Mercator Projection (1569): Gerardus Mercator's World Map

The Mercator projection is the method of drawing the world that Gerardus Mercator introduced on his great world map of 1569, published in Duisburg in the Duchy of Cleves. Designed for sailors, it showed lines of constant compass bearing as straight lines, which made it the standard for nautical charts for centuries. The same feature that makes it so useful also inflates the size of lands near the poles, and the projection still shapes how many people picture the world.

Background: a problem for navigators

By the 16th century European ships were crossing oceans routinely, but their charts were poorly suited to long voyages. Most sea charts, the so-called portolan charts, used a simple grid in which a degree of latitude and a degree of longitude were drawn the same length everywhere. Over short distances in the Mediterranean this worked well enough.

On an ocean crossing it did not. A sailor in the age of sail usually steered a constant compass bearing, a course known as a rhumb line or loxodrome. On the globe such a line is a spiral that curves towards the pole. On the old plane charts, a straight line drawn between two ports did not match the bearing that would actually take the ship there, and errors grew with latitude.

The Portuguese mathematician Pedro Nunes had analysed rhumb lines in the 1530s and shown that they were curved on a sphere. What was missing was a flat map on which they would appear straight. That was the problem Mercator set out to solve.

Gerardus Mercator

Mercator was born Gerard de Kremer on 5 March 1512 at Rupelmonde in Flanders, then part of the Habsburg Netherlands. He studied at the University of Leuven, where he learned mathematics, astronomy and instrument-making with the cosmographer Gemma Frisius. He became an outstanding engraver and maker of globes, scientific instruments and maps, producing a map of Palestine in 1537, a world map in 1538, a map of Flanders in 1540 and a terrestrial globe in 1541.

In 1544 he was arrested with several others on suspicion of Lutheran heresy and held for about seven months at Rupelmonde before being released. Some of those arrested with him were executed. In 1552 he moved to Duisburg, in the more tolerant Duchy of Cleves, where he spent the rest of his life working as a cartographer and teacher. He died there on 2 December 1594.

The 1569 world map

Mercator’s map carried a long Latin title which translates as “A new and augmented description of the Earth, corrected for the use of navigators”. It was engraved on copper and printed on 18 sheets which, assembled, measure about 202 by 124 centimetres. Only a handful of original copies survive, held in libraries in Paris, Basel and Rotterdam among others.

Besides the geography, the map contains several long text panels in which Mercator explained his sources and his method. One of them describes the key idea: to keep shapes correct and make rhumb lines straight, the distances between parallels of latitude had to be increased in proportion to the stretching of the parallels themselves. He did not publish a formula or tables, and it is unclear exactly how he calculated the spacing; historians generally think he used a graphical or approximate method.

The geography reflected the knowledge of its time. The coasts of Europe, Africa and southern Asia are fairly recognisable, while the Americas are distorted and a huge imagined southern continent fills the bottom of the map. An inset shows the North Pole as four large islands around a black rock, an idea Mercator drew from a lost medieval account. He also marked a magnetic pole, separate from the geographic pole, to explain why compasses do not point exactly north.

How the projection works

The Mercator projection is a cylindrical projection: imagine wrapping a sheet of paper around the globe at the equator. Meridians, the lines of longitude, become evenly spaced vertical lines. On a real globe they meet at the poles, so drawing them parallel stretches every east-west distance, and the stretch increases with latitude. At 60 degrees north, for example, east-west distances are doubled.

Mercator’s insight was to stretch north-south distances by exactly the same factor at each latitude. Because the stretching is equal in both directions at any given point, small shapes and angles are preserved. Mathematicians call this property conformal. Its practical result is that a course of constant compass bearing becomes a straight line on the chart, which is what navigators needed.

The price is that areas grow enormously towards the poles. The poles themselves lie at infinity and cannot be shown, so Mercator maps are cut off at some latitude, usually between about 70 and 85 degrees. A Mercator map is also poor for measuring distances over large areas, and the shortest route between two places, a great circle, appears as a curve.

From invention to standard

Navigators did not adopt the new chart at once. Mercator gave no instructions for constructing it, and many pilots preferred familiar methods. The decisive step came from England. The mathematician Edward Wright worked out the mathematics and published tables for drawing the projection in his book Certaine Errors in Navigation in 1599.

Later in the 17th century it was noticed that Wright’s tables matched values of the logarithm of the tangent function, a connection proved mathematically by James Gregory and Isaac Barrow between 1668 and 1670. By the 18th century the Mercator projection had become the normal form for sea charts, used by the navies and merchant fleets of Europe. Combined with better ways of finding longitude at sea, it made ocean navigation far more reliable.

Mercator himself went on to new projects. He worked for decades on a great collection of maps of the world, and the first parts of it appeared in the 1580s. The complete work was published by his son Rumold in 1595, a year after his death, under the title Atlas. It is the reason that word is used for a book of maps today.

Key people

• Gerardus Mercator (1512–1594): Flemish cartographer, engraver and globe-maker who designed the projection and published the 1569 map.
• Gemma Frisius (1508–1555): Leuven mathematician and cosmographer who trained Mercator and worked with him on globes.
• Pedro Nunes (1502–1578): Portuguese mathematician whose study of rhumb lines set out the navigational problem.
• Edward Wright (1561–1615): English mathematician who published the tables that made the projection usable in 1599.

Myths and facts

Myth: Mercator designed his map to make Europe look important. The projection was a technical solution for navigation, and its size distortion follows from the mathematics, not from political intent. Its enlargement of high latitudes affects Canada, Russia and Antarctica as much as Europe.

Myth: Mercator invented the first cylindrical map. Simple rectangular grids existed long before him. Some historians also point to the German instrument-maker Erhard Etzlaub, whose small maps of about 1511 appear to use increasing spacing of parallels. Mercator’s achievement was a large world map built deliberately on the conformal principle for navigation.

Fact: Africa is about 14 times larger than Greenland. Africa covers about 30 million square kilometres and Greenland about 2.2 million, yet on a Mercator world map they look similar in size.

By the numbers

Legacy and controversy

The Mercator projection became so common in school atlases and wall maps during the 19th and 20th centuries that many people came to think of it as the shape of the world. Critics argued that it gave a misleading impression of the relative size of countries, enlarging Europe and North America while shrinking the tropics.

In 1973 the German historian Arno Peters promoted an equal-area projection, now usually called the Gall–Peters projection, as a fairer alternative. Cartographers pointed out that equal-area maps had existed for centuries and that Peters’s map badly distorts shapes. Many geographers argued that no single projection is best and recommended compromise projections such as the Robinson or Winkel tripel for general world maps.

The projection gained a new life in the internet age. Online mapping services adopted a variant called Web Mercator in the mid-2000s because it keeps streets and buildings at their correct angles whatever the zoom level. Mercator’s design therefore still guides navigation, now on phones as well as ships.

Timeline

• 1512, 5 March: Gerard de Kremer, later known as Gerardus Mercator, is born at Rupelmonde in Flanders.
• 1544: Mercator is imprisoned for about seven months on suspicion of heresy and then released.
• 1552: He moves to Duisburg in the Duchy of Cleves.
• 1569: Mercator publishes his 18-sheet world map on the new projection.
• 1594, 2 December: Mercator dies in Duisburg.
• 1595: His collection of maps is published in full under the title Atlas.
• 1599: Edward Wright publishes tables for constructing the projection in Certaine Errors in Navigation.
• 1973: Arno Peters launches a public campaign against the Mercator projection.

Why it matters

Mercator solved a real problem for ocean navigation, and his projection became the basic tool of seafarers for centuries. It sits in a line of landmark maps from the Waldseemüller map of 1507 to the Theatrum Orbis Terrarum of Abraham Ortelius, and it helped make possible the long voyages of the age that followed the Magellan-Elcano circumnavigation. Its distortions also offer a lasting lesson: every flat map of a round Earth involves a choice about what to keep and what to sacrifice.