World maps constructed on interrupted forms of projections have appeared repeatedly during the last five centuries. In a sense, they represent a practical alternative to obtaining relatively undistorted views of parts of the earth by rotating a globe.

Actually any flat map is interrupted, because a map always has an outer edge where the representation stops, even though the surface on the globe is continuous. In this chapter we refer to additional and internal interruptions. If we prepare individual maps of separate, smaller portions of the globe, using projections better suited to the particular area, we can join these maps into a single map, but it will have several discontinuities. The overall representation of regions can thus be improved, but at the expense of adding interruptions.

Earlier interrupted projections preserved strict symmetry by balancing the separate parts, but in the 20th century, inventors began to move away from strict symmetry, with notable improvements in the usefulness of a map for a given function.

Symmetrically Interrupted Arrangements
Perhaps the most familiar earlier types of symmetrical interruptions are the continuous hemispheres with various centers (Chapter 4). Projections arranged to portray eastern and western hemispheres preserve continuity along the equator, which serves as the map axis. Those portraying northern and southern hemispheres preserve continuity along a meridian connecting the two central poles. The familiar land and water hemispheres can be made to touch so that an oblique great circle serves as the axis for the map.

Another type of symmetrical projection arrangement preserves continuity of the portion of the globe in the middle latitudes. Probably the best known is the Butterfly projection of Cahill introduced around 1909 (Figure 2-1). This arrangement is based on a regular polyhedron with eight faces, each face bounded by the equator and two meridians 90° apart. Of Cahill's three variations, the equal-area graticule illustrated here is perhaps most familiar. Using another polyhedron as a base, in 1943 Fisher constructed a world map using Gnomonic projections on the 20 faces of a regular icosahedron (Figure 2-2).

Bartholomew developed at least four symmetrical projections of this type that appear in one or more world atlases, such as The Times Atlas of the World (1958). The Regional projection was devised to portray the continents. It includes a conic projection that is continuous between 22°30' N and 80° N. Of similar concept and design, the Lotus projection was used for a world bathymetric chart, and avoids interruption between 22°30' S and 80° S.

Continuity in a polar region is preserved by centering the projection on a pole, with numerous radial extensions. The best-known star projection of this class was introduced by Berghaus in 1879 (Figure 2-3). It was used widely in textbooks and atlases in the late 19th century and has had high visibility ever since its adoption in 1911 for the logo of the Association of American Geographers.

Non-Symmetrically Interrupted Arrangements
Non-symmetrical graticules differ in at least two ways from those of the symmetrical group: 1) the projection axes are chosen so as to pass through the middle of the main areas of interest; and 2) the widths of the map components are adjusted so as to provide continuity to these regions. Both adjustments are based on the purpose of the map and result in a loss of symmetry.

The most widely used projections in this group have straight parallels, equally spaced curved meridians, and oval outlines. When interrupted, continuity is preserved along the equator with the northern and southern hemispheres separated into lobes. The mid-meridian of each lobe is selected to fit the distribution of the items of interest (such as landforms or oceans); this often results in mid-meridians in opposite hemispheres being offset along the equator.

The Goode interrupted Homolosine was introduced in 1923 and quickly gained popularity. This equal-area projection combines high-latitude sections of the Mollweide projection with a low-latitude (central) Sinusoidal section. Kinks in the meridians result where the elliptical curves of the Mollweide join the sine curves of the Sinusoidal near the 40th parallels. The standard arrangement of the Homolosine for continental areas is shown in Figure 2-4). That for the oceans is shown in Figure 2-5. In each of these examples, the projection comprises central portions of six separate developments of the Sinusoidal and Mollweide projections.

A different type of interrupted projection, a hemisphere with extensions introduced by Frye in 1895, consisted of the land hemisphere on an oblique Azimuthal Equidistant projection with extended lobes of different construction for Australia and South America (see Figure 3-2). This was followed by many similar arrangements in the first half of the 20th century.

Some interrupted projections have lobes attached at either the North Pole to portray continental distributions or at the South Pole to portray the ocean basins. In 1928 Goode introduced a complex equal-area arrangement, with nine views of the Werner projection, centered at the North Pole, to depict the continents. In 1904 Schjerning introduced an equal-area projection, shown in Figure 2-6, to depict the major oceans favorably. It comprises the central segments of three cases or centerings of the heart-shaped Werner projection joined at the South Pole. In recent years, Spilhaus proposed various interruptions and combinations of projections to show the continuity of the world's oceans (see chapter 3).

In 1943, Fuller launched a non-symmetrical interrupted world map called the Dymaxion Globe in Life magazine. It first consisted of six squares and eight triangles that could be arranged on the plane in a variety of patterns. Fuller later changed to the icosahedron with its 20 triangles.

Summary A wide variety of interrupted arrangements of projections have been proposed or devised by inventors from many disciplines and nations over the past five centuries. These arrangements are often controversial; few have made their way into the mainstream of map projection use. However, relaxation of the earlier symmetrical constraints stimulated a wealth of experimentation for non-symmetrical functional arrangements.

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