# Wagner IV

## Description

The Wagner IV is an equal-area pseudocylindrical projection for world maps. Its meridians follow a portion of ellipses compared to the Eckert IV projection whose meridians are semiellipses.

The Wagner IV projection was introduced by Karl Heinrich (Karlheinz) Wagner in 1932. It was independently developed by Reinholds V. Putniņš in 1934, therefore it is also known as Putniņš P'2 projection. It is available in ArcGIS Pro 1.2 and later and in ArcGIS Desktop 10.4 and later.

## Projection properties

The subsections below describe the Wagner IV projection properties.

### Graticule

Wagner IV is a pseudocylindric projection. The meridians, except the central meridian, are following portions of ellipses, and they bulge away from the central meridian. The meridians at 103°55' away from the central line are circular arcs. The central meridian is a straight line, half the length of the projected equator. All parallels are straight lines, perpendicular to the central meridians, and unequally spaced. Both poles are displayed as straight lines, half the length of projected equator. The graticule is symmetric across the equator and the central meridian.

### Distortion

Wagner IV is an equal-area (equivalent) projection. Shapes, directions, angles, and distances are distorted and stretched north-south in tropical and mid-latitude areas. Nearer the poles, features are compressed in the north-south direction. Points 42°59' north and south of the central meridian have zero distortion. Distortion values are symmetric across the equator and the central meridian.

## Usage

The projection is appropriate for small-scale mapping, especially for thematic world maps illustrating area characteristics and analysis requiring accurate areas.

## Limitations

For an ellipsoid of revolution, geodetic latitudes are first converted to authalic latitudes and an authalic radius is used for the radius.

## Parameters

Wagner IV parameters are as follows:

• False Easting
• False Northing
• Central Meridian
• Latitude Of Origin

## Sources

Wagner, K. (1932). "Die Unechten Zylinderprojektionen." Aus dem Archiv der Deutschen Seewarte, 51 (4).

Putniņš, R. (1934). "Jaunas projekci jas pasaules kartēm." Geografiski Raksti, Folia Geographica 3 and 4, p. 180-209.

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.