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Bonne's Projection

Bonne's projection applies the true scale along the parallels of the Sinusoidal to the parallels of the Simple Conic instead of the parallels of the Plate Carrée, thus giving a projection that looks like this:

At one time, due to the simplicity of its construction, it was often used in atlases where equal-area maps were desired. However, it gives the least angular error along the standard meridian and the standard parallel, while falling off badly with distance from the center in other directions. Thus, Lambert's azimuthal equal-area projection is, quite reasonably, much preferred at the present time.

It is interesting to note, however,

that Bonne's projection can be interrupted just as the Sinusoidal can be: this allows one to favor the Northern Hemisphere at least slightly in an interrupted world map, as shown above with a standard parallel of 20 degrees N. Or one can favor it more strongly, as this map illustrates:

having a standard parallel of 50 degrees North latitude.

As well, since Bonne's projection provides uniform scale and conformality along its standard meridian, it is possible to mate the projection at the standard meridian with a Bonne's projection with a different standard parallel, or a Sinusoidal projection, or even the map Equator of a Sinusoidal projection in transverse aspect.

The image above illustrates a very simple example of this sort of thing; the left half of the map (from 170 degrees West to 10 degrees East longitude) has 40 degrees North as its standard parallel, while the right half has 20 degrees North as its standard parallel. Here, no interruption is made within the Eurasian landmass, as avoiding that would perhaps be the purpose of changing parallels like this, but the cost is severe distortion in Siberia. Achieving an equal-area world map with tolerable distortions everywhere, and yet no interruptions in major landmasses is difficult, but the flexibility of Bonne's projection together with the Sinusoidal projection lends itself to constructing patchwork projections of many kinds.

The following picture

shows a world map which uses an interrupted Bonne's projection with 40 degrees North as standard parallel for most of the Western Hemisphere, and for the rest of the world, uses two transverse Sinusoidal projections (one of which is for Antarctica), one oblique Sinusoidal projection, and an oblique Bonne projection for Australia, whose standard parallel (in terms of the map construction) is 20 degrees. The difficulty of keeping the entire area from Africa to Australia connected has resulted in Africa being significantly distorted; Australia was severely distorted as well, before the second Bonne's projection was introduced. The boundary between the oblique Sinusoidal which is used for most of Asia and the transverse Sinusoidal used for much of Europe and Africa is a horizontal line pointing eastwards and starting from 10 degrees East longitude and 70 degrees North latitude.

Of course, Bonne's projection could also be mated, along a standard meridian, with the Polyconic, and the Sinusoidal could be joined, along the Equator, with the Mercator or the Miller Cylindrical; as long as the two projections are everywhere conformal and have uniform scale where joined, they do not have to have the same properties elsewhere.

One example of this is:

which uses a Lambert Conformal Conic north of the standard parallel for both projections of 20 degrees North, and Bonne's projection south of that parallel. A similar idea, but with more northerly standard parallels, is used in one form of Bartholemew's Regional Projection.

Retaining the equal-area property, one can mix a transverse Cylindrical Equal-Area projection with an oblique Bonne's projection having a standard parallel of 10 degrees in the map coordinate system, and centered on 110 degrees East longitude and 80 degrees North latitude, and another Bonne's projection with standard meridian 110 degrees East longitude and standard parallel 10 degrees South latitude as follows:

This projection keeps the shapes of the major land masses reasonably accurate, and also avoids interrupting the area in the North Atlantic and around the Arctic Circle that shows the relationship between North America and Eurasia.

For ease of understanding, the standard parallels are shown in orange, and the regions in which the three projections are used each have their own color.

It can be seen that the area in which the Cylindrical Equal-Area projection is used is too wide for it to be replaced there by the Sinusoidal projection. However, an equal-area projection derived by placing the world on a Cylindrical Equal-Area projection on one scale on a Cylindrical Equal-Area projection at a larger scale, to give a projection with a flat pole-line and sinusoids for meridians could be used; the Eckert VI projection and the MacBryde-Thomas Flat-Polar Sinusoidal projection are projections of this type; however, it is necessary that the equator be the standard meridian of the projection. One could even use Adams' Equal-Area projection at some points, and if one wished, one could put half of Antarctica on Lambert's Azimuthal Equal-Area projection with its help.

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