Mercator Projection - Properties and Historical Details

Properties and Historical Details

Mercator's 1569 edition was a large planisphere measuring 202 by 124 cm, printed in eighteen separate sheets. As in all cylindrical projections, parallels and meridians are straight and perpendicular to each other. In accomplishing this, the unavoidable east-west stretching of the map, which increases as distance away from the equator increases, is accompanied by a corresponding north-south stretching, so that at every point location, the east-west scale is the same as the north-south scale, making the projection conformal. A Mercator map can never fully show the polar areas, since linear scale becomes infinitely high at the poles. Being a conformal projection, angles are preserved around all locations. However scale varies from place to place, distorting the size of geographical objects and conveying a distorted idea of the overall geometry of the planet. At latitudes greater than 70° north or south, the Mercator projection is practically unusable.

All lines of constant bearing (rhumbs or loxodromes—those making constant angles with the meridians) are represented by straight segments on a Mercator map. The two properties, conformality and straight rhumb lines, make this projection uniquely suited to marine navigation: courses and bearings are measured using wind roses or protractors, and the corresponding directions are easily transferred from point to point, on the map, with the help of a parallel ruler or a pair of navigational protractor triangles.

The name and explanations given by Mercator to his world map (Nova et Aucta Orbis Terrae Descriptio ad Usum Navigantium Emendata: "new and augmented description of Earth corrected for the use of sailors") show that it was expressly conceived for the use of marine navigation. Although the method of construction is not explained by the author, Mercator probably used a graphical method, transferring some rhumb lines previously plotted on a globe to a square graticule, and then adjusting the spacing between parallels so that those lines became straight, making the same angle with the meridians as in the globe.

The development of the Mercator projection represented a major breakthrough in the nautical cartography of the 16th century. However, it was much ahead of its time, since the old navigational and surveying techniques were not compatible with its use in navigation. Two main problems prevented its immediate application: the impossibility of determining the longitude at sea with adequate accuracy and the fact that magnetic directions, instead of geographical directions, were used in navigation. Only in the middle of the 18th century, after the marine chronometer was invented and the spatial distribution of magnetic declination was known, could the Mercator projection be fully adopted by navigators.

Several authors are associated with the development of Mercator projection:

• German Erhard Etzlaub (c. 1460–1532), who had engraved miniature "compass maps" (about 10×8 cm) of Europe and parts of Africa, latitudes 67°–0°, to allow adjustment of his portable pocket-size sundials, was for decades declared to have designed "a projection identical to Mercator's".
• Portuguese mathematician and cosmographer Pedro Nunes (1502–1578), who first described the loxodrome and its use in marine navigation, and suggested the construction of a nautical atlas composed of several large-scale sheets in the cylindrical equidistant projection as a way to minimize distortion of directions. If these sheets were brought to the same scale and assembled an approximation of the Mercator projection would be obtained (1537).
• English mathematician Edward Wright (c. 1558–1615), who published accurate tables for its construction (1599, 1610).
• English mathematicians Thomas Harriot (1560–1621) and Henry Bond (c.1600–1678) who, independently (c.1600 and 1645), associated the Mercator projection with its modern logarithmic formula, later deduced by calculus.