# McBryde-Thomas flat-polar quartic

## Description

McBryde-Thomas flat-polar quartic is an equal-area pseudocylindrical projection. The projection is based on the quartic authalic projection. Its boundary meridians bulge outward excessively, producing considerable shape distortion near the map outline.

It is the fourth projection of the McBryde-Thomas series and has received the most attention. F. Webster McBryde and Paul D. Thomas introduced it in 1949 for world statistical maps. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.0 and later.

## Projection properties

The subsections below describe the McBryde-Thomas flat-polar quartic projection properties.

### Graticule

McBryde-Thomas flat-polar quartic is a pseudocylindric projection. The equator and the central meridian are projected as straight lines, where the projected central meridian is about 0.45 times as long as the equator. The other meridians follow fourth-order algebraic curves, bulging away the central meridian and equally spaced. The parallels are unequally spaced straight lines perpendicular to the central meridian. The poles are also straight lines, one-third the length of the equator. The graticule is symmetric across the equator and the central meridian.

### Distortion

McBryde-Thomas flat-polar quartic is an equal-area (equivalent) projection. Shapes, directions, angles, and distances are generally distorted. Points 33°45' north and south at the central meridian have zero distortion. The scale is correct along the 33°45' north and south parallel and constant along any given parallel. Bulging meridians produce considerable distortion toward the edge of the projection. Distortion values are symmetric across the equator and the central meridian.

## Usage

The McBryde-Thomas flat-polar quartic projection is appropriate for thematic world maps although its use is not advisable.

## Limitations

The McBryde-Thomas flat-polar quartic projection is supported on spheres only. For an ellipsoid, the semimajor axis is used for the radius. The projection does not maintain the equal-area property when an ellipsoid is used.

## Parameters

McBryde-Thomas flat-polar quartic parameters are as follows:

• False Easting
• False Northing
• Central Meridian

## Sources

Snyder, J. P. (1987). Map Projections: A Working Manual. U.S. Geological Survey Professional Paper 1395. Washington, DC: United States Government Printing Office.

Snyder, J. P. (1993). Flattening the Earth. Two Thousand Years of Map Projections. Chicago and London: University of Chicago Press.

Snyder, J. P. and Voxland, P. M. (1989). An Album of Map Projections. U.S. Geological Survey Professional Paper 1453.Washington, DC: United States Government Printing Office.