Bearings Straight—An Introduction

Mariners share two fears: bad weather and getting lost. Their deep respect for the Mercator projection reflects the map’s value for plotting an easily followed course that can be marked off with a straightedge and converted to a bearing with a protractor similar to the semi-circular plastic scales fourth graders use to measure angles. In a less direct way, the Mercator map also addresses the sailor’s fear of storms by providing a reliable base for plotting meteorological data for tropical regions. But that’s another story.


Picture yourself as a seventeenth-century navigator who knows where he is and where he wants to go. You plot both locations on a chart, join them with a straight line, and measure the angle your line makes with the map’s meridians, which run due north. If the chart is a Mercator map, all its meridians are straight lines, parallel to one another, and the course you’ve just plotted is a rhumb line, also called a loxodrome (fig. 1.1). The derivation of rhumb is obscure—possible origins include a Portuguese expression for course or direction (rumbo) and the Greek term for parallelogram (rhombos)—but math ematician Willebrord Snell (1580–1626) coined loxodromein 1624 by combining the Greek words for oblique (loxos) and course (dromos). Manuals on piloting accept rhumb as a normal part of the seaman’s language and define rhumb line as a line that intersects all meridians at the same angle. The angle between a course and a meridian is a bearing, thus a rhumb line is a line of constant bearing. Stay the course, and you’ll reach your destination.


Look down at a globe, on which the meridians meet at the North Pole, and you’ll understand why loxodromes are spirals that converge toward the pole as they wind round and round, always crossing the meridians at a constant angle (fig. 1.2). The only exceptions are rhumb lines running directly north–south, along a meridian, or directly east– west, along a parallel. The former reach the pole along the shortest possible route, whereas the latter never get any farther north or south. If a bearing is close to due north, its loxodrome approaches the pole rapidly. If a bearing is nearly due east, convergence is notably slower, with a loxodrome that originates in the tropics and circles the globe many times before crossing the Arctic Circle. Follow a loxodrome in the other direction, and it crosses the equator and starts spiraling toward the South Pole. What works in the northern hemisphere works equally well south of the equator.
Gerard Mercator (1512–94) understood loxodromes. Skilled in engraving and mathematics, he crafted globes and scientific instruments as well as maps. Like other sixteenth-century globe makers, he engraved the grid lines, coastlines, and other features on copper plates and printed the curved surface in flat sections, called gores, which were trimmed and pasted onto a ball, typically made of papier-mâché. His first experience with globe making occurred around 1537, when he engraved the lettering for a terrestrial globe designed by his mathematics tutor, Gemma Frisius (1508–55). That same year Mercator produced his first map, a six-sheet representation of the Holy Land. In 1541, he devised a navigator’s globe on which rhumb lines spiraled outward from compass roses. Intended as a navigation instrument, the globe was approximately 16.5 inches (42 cm) in diameter and consisted of the twelve gores and two polar caps pasted onto a hollow wooden ball for use at sea. According to cartographic historian Robert Karrow, this navigator’s globe was the first of its kind, and sixteen surviving copies, crafted between 1541 and 1584, attest to its success and durability.


Mercator published his celebrated world map of 1569 as a set of eighteen sheets, which form a wall-size mosaic 48 inches (124 cm) tall by 80 inches (202 cm) wide. Its projection revolutionized navigation by straightening out rhumb lines on a flat map—not just the globe’s meridians and parallels, but any rhumb line a seaman might plot. To accomplish this, Mercator progressively increased the separation of the parallels. On a grid with a constant separation of ten degrees between adjoining meridians and parallels—cartographers call this a ten-degree graticule—parallels near the equator are relatively
close, whereas those farther poleward are more widely spaced, as shown in figure 1.3. The parallels at 70°and 80°N,for instance, are much farther apart than the equator and its neighbor at 10N. And the separation between 80and 90 N cannot be shown completely because the North Pole lies at infinity. Although loxodromes converge toward the poles,on a Mercator projection they never really get there.
Mercator’s intent is readily apparent in his map’s title, "New and More Complete Representation of the Terrestrial Globe Properly Adapted for Use in Navigation.” In 1932, the Hydrographic Review published a literal translation of the map’s numerous inscriptions, elegantly engraved in Latin. Although the chartmaker’s words reveal little about how he spaced the parallels, Mercator clearly recognized the need “to spread on a plane the surface of the sphere in such a way that ... the forms of the parts be retained,so far as is possible, such as they appear on the sphere. "Accurate bearings, he reasoned, demand a locally exact representation of angles and distances, even though “the shapes of regions are necessarily very seriously stretched.”
To compensate for the local deformation that would otherwise occur, Mercator “progressively increas[ed] the degrees of latitude toward each pole in proportion to the lengthening of the parallels with reference to the equator. «Sounds complicated, but it’s not. At 60° N ,for instance, the distance on a globe between two meridians is half the corresponding distance at the equator. Because the projection doesn’t let the meridians converge, it must stretch the sixtieth parallel to twice its true length. To compensate for this pronounced east–west stretching along the map’s parallels, the projection imposes an identical stretching in the north–south direction, along the meridians. Farther north, as east–west stretching grows progressively larger, north– south stretching increases proportionately. At the North Pole, a mere point on the globe, map scale becomes indefinitely large—the result of stretching a dimensionless spot to a measurable distance—and the pole lies “at infinity, ”or at least well off the map. That’s why Mercator world maps typically cut off northern Greenland and omit most of an otherwise humongous Antarctica.
Forcing north–south scale to equal east–west scale at all points not only preserves angles and bearings but prevents the deformation of small circles into ellipses. Modern cartographic textbooks consider this locally exact portrayal of angles and small shapes, called conformality, highly desirable for detailed, large-scale maps of small areas. In addition to depicting city blocks as rectangles, not parallelograms, a conformal map keeps squares square and circles circular. Although more than a century passed before Edmund Halley (1656–1742) recognized conformality as a mathematical property, Mercator’s 1569 world map became the first conformal projection to portray meridians and parallels as straight lines.
In addition to drawing on his experience in making globes, Mercator borrowed a concept embedded in fourteenth-century regional sailing charts. Portolan sailing charts, named after the portolani, or pilot books, that guided sailors across the Mediterranean Sea or along the coast of Europe, were distinguished by a network of straight-line sailing directions that converge at assorted compass roses. A typical portolan chart was oriented to magnetic north, covered less than one fiftieth of the earth’s surface, and lacked a consistent grid of meridians and parallels. Originally drawn to illustrate books of written sailing directions, portolan charts reduced the uncertainty of navigating across open waters. As the first whole-world sailing chart, Mercator’s map made a transatlantic journey look as straightforward as a voyage from Athens to Alexandria.

However easy to navigate, a loxodrome is rarely as direct as the great circle crudely approximated by a taunt thread stretched across a globe between a route’s origin and destination. Great circles, so called because they are the largest circles one can draw on a sphere, define the shortest path between two points. Although geometrically efficient, they are difficult to navigate because the bearing is constantly changing. The only exceptions are routes along a meridian or the equator. Because a loxodrome is not a great circle, the sailor taking its more easily followed course takes an indirect route. But if the increased distance is long enough to make a difference, the navigator can divide the route into sections and follow the rhumb line for each part. In figure 1.4,a dotted line illustrates a sectioned route from Cape Town to New York. Because the Mercator grid distorts distance, the single rhumb line marking the constant-bearing route looks deceptively shorter than either the great-circle route or its multi-rhumb approximation.
Mercator sought to reconcile the navigator’s need for a straightforward course with the trade-offs inherent in flattening a globe. These trade-offs include distortions of distance, gross shape, and area. Although all world maps distort most (if not all) distances, some projections, including Mercator’s, afford negligible distortion on large-scale detailed maps of small areas. Only a globe can preserve continental outlines, however, which cannot be flattened without noticeable stretching or compression. Relative size, which is preserved on map projections with a property called equivalence, is markedly misrepresented on Mercator charts because of the increased poleward separation of parallels required to straighten out loxodromes. Distortion of area is most apparent in the chart’s inflated portrayal of Greenland as an island roughly the size of South America. On a globe Greenland is not quite an eighth as large.

Like many innovations, the new projection did not catch on right away. One impediment to a wider, swifter adoption was the lack of a detailed procedure for progressively separating the parallels. Wordy inscriptions explained the map’s purpose but offered no instructions for constructing or refining its grid. That Mercator produced a generally accurate solution for the lower and middle latitudes was quite an accomplishment in an era with neither logarithms to expedite calculation nor integral calculus to derive a concise mathematical formula. Trigonometric tables of secants and tangents, which might have been especially useful, were also lacking. Some scholars think Mercator used a mathematical approximation to lay out parallels ten degrees apart; a few suggest that he developed the separations graphically by copying loxodromes from a globe to a map. Whatever his approach, Mercator’s map stimulated further work by English mathematicians Edward Wright (1561–1615) and Henry Bond (1600–1678), discussed in chapter 5. In 1599, in a treatise with a long title that begins Certaine Errors in Navigation, Wright included a table of “meridional parts,” with which a chartmaker or seaman could efficiently lay down a Mercator grid. And in 1645, Bond suggested a mathematical formula after discovering a similarity between Wright’s table and a table of logarithmic tangents.

Another obstacle was the primitive technology for taking compass readings at sea and correcting for magnetic declination. An inscription on the 1569 world map discusses the vexing discrepancy between the poles that anchor the earth’s grid and the poles believed to attract compass needles. Eager to include a north magnetic pole on his map, Mercator consulted “a great number of testimonies, "which suggested diverse positions for a magnetic meridian aimed at the magnetic pole. Some observations placed this magnetic meridian in the Cape Verde Islands, where magnetic north coincided with true north; others placed it at Corvo,in the Azores. Equally suggestive was Marco Polo’s report that “in the northern parts of Bargu [in northeast Asia] there are islands, which are so far north that the Arctic pole appears to them to deviate to the southward.” Without marking the Corvo meridian explicitly on his map, Mercator extended it up over the pole and then south toward Asia. In doing so, he wrongly assumed that compass needles point along great circles that converge at the magnetic poles.
Aware that, because of this uncertainty, the location didn’t warrant an X or a compass rose, Mercator marked the spot with what looks like a fried egg with a very small yoke (fig. 1.5). An adjacent inscription restates the premise: “It is here that the magnetic pole lies if the meridian which passes through the Isle of Corvo be considered at the first. To hedge his bets, the chartmaker placed a second magnetic north pole farther south and a bit to the east, where a larger symbol that cartographic historians Helen Wallis and Arthur Robinson describe as “a high rocky island” carries a more confident explanation: “From sure calculations it is here that lies the magnetic pole and the very perfect magnet which draws to itself all others, it being assumed that the prime meridian be where I have placed it.” Confronting uncertainty, Mercator used a pair of “extreme positions” to bracket the magnetic pole’s true location “until the observations made by seamen have provided more certain information. "Too few present-day cartographers, sad to say, are as frank about geographic ambiguity.


Ships carried magnetic compasses as early as the twelfth century, but seamen seldom used them because of an innate mistrust of innovations as well as quirky needles that didn’t point directly north. Magnetic declination was not discovered until the fifteenth century, and as Mercator’s experience illustrates, geomagnetism proved less wellbehaved than sixteenth-century mapmakers had originally believed. Adjustment for geomagnetic distraction was not possible until 1701, when Edmund Halley published a pioneering but simplistic map of isogons (lines of equal magnetic declination) for the Atlantic Ocean (fig. 1.6). Determining a ship’s location at sea was equally troublesome. Latitude could be figured simply by sighting on the northern star at night or by measuring the sun’s noontime elevation above the horizon, but longitude, calculated from the difference between local time and time at the prime meridian, required a highly accurate chronometer, not available until the mid-eighteenth century, when John Harrison (1693–1776) devised a clock that lost only fifteen seconds in 156 days. The ship’s compass, magnetic adjustment, and an accurate chronometer were parts of a puzzle that included Mercator’s projection. Not until all the pieces were in place could mariners fully appreciate Mercator charts.


Navigators began to use the Mercator map in the early 1600s, after British geographer Richard Hakluyt (1552–1616) included a world map drawn by Wright in the second edition of his Principall Navigations, Voiages, Traffiques and Discoveries of the English Nation, published in 1599. Wright not only corrected inaccuracies in Mercator’s grid but provided an updated view of world geography, taken from a 1592 globe by Emery Molyneux (d. 1598/9). Measuring 17 inches (43 cm) tall by 25 inches (64 cm) wide and printed in two sections, the Wright-Molyneux map, as it’s often called, is smaller and more readily reproduced, displayed, and archived than Mercator’s eighteen-sheet mosaic. According to Robert Karrow, nineteen copies of the Wright Molyneux map exist, in contrast to only three copies of Mercator’s, which is seldom reproduced in one piece because of its size. Despite suggestions that the grid be called the Wright projection, Mercator’s name stuck, reinforced no doubt by his impressive contribution as an atlas publisher. Cartographic historians celebrate Gerard Mercator for two epic achievements: his world map of 1569 and his monumental three-volume world atlas, completed in 1595.
Mercator might not have been the first to use the projection that bears his name. In 1511,Erhard Etzlaub (ca. 1460–1532),a Nuremberg compass maker, crafted a portable sundial with a map on its lid. A mere 3.1 inches (80 mm) wide and 4.3 inches (108 mm) tall, Etzlaub’s map puts south at the top and covers only Europe and North Africa (fig. 1.7). It lacks a graticule ,but latitude gradations at one-degree intervals along the sides and numerical labels every five degrees reflect the progressively spaced parallels of the Mercator grid. This similarity is hardly an accident. Etzlaub produced a similar but slightly larger sundial map two years later and presumably made others that didn’t survive. An instrument maker and physician with an active interest in astronomy and cartography, he produced several other maps, principally woodcuts with south at the top. Especially note-worthy is his 1500 road map of central Europe, cast on a stereographic projection—also conformal—to promote the accurate alignment of compass points with travel directions. According to cartographic historian Brigitte Englisch, his 1511 “compass map” not only was the earliest rectangular conformal projection but also accords exceptionally well with modern versions of the Mercator projection. Englisch argues that Mercator no doubt knew of Etzlaub’s invention and that “the projection of varying latitudes should be known as the Etzlaub-Mercator projection.”


Wright and Etzlaub are not the only mapmakers in line to share Mercator’s fame. Another contender is the unidentified Chinese scholar who drafted the tenth-century Dunhuang star map. According to The Timetables of Science, a chronology published in 1988 and cited on several Web sites, the star chart “uses a Mercator projection [and is] the first known use of this kind of map projection. "I tracked this assertion no further than the multivolume History of Cartography, which includes a black-and-white photo of the narrow, scroll-like map. How the claim arose is a puzzle insofar as the chart contains neither a grid nor marginal tick marks. As a key sentence in its caption tellingly observes: “There is no attempt at a projection on this rather crude chart.” Projection guru John Snyder wholly ignored the Dunhuang star chart in his epic history of map projection, in which he noted Etzlaub’s “similar projection "but concluded that “the principle remained obscure until Mercator’s independent invention.”
Anyone who thinks cartographic folklore inflates Mercator’s contribution should be mollified if not amused by an offhand comment in the U.S. Coast and Geodetic Survey’s bible on map projection, introduced in 1921 and shepherded through numerous revisions by Charles Deetz and Oscar Adams. In discussing the sinusoidal projection, on which converging meridians yield a world map shaped like an antique Christmas ornament, Deetz and Adams noted the occasional use of an alternative name, Sanson-Flamsteed projection, commemorating Nicolas Sanson and John Flamsteed, who used it around 1650 and 1729, respectively. In their opinion, the projection “might well have been termed the ‘Mercator equal-area projection’ in the first place, from the fact that the early atlases bearing his name gave us the first substantial maps in which it is employed. Mercator’s name has, however, been so clearly linked with his nautical conformal projection that it becomes necessary to include with his name the words equal area if we wish to disregard the later claimants of its invention, and call it the Mercator equal-area projection.” To underscore the point, they titled the section “Sinusoidal or Mercator Equal-Area Projection.”
Whatever its authorship, the better-known Mercator conformal projection gathered adherents among scientists as well as navigators. Noteworthy adoptions include Robert Dudley’s pioneering sea atlas of the world, published in 1647, and Edmund Halley’s revolutionary maps of the trade winds and magnetic declination, published in 1686 and 1701, respectively. In 1769 the Mercator grid provided the geographic framework for a ground-breaking Gulf Stream chart by Benjamin Franklin and whaling captain Timothy Folger, and in the early nineteenth century it gained wider exposure in the influential line of geography textbooks written and published by Jedidiah Morse, father of portrait painter and telegraphic experimenter Samuel F. B. Morse. In 1919 Vilhelm Bjerknes, the Norwegian meteorologist who discovered fronts and air masses, proposed the Mercator projection as the world standard for weather maps of the tropics, and in 1937 the World Meteorological Committee recognized the importance of conformality on atmospheric maps by endorsing Bjerknes’s recommendation. In the commercial sphere, publishers of reference atlases and wall maps adopted the Mercator grid for regional maps of Australia, the Pacific islands, and the world’s oceans.
To the disgust of geographic educators, Mercator’s grid framed many whole-world maps with no bearing on navigation, weather, or geophysics. As I show in chapter 9, geopolitical motives were apparent in a few cases, but much of the projection’s misuse reflects a mix of comfortable familiarity, public ignorance, and institutional inertia. No one was hawking the Mercator brand, at least not overtly, but no one had to—many people who grew up with the map apparently believed this was how a flattened earth should look. How else to explain the ascendancy of an utterly inappropriate perspective and widespread resistance to superior substitutes?
If there is a villain here, it's not Gerard Mercator, who used equal area maps in his atlases and was quite clear about why he devised a rectangular conformal projection. Wary of wrongheaded finger pointing, Deetz and Adams chided the chartmaker’s critics in verse:
Let none dare to attribute the shame
Of misuse of projections to Mercator’s name;
But smother quite, and let infamy light
Upon those who do misuse, Publish or recite.

Although educators and scientists understood the problem, few seemed willing to challenge the conventional stupidity.

The most famous attack on the Mercator map’s undeserved prominence came well after the tide had turned. In the 1970s German historian Arno Peters (1916–2002) proposed a ludicrously inapt solution now known as the Peters projection. As chapter 11 explains, the Peters map is not only an equal-area map but an exceptionally bad equal-area map that severely distorts the shapes of tropical nations its proponents profess to support. Its popularity among Third World advocacy groups like Oxfam and the World Council of Churches is hard to explain. Perhaps it’s a reflection of what I call the Monty Python Effect, named for the parody troupe’s well-known transition line, "And now for something completely different." To most people who see it for the first time, the Peters map is indeed different: as figure 1.8 illustrates, Africa and South America look like land masses stretched into submission on a medieval torture rack. In asserting a new solution to an old problem, Peters ignored other, demonstrably better equivalent projections. And in claiming his projection was original, he overlooked an identical map presented in 1855 by James Gall (1808–95),a Scottish clergyman. Dare I say it? Peters had a lot of Gall in as many ways as possible. Mercator’s legacy is much more than the life and works of a Flemish chartmaker. As the remaining chapters illustrate, the Mercator projection lies at the intersection of a diverse collection of intriguing tales about navigation, cartographic innovation, military precision, media mischief, and political propaganda.


Early Sailing Charts

As predecessors go, portolan charts are an impressive lot. In addition to having held the mathematically superior Mercator projection at bay for a century or two after its initial presentation in 1569, they attract a far greater following among map historians, who recognize them as a distinct cartographic genre. And as this chapter observes, portolan charts not only taught mariners to rely on sailing charts but also left a legacy of geographic detail for later mapmakers.

It’s easy to treat portolan charts as both enigma and innovation. They appeared suddenly in the late thirteenth century with crisscrossed rhumb lines and abundant place names, all in sharp contrast to the prevailing religious cartography typified by small, sparse, eastup world maps centered on Jerusalem. Unlike the medieval mappae mundi, which were largely inspirational, portolan charts were practical tools for crossing open waters. And unlike the well-documented publication of Gerard Mercator’s world map, the murky origin of the portolan charts has invited much speculation, not likely to be resolved, about whether Italians or Catalan Spaniards crafted the ultimate prototype, which historians have yet to find.

In their handbook of cartographic innovations, map historians Helen Wallis and Arthur Robinson list four key characteristics of portolan charts. Foremost is the web of intersecting rhumb lines, typically originating on the circumference of a circle, around which sixteen equally spaced points represent the eight principal wind directions (N,NE,E,SE,S,SW,W,and NW) and the eight half-winds (NNE,ENE, ESE,... ) of the mariner’s compass (fig. 2.1). On most charts the circle is readily apparent in the points at which rhumb lines converge like spokes in a wheel. Look closely at the portolan chart in figure 2.2, which covers the western Mediterranean, and you’ll see traces of a large circle centered at the middle of the chart and touching the top and bottom edges. Rhumb lines also converge at the circle’s center, and at the lower right, over North Africa, one of the sixteen intersection points on its perimeter serves as a compass rose. On some oblong portolan charts, like the example in figure 2.3, adjacent circles cover eastern and western parts of the map.

Closer inspection of the chart in figure 2.2 reveals a second distinguishing trait: an abundance of closely spaced, hand-lettered place names perpendicular to the shoreline and always inland, to avoid conflict with coastal details. Additional labels over water identify small is lands. Because chartmakers inked in these names one after the other in a continuous coastwise sequence, labels appear inverted where the shoreline reverses direction. A third characteristic is color-coded names and directions. More important places, labeled in red, stand out from less significant neighbors, lettered in black. Color also reduces confusion among rhumb  lines, inked in black or brown for the eight principal winds, in green for the eight half-winds, and in red for the sixteen interspersed quarter-winds. The fourth trait is a functional generalization that rounds minor coastal irregularities, overstates bays and headlands, and uses crosses and dots to point out rocks and shoals. Except for lavishly decorated versions intended for royal collectors, portolan charts showed what mariners needed to know and not much else.


Inked on treated animal skin called vellum, portolan charts withstood rough handling at sea better than paper navigation charts, which did not become common until the eighteenth century. Animal hides were especially suited to the Mediterranean’s pronounced east–west elongation. After splitting the calf’s or sheep’s skin along the stomach, the vellum maker removed the appendages and head but kept the neck, which formed the noticeably narrowed end of a large oblong drawing surface. The typical portolan chart is drawn on a single skin with the tapered end pointing west, to accommodate the Mediterranean’s narrowed reach toward the Atlantic. The flesh side of the skin provided a smooth writing surface; younger animals, with fewer scars, were preferred. Treatment included soaking the hide in lime, scraping off hair and flesh, stretching over a drying frame, rubbing with pumice to smooth the surface, and massaging with chalk to create a neutral, off-white background. Although the charts could be rolled for easy storage—like a thin leather glove, vellum is flexible— some were mounted on wood or cardboard to prevent shrinkage.

Medieval chartmakers are not wholly anonymous. Tony Campbell, the British Library’s former map librarian who wrote the chapter on portolan charts for the multivolume History of Cartography, lists forty-six individuals known to have produced portolan maps or atlases before 1500. Especially noteworthy are Pietro Vesconte, a Genoese mapmaker whose earliest known nautical map is a 1311 chart of the Mediterranean and the Black Sea,and Giovanni da Carignano, a Genoese abbot once credited with the earliest dated portolan chart, believed to have been drafted around 1300. No one questions Carignano’s authorship of the chart, which was destroyed during World War II, but comparison of photographic copies with other maps of the period reveals places names not widely known or used until the 1320s. Cartography was not Carignano’s vocation, but by the late fourteenth century demand for sailing charts was supporting specialist chartmakers in the Italian ports of Genoa and Venice as well as their Catalan counterparts of Barcelona and Majorca.

At least a few medieval chartmakers benefited from an edict endorsing navigation maps. In 1354 King Peter of Aragon ordered all ships to carry two portolan charts, the second perhaps as backup if the other were ruined. Peter’s ordinance reflected the charts 'value as navigation aids as well as the consequences of a ship foundering or getting lost. The earliest surviving record of a chart used at sea is an account of a 1270 voyage by France’s King Louis IX. Because of rough weather the captain decided to seek shelter at Cagliari, in Sardinia, and brought out a chart to reassure the frightened monarch that land was nearby.

The oldest known portolan chart is the Carte Pisane, drafted around 1290 in Genoa but named after Pisa, where it was discovered. Shown schematically in figure 2.3, the chart measures 20 by 41 inches (50 by 104 cm),encompasses the Mediterranean and part of the Black Sea, and includes all four characteristics of its genre. Separate circles anchor two networks of rhumb lines. Hidden on later charts, the circles here are inked in and obvious. Beyond the circles are several squarish grids, with no apparent role. Although seventeenth-century mapmakers used temporary grids, sketched in pencil, as guides for copying features from other charts, erasable pencils were not available until the sixteenth century. Tattered edges and missing fragments of vellum toward the upper right reflect repeated handling. Acquired in 1839 by the Bibliothèque Nationale, the Carte Pisane is a lucky survivor. Campbell, who uncovered fewer than two hundred pre-1500 portolan charts in public and private collections, dedicated his chapter to “the thousands of ordinary charts that served their purpose and then perished.”

Although scholars have yet to uncover a detailed description of medieval chartmaking, they’re certain that portolan charts were copied by hand from existing charts. Microscopic analysis of inked lines and tiny pinholes indicates that chartmakers first laid out the rhumb circle by using dividers (an instrument with two sharp points for transferring exact dimensions) to mark its center and sixteen equally spaced points on its circumference. Using the pinpricks as guides, artisans inked in the network of rhumb lines with pen and straightedge. They then transferred the shorelines from a master map, but exactly how remains a mystery. Some chartmakers apparently forced a fine powder through small holes in a master pattern placed over the fresh vellum, some used a crude form of carbon paper, and some are alleged to have anchored the master map on a transparent frame or table, placed the vellum on top, positioned a strong light source on the opposite side, and traced coastlines and other features directly. Still others might have been exceptionally good at visual transfer—what my cartography students call “eyeballing it.” Once the shorelines were laid down, transferring the place names was a straightforward yet painstaking process.

The prevalence of copying raises questions about the ultimate master chart: who crafted it, when, and how? Although map historians hold little hope of identifying the first chartmaker, they’re certain the prototype portolan chart—if indeed there was only one—was compiled from maps of smaller areas based on books of sailing directions called portolani. Written to help seamen find ports and avoid hazards along the Mediterranean coast, these medieval Italian sailing guides have an equally obscure origin. Although sailors had been taking notes on coastal navigation for over a millennium, pilot books with distances and bearings as well as shoreline narratives emerged at about the same time as the portolan charts. Or perhaps a bit before: extant portolan charts greatly outnumber surviving portolani, which were not decorated and never caught the fancy of royal collectors.

Wary of untested assumptions, Jonathan Lanman, a retired medical researcher and map collector, compiled sailing maps from the Lo Compasso de Navigare, a pilot book from the late thirteenth century, and the Parma-Magliabecchi Portolano, from the fifteenth century. Although fragments of older sailing guides exist, these were the earliest, most complete examples he could locate. To assess the cartographic validity of their sailing directions, he reconstructed the Mediterranean shoreline by chaining together straight-line segments based on distances reported in Italian sea miles,1 sea mile equaling 0.67 nautical miles (1.23 km), and bearings based on a thirty-two-point compass rose. Rotation of the resulting plots and careful alignment with the present-day shoreline revealed a realistic representation of the Mediterranean coast. Despite less than perfect matches, Dr. Lanman demonstrated that the information in the sailing guides was fully adequate for drawing dependable portolan charts.

Curious about the roles of map projection and magnetic declination, Lanman examined the geometric accuracy of the Carte Pisane and a second chart drawn in 1559 by Matteo Prunes, a Majorcan chartmaker. Although cartographic historians generally consider portolan charts “projectionless” for lack of a graticule, Lanman suggested they were “drawn on a square grid” noticeably skewed as a result of magnetic declination. Although evidence of an overt grid is speculative— Lanman’s argument rests largely on small squares within the rhumb circles of the Carte Pisaneand few other charts—locally reliable shapes reflect at least an unconscious appreciation of conformality, a key property of the Mercator projection. Researchers who have confirmed this proto-conformality (my term) include Waldo Tobler,a pioneer in computer cartography, who observed a strong similarity between a 1468 chart by Majorcan chartmaker Petrus Roselli and an oblique Mercator projection. And in a cartometric analysis of twenty-six charts, Scott Loomer, a cartography instructor at West Point, found strong correlations with conformality and straight loxodromes—exactly the properties needed for reliable navigation over open waters. Because a medieval sailing chart typically covered a small area, its informal, ad hoc projection was not a serious weakness.

Some historians recognize the 4 by 4 grids within the Carte Pisane’s rhumb circles as linear scales, running vertically as well as horizontally. Intersecting grid lines divide a distance of roughly 200 miles into four equal parts, and horizontal and vertical scales that are similar—or would be if the interior elements were perfect squares—signify the chartmaker’s unconscious pursuit of conformality. At least that’s how map historians interpret the grid. Unlike the scale bars on contemporary maps, scales on portolan charts didn’t specify distance.
The role of the magnetic compass in the compilation and use of portolan charts remains contentious. Did the compass play an important part in the compilation of early prototypes,or did it merely contribute to a more effective use of sailing charts and later updates? According to Lanman, the orientation of map features accords well with historic trends in magnetic declination. But in Tony Campbell’s view the jury is still out. The magnetic compass was in use by the thirteenth century, but it’s questionable whether instruments available around 1290 were sufficiently reliable to have contributed significantly to either the Carte Pisaneor contemporary portolani. Magnetic variation, which could provide a clue, is difficult to reconstruct, especially before 1600. Although a westward increase in magnetic deviation in the region was apparent until the seventeenth century, local magnetic anomalies thwart a reliable reconstruction of local details. What’s certain is that chartmakers corrected their bearings after better measurements became available around 1600.

Four centuries of portolan charts document European exploration of the African, American, and Asian coasts as well as advances in seamanship in England, Portugal, and what is now the Netherlands. For an appreciation of these improvements, compare the vague rendering of the Mediterranean coast on the Carte Pisane (see fig. 2.3) with the more detailed shorelines in the 1544 map by Venetian mapmaker Battista Agnese (see fig. 2.2). The more recent map is a double-page spread from a portolan atlas in the U.S. Library of Congress’s cartographic collection. Several of the atlas’s nine charts encompass the east and west coasts of North and South America, and a world map depicts the global journey of Ferdinand Magellan’s crew—the explorer died en route— as well as a meandering course from Spain to Panama and then down the coast to Peru. As the charted world expanded beyond the Mediterranean, navigators found the atlas format, with maps on vellum bound in leather, convenient for protecting their charts as well as accommodating new knowledge too detailed for a single map.

Expansion of detailed coverage into the Atlantic encouraged cartographers to correct scale disparities between the charts 'Atlantic and Mediterranean sections. Because pilot books for these areas had been compiled independently, with no attempt to resolve inconsistencies, early portolan charts underestimated distances along the North Atlantic coast by 16 to 30 percent relative to distances in the Mediterranean. These discrepancies persisted until 1403, when Francesco Beccari responded to feedback from mariners with a new chart that also corrected another reported deficiency. As the Genoese chartmaker’s inscription reveals, “It was several times reported to me by many owners, skippers and sailors proficient in the navigational art that the island of Sardinia ... was not placed on the charts in its proper place. Having listened to the aforesaid persons I placed the said island in the present chart in the proper place.” Several decades passed before other chartmakers adopted Beccari’s adjustments.

Since portolan charts were constructed from bearings and distances rather than a determination of geographic coordinates, they lacked indications of latitude and longitude and explicit projections. In the sixteenth century, latitude scales made a halting appearance on sailing charts, but even then, they were simply laid over the framework of rhumb lines, rather than integrated with it. Figure 2.4,a chart from a 1582 atlas by Spanish cartographer Giovanni Martines, shows this disconnect. The north–south and east–west lines on the chart do not represent particular meridians or latitudes; they are simply the extensions of these cardinal directions from the various wind roses. Even so, a navigator with dividers could determine his destination’s latitude, use a quadrant or astrolabe (instruments for measuring latitude at sea) to guide him north or south to the right parallel, and then sail due east or west to the intended port. Mariners call this parallel sailing.






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