Poles: Lines one-third as long as the Equator
Symmetry: About the central meridian or the Equator


True along latitudes 33°45' N. and S. Constant along any given latitude; same for the latitude of opposite sign


Distortion is severe near outer meridians at high latitudes but less than the corresponding distortion on pointed-polar projections. Free of distortion only at latitudes 33°45' N. and S. at the central meridian.


Examples in various geography textbooks. Basis of merged projections by McBryde.


Presented by F. Webster McBryde and Paul D. Thomas through the U.S. Coast and Geodetic Survey in 1949

Other names

Flat-Polar Quartic projection

Similar projections

Quartic Authalic projection, the basis of this projection, has pointed poles.
Other McBryde-Thomas projections also have poles one-third the length of the Equator and otherwise resemble the projection described here.

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.