Atlas sive Cosmographicae Meditationes

The problem it solved

Every flat map of a round world is wrong, and until the sixteenth century nobody had to decide precisely how.

The mathematics had been understood since Ptolemy: a sphere cannot be flattened without distorting distance, area, shape or bearing, and any projection sacrifices some to preserve others. In practice mapmakers had chosen by convention and instinct rather than by calculation, and had not told their readers what the choice implied.

For navigators this had become dangerous. Ocean sailing had grown enormously, and a navigator's basic technique is to hold a compass bearing. On the charts then in use, a constant bearing is not a straight line, so a course plotted with a ruler was not the course sailed. Errors accumulated over an ocean crossing into hundreds of miles.

The second problem was the atlas as a form. Ortelius had shown in 1570 what a bound, uniform, sequenced collection of maps could be, and had shown it as a publisher rather than a geographer - assembling other men's work. Nobody had built one from the ground up, with a single mapmaker's projection, conventions and judgement running through the whole.

And nobody had a name for it. Ortelius called his a theatre. Others called them mirrors, or descriptions, or simply books of maps.

Mercator also had a cartographer's frustration with the trade. Maps were copied and reissued without correction, so an error introduced once persisted through decades of reprints, and a mapmaker who improved a survey had no way to stop the old version circulating alongside the new.

The genre also had no settled scale conventions, so even a well-made collection could not be used for measurement across sheets - the defect Ortelius solved by standardising the page and Mercator by controlling the maps themselves.

And navigators had no way to test a chart except by using it. A projection error and a survey error produce the same result at sea, so a method that separated the two was worth more than any single accurate map.

The commercial position was also awkward. Ortelius had the market, and a rival product had to justify itself by being something the Theatrum was not - which pushed Mercator toward original geography rather than compilation.

The work itself

Mercator gave the form a name, a philosophy and a consistent hand.

The projection came first, in 1569, on a large wall map: latitude spaced so that a rhumb line - a course of constant compass bearing - plots as a straight line. Area is sacrificed, badly and increasingly toward the poles. Mercator states the purpose plainly: this map is for navigation, and the stretching is the price.

The Atlas itself was issued in parts from 1585 and completed by his son after his death in 1594. It is a mapmaker's atlas rather than a collector's: the maps are his own work, engraved to his conventions, at scales he chose, and the geography is corrected rather than merely gathered.

The title is the part everyone remembers. He explains it in the preface - Atlas as a king of Mauretania renowned for learning, a scholar rather than the Titan holding up the sky - and offers him as a model for the contemplation of the world. The frontispiece shows him as a philosopher with a globe.

The book also opens with cosmography and creation before it reaches the maps, because Mercator's plan was a complete description of the world from its making onward. He never finished the earlier parts. What survives is the map section, which is what everyone wanted.

The projection was not accompanied by a mathematical proof. Mercator constructed the spacing empirically; the rigorous derivation came from Edward Wright in 1599, which is why navigators could use the chart for thirty years before anybody could fully explain why it worked.

His lettering deserves a mention: Mercator popularised italic script for map labels, which fits more text into a crowded space legibly than the gothic hands then usual, and the convention persists on maps to this day.

Rumold's completion also shaped what survives. He assembled the 1595 edition from his father's finished sheets and his own additions, so the book bearing Mercator's name is partly a son's editorial judgement about which parts were ready.

The 1595 volume is also incomplete as a world atlas: the coverage is strongest in northern Europe, where Mercator had worked, and thin elsewhere, which is what happens when one man draws the maps instead of buying them.

What followed

The name took over completely. Within a generation any bound collection of maps was an atlas, in every European language, and Ortelius's Theatrum was retrospectively described as the first one - which it was, except in name.

The business went to Hondius, who bought the plates in 1604 and issued expanded editions that dominated the market for decades, then to Blaeu and the great Amsterdam houses. Mercator's atlas is the beginning of the Dutch golden age of cartography as a commercial phenomenon.

The projection had the longest life and the most complicated one. It is still the correct choice for navigation and for any application preserving local angles, and it became the default world map for four centuries, in classrooms and on walls, where preserving bearing is irrelevant and distorting area is actively misleading. Generations learned a picture of the world in which the tropics are small and the northern latitudes vast.

That is not Mercator's error. He specified the purpose and the cost. It is what happens when a reference tool designed for one job becomes the default for every job, and the caveat gets dropped somewhere in the reproduction.

The general lesson belongs with the Handy Tables and the DSM. A tool that answers one question well will be used to answer others, and the stated limits travel less well than the tool does.

The unfinished parts are worth noting as well. Mercator planned a cosmography beginning with the creation and running through astronomy, geography and history, and completed only fragments - so the book that named the genre is the surviving section of a much larger work that no one now remembers.

The projection debate has also become a proxy for larger arguments about representation, with alternative world projections promoted on political grounds - a fight about a sixteenth-century navigational instrument that Mercator would have found bewildering and not entirely unreasonable.

The Titan confusion has proved unkillable. Mercator explicitly chose the Mauretanian king and explained why, and the figure holding the globe on the frontispiece is a philosopher - but the image of a strongman shouldering the world is what the word now calls up.