Mercator map projection

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Mercator projection, the chart projection in which parallels of latitude and longitude cut each other at right angles so that a rhumb line appears as a straight line. The first work to embody these principles was published in 1569 by the Flemish mathematician Gerhard Kremer (1512–94), who used a Latinized form of his name, Gerardus Mercator. However, it was another 70 years before its use became widespread at sea.

This form of chart depends on the proposition that the convergence of the meridians as they approach the poles will be proportional to the cosine of the latitude, and that if a proportional misplacement is introduced in the spacing between the parallels of latitude on the chart as they move north and south from the equator, then a rhumb line, which cuts all meridians at the same angle, must become a straight line, although on a globe they are spirals. As ships normally steer rhumb line courses such a projection would obviously be of great value for navigation. Mercator's own description of his chart does not seem to have materialized, but towards the end of the century Edward Wright published an explanation of it in his Certaine Errors in Navigation (1599), and Mercator charts and Mercator sailing eventually replaced the old plain chart and plain sailing.

In geometrical terms, Mercator's projection can be envisaged as a cylinder touching the globe at the equator, on to which the meridians and parallels are projected from the earth's centre, which is then developed (i.e. unwrapped) to form a flat chart. As the axis of the cylinder is the same as the polar axis of the globe, the projection of each pole will be at infinity and the polar regions therefore cannot be shown. The ‘distortion’ is least at the equator and increases progressively towards high latitudes. By distortion is meant that the linear scale for north–south distances becomes more and more divergent from that for east–west distances, increasing with the latitude, though not in the same proportion. This means that in a chart covering an area with a considerable north–south dimension, such as North or South America, the regions in high latitudes, e.g. Baffin Land or Tierra del Fuego, appear exaggerated in size compared with tropical areas such as the Isthmus of Panama; they also appear distorted in shape, e.g. Greenland appears to stretch out almost indefinitely to the north because, as the Arctic is approached, the projection become less and less convenient. Nevertheless, for nautical purposes the projection has the unique advantage that rhumb lines always appear as straight lines.

In measuring distances on a Mercator chart, therefore, it is essential to measure the span of degrees of latitude on the sides of the chart which lie on the same latitude as the distance being measured. These degrees will each represent 60 nautical miles (112 km) for the measurement required. Degrees measured in other parts of the chart (i.e. not on the same latitude as the distance to be measured) will not, and of course the scale of degrees of longitude in the top and bottom margin is useless for measuring distances. For this reason no linear scale of miles can be included in any Mercator chart, except in the largest-scale ones showing a small area only. No linear scale could be drawn that would be accurate for different latitudes on a chart of any considerable area.

Mercator's projection can also be used with the axis of the cylinder not coinciding with the axis of the earth through the poles, and the resulting projections are known as transverse Mercator (if the axis is at right angles to the polar axis) or oblique Mercator. The former results in the projection being least distorted along a given meridian, instead of along the equator, and is useful for mapping regions extending in a north–south direction, e.g. the British Isles on the Ordnance Survey. Oblique Mercator gives a line of least distortion which can be arranged to suit the area being mapped, running at an angle to both meridians and parallels of latitude. Both these varieties, however, are useless for navigation.

Bibliography

Crane, N. , Mercator: The Man who Mapped the Planet (2003).

Mer·ca·tor pro·jec·tion / mərˈkātər/ (also Mer·ca·tor's pro·jec·tion) • n. a projection of a map of the world onto a cylinder in such a way that all the parallels of latitude have the same length as the equator, used esp. for marine charts and certain climatological maps.

Mercator projection a projection of a map of the world on to a cylinder in such a way that all the parallels of latitude have the same length as the equator, invented by the Flemish geographer and cartographer Gerardus Mercator (1512–94). It was first published in 1569 and used especially for marine charts and certain climatological maps.