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Mercator -Travelers’Aide (I)


Edward Wright’s denunciation of “the ordinarie erroneous making or using of the sea chart” had little immediate impact on mariners, who resisted his “new map” well into the eighteenth century. Most naviga­tors trusted tradition more than science, and the plane chart, though not perfect, was at least familiar and straightforward. Appreciation of the Mercator projection called for computational savvy, and its effec­tive use required reliable methods for taking bearings and determining position. What’s the point of precisely plotted rhumb lines when magnetic declination was unpredictable and longitude estimated us­ing astronomical tables might be off by several degrees? Because all the prerequisites for reliable “Mercator sailing”—most notably, the sextant (for measuring precise angles), the marine chronometer, the nautical almanac, and charts of magnetic declination—were not in place until the late eighteenth century, Wright’s tables were ahead of their time by nearly two centuries.

Mariners were not the only doubters. A bitter exchange between mathematics teacher Thomas Haselden and three London entrepreneurs suggests that not all British scientists were quick to adopt Mer­cator’s map as the one true chart. The dispute followed a July 1719 ad­vertisement in a London daily newspaper, the Post Boy:

                                
In a short 1722 book Haselden denounced the “authors” for touting a “Globular Chart” with curved meridians and fraudulently securing a “recommendation certificate” from “the Celebrated Dr. Edmund Hal­ley,” whom Haselden addressed in his preface:

                                

Demonstrating that map projection could be a controversial topic three centuries ago, Haselden made the debate both Manichean and personal in defending “the Mercator’s-Chart ... which has stood the Test of many Years, and is now generally receiv’d as the best Way of representing the Surface of the Terraqueous Globe, by all who know the Excellency thereof: [which] the Authors of this Globular Performance, like crafty Politicians, who know the Necessity of getting rid of a Formidible Enemy, before they can secure themselves, have represented not only as Puzling and Difficult, but False.” One author’s treachery was all the more vile for his having endorsed the Mercator map several years earlier: “I cannot but think it would have been much more for the Reputation of Mr. Henry Wilson [sic], the pretended Author of this Globular Chart, if he had continued to recommend (as I can shew under his own Hand, he not long since did) the Mercator’s as the only chart, and had not in so prevaricating a Manner endeavour’d to set both the one and the other in a false Light; for by so doing, he had acted the honester Part, and avoided the just Censure of the knowing World.”

To bolster his argument, Haselden described the use of the Mercator chart for fourteen typical navigation tasks. The only concession to his opponents’ “many groundless Objections” was an admission that accurately measuring and laying off distances with dividers could be troublesome. As modern textbooks on navigation demonstrate, estimating the length of a diagonal course on a Mercator chart is surprisingly simple if the course is no longer than 1,200 miles and does not extend into polar areas, where scale varies enormously. Merely extend the compass between the two end points, as shown in figure 6.1, and transfer the measurement to the scale of latitude graduated in degrees and minutes along the left or right edge of the chart. Distance is easily estimated because a minute of latitude covers roughly one nautical mile. But because north–south scale varies with latitude, it’s important to align the dividers vertically with the middle of the course. For a longer course plotted on a small-scale chart, it’s wise to divide the route into sections, estimate distance separately for each, and sum the results.

Atlantic (fig. 6.2, right), the gnomonic perspective distorts angles as well as area.

Navigation handbooks compare Mercator sailing, based on an exact representation of bearings and rhumb lines, with great-circle sailing, which affords a minimum-distance route across a spherical earth. Before radio beacons and electronic navigation simplified great-circle sailing, navigators typically determined a number of intermediate points along a great-circle route, transferred them to a Mercator chart, and sailed the course as a chain of constant-bearing segments. A gnomonic projection, on which great circles are straight lines and vice versa, simplifies the otherwise tedious mathematics of finding intermediate points along a great-circle route. In use as early as the sixth century BC, the gnomonic perspective involves lines of projection radiating from the center of the globe and a tangent plane, which may be positioned anywhere (fig. 6.2, left). Point of tangency is important because scale increases dramatically with distance from the map’s center, and a single projection cannot cover a full hemisphere. And as Tissot’s indicatrix demonstrates for a map centered in the mid-niques pioneered by eighteenth-century land surveyors. In the late eighteenth century, when the skills and needs of map users converged with the skills and needs of mapmakers, the Mercator map became the gold standard of marine cartography.

By the mid-nineteenth century, the Mercator projection was so well established that neither Matthew Fontaine Maury (1806–73) nor his biographers considered it worth mentioning. An American naval official hailed as the father of oceanography, Maury used the Mercator projection for maps in his seminal textbook The Physical Geography of the Sea, published in 1855, as well as for a set of navigation charts widely credited with making ocean sailing faster and safer. A strong interest in navigation technology and astronomy led to his appointment in 1842 as superintendent of the navy’s Depot of Charts and Instruments (later the Naval Observatory), where he discovered a collection of old ships’ logs, with daily records of wind and current directions. Curious about world patterns and seasonal effects, Maury summarized the data on “Track Charts” for the Atlantic, Indian, and Pacific oceans, published in early 1848.

Merchant seamen were reluctant to use the charts until a Captain Jackson, sailing out of Baltimore, followed Maury’s recommended route to Rio de Janeiro and cut seventeen days off a round trip that normally took fifty-five days. Word of Jackson’s voyage spread rapidly, and enthusiastic support among ship owners led to the regular publication of “Wind and Current Charts” in six separate series: Pilot Charts, Storm and Rain Charts, Thermal Charts, Track Charts, Trade-Wind Charts, and Whale Charts—all on a Mercator grid. Eager to make his maps more reliable, Maury struck a deal with merchant captains: Turn over your systematic notes on ocean currents, winds, barometric pressure, air and water temperature, and (of course) position, and I’ll give you a free set of our most recent charts. Many complied, and those who did not happily purchased new charts. (Naval captains, who had little choice, were equally eager.) Between 1848 and 1861, when Maury resigned to join the Confederate Navy, the Depot issued two hundred thousand Wind and Current Charts. The project also yielded insightful illustrations (fig. 6.3) for his influential text on oceanography.

Earlier in his career Maury interacted briefly with another pioneer of American hydrography, Ferdinand Hassler (1770–1843), the Swiss-born mathematician-geodesist hired in 1832 to reorganize the Survey of the Coast (later the U.S. Coast Survey). In 1839, Maury was the most junior lieutenant in the navy. Bored with his assignment, an examination of southern harbors, he wrote Hassler twice, asking to lead a triangulation party, but got nowhere. It’s unlikely they talked much when Maury came to Washington in 1842 as the navy’s chief hydrographer. Hassler (fig. 6.4) was a feisty fellow, focused on his work and notoriously difficult to get along with. He was not the least afraid of a Congress eager for results and worried about cost, and on one occasion he berated a delegation sent to inspect his shop: “You come to ’spect my vork, eh? ... You knows notting at all ’bout my vork. How can you ’spect my vork, ven you knows notting? Get out of here; you in my way. Congress be von big vool to send you to ’spect my vork. I tailed charts based on original surveys of shorelines and coastal waters. As the nation’s measurement guru and the author of a textbook on analytical trigonometry, Hassler resented congressional busybodies who thought he could save time and money by estimating longitude with a chronometer, like a navigator at sea. His experience in Switzerland, as a geodetic engineer, had taught him the importance of exact measurements and a carefully designed triangulation network. To overcome the dense vegetation of salt marshes and coastal thickets, his field parties used precise theodolites mounted on four-foot-high wooden platforms to measure angles between tall poles several miles away.

Equally important was a map projection that would minimize distortion, particularly the distortion of distance. All flat maps stretch or compress some distances—there is no other way to flatten the earth—but distortion is generally low near a standard line, where the globe touches or intersects the projection’s “developable surface” (plane, cone, or cylinder). Hassler was especially impressed with the tangent conic projection, which, by definition, touches the globe along a single standard parallel. A thin belt of low distortion straddles the standard parallel, usually positioned near the center of the mapped region. Why not extend this concept, he reasoned, with a map based on many belts of low distortion—better yet, an infinite number of belts, produced mathematically by an infinite number of cones tangent along an infinite number of standard parallels. His solution was the polyconic projection, sometimes called the American polyconic projection or Hassler’s polyconic projection.

If this notion seems farfetched, consider carefully the three cones in cross section on the left side of figure 6.5. Each cone defines a conic projection with its own band of low distortion. As shown in the right side of figure 6.5, the bands can be configured to divide the northern hemisphere into the three zones of relatively low distortion. Although the bands don’t fit together perfectly—noticeable gaps intervene— they align conveniently along a central meridian. Doubling the number of cones makes the belts narrower and the gaps thinner. Keep doubling, again and again, until microscopically thin gaps separate an indefinitely large number of infinitesimally narrow belts aligned along area. Because each chart had its own central meridian, toward which its other meridians converged ever so faintly, charts of adjoining areas immediately to the east or west would not line up. Mapmakers could overcome this difficulty by plotting a single dense grid for the new map and painstakingly transferring features, but navigators much preferred the Mercator chart’s standard worldwide grid, anchored at the equator so that adjoining sectional charts at the same scale aligned perfectly. Hassler’s polyconic projection was similarly awkward for small-scale sailing charts showing longer courses on a single map sheet: its straight lines were not rhumb lines, its angles were noticeably distorted, and its curvilinear grid thwarted the straightforward reading of latitude and longitude, a simple task with a pair of dividers and the graduated scales along the edges of the Mercator grid.

                                                                                                                                                         

Although historians attribute the polyconic projection to Ferdinand Hassler, its prominence in American cartography is largely the result of his successors, who not only insisted on a polyconic base for all coastal surveys but also published extensive tables with which other mapmakers could easily lay out a polyconic framework. In his 189-page plan for a systematic coastal survey, published in 1825 in the Transactions of the American Philosophical Society, Hassler vaguely alluded to the polyconic projection in the last paragraph: “This distribution of the projection, in an assemblage of sections of surfaces of successive cones, tangents [sic] to or cutting a regular succession of parallels, and upon regularly changing central meridians, appeared to me the only one applicable to the coast of the United States.” Few charts had been published at the time of Hassler’s death in 1843, from a fall and severe exposure while trying to save his instruments during a hailstorm. The Coast Survey’s early charts used a simple rectangular projection, no doubt approved by Hassler, and the ostensibly conic framework of charts published in 1844, under his successor, might well be based on tables for the somewhat similar “pseudo-conic” equal-area projection featured in a 1752 maritime atlas by French cartographer Rigobert Bonne (1727–95). Although the Swiss surveyor apparently conceived the polyconic projection around 1820, its widespread use awaited the Coast Survey’s publication of a detailed description in 1853 and projection tables in 1856.

Readily available projection tables partly explain the adoption of the polyconic projection by the U.S. Geological Survey, established in 1879. Faced with the enormous challenge of developing reliable base maps for a vast territory only the coastal fringes of which had been systematically surveyed and mapped, USGS topographers could not resist the momentum of more than a quarter-century of precise coastal mapping on a polyconic framework.

Although adequate for piloting harbors and coastal waterways, America’s polyconic nautical charts were an annoyance to mariners, who appreciated their accurate shorelines and soundings but preferred a coastal map more geometrically compatible with the chart they used at sea. In 1910, after years of lobbying by the navy, the renamed Coast and Geodetic Survey initiated a program of chart reconstruction. Even so, the Survey’s annual report for 1915 indicates that conversion was not equally urgent for all charts: “There is no practical difference except in high latitudes between the Mercator projection and the Polyconic projection, in so far as charts on a scale of 1:80,000 or larger are concerned, but the differences between the projections is appreciable for the smaller scales and is an objectionable feature of the old series of chart.” Five years later, when less than half the charts requiring reconstruction had been converted to a Mercator framework, a stronger sense of embarrassment reinforced the annual appeal for a bigger budget: “Some of our charts ... are so antiquated as to be of questionable value. They were constructed many years ago on projections which have long since been discredited for navigational use ... they are on the polyconic instead of the Mercator projection.” By 1930 conversion was essentially complete, except for Great Lakes charts, some of which have yet to be converted. Paradoxically, the Geological Survey did not abandon the polyconic projec­tion until the early 1950s, and coastal hydrographers at NOAA (the National Oceanic and Atmospheric Administration, which was formed in 1970 by combining the Coast and Geodetic Survey, the Weather Bureau, the Bureau of Commercial Fisheries, and several related agencies) continued to plot raw survey data on polyconic maps until several years ago, when digital measurement technology made this intermediate step unnecessary by delivering latitude-longitude coordi­nates readily converted to a Mercator framework (or to any other projection, for that matter).
Although the polyconic map was discredited as a navigational tool, cartographic officials at the Coast and Geodetic Survey remained committed to the conic perspective, which is well suited to a mid-latitude region with a pronounced east–west elongation like the conterminous United States. In 1920 they developed a single-sheet national outline map at a scale of 1:5,000,000 using the Lambert conformal projection. With standard parallels at 33° and 45°N, their new base map combined a minimal distortion of distance with a true depiction of angles and infinitesimally small shapes—ideal properties for the national series of aeronautical charts that the Coast and Geodetic Survey initiated in 1930 and completed in 1937. Unlike the obsolete polyconic nautical charts, the ninety-two “sectional airway maps” (fig. 6.7) abutted neatly along their east and west margins. Scale was not constant—it never is on a flat map—but commercial pilots considered these deviations far less troublesome than the corresponding distance variations on a Mercator projection. At a scale of 1:500,000, the sectional maps covered sufficient territory for convenient flight planning and were sufficiently detailed for “contact piloting” based on major roads, rivers, and other visible landmarks. Pilots could cut them up and assemble their own “strip charts,” a standard format for aeronautical charts in the 1920s.

Selection of Lambert’s conformal conic projection for the sectional airway maps fueled a debate over the relative merits of the Lambert and Mercator projections for aviation cartography. Captain George Bryan, head of the navy’s Hydrographic Office during World War II, was an unflinching supporter of the Mercator framework, which the navy had consistently favored for charts supporting navigation, whether on water or in the air. Distance measurement was a red herring, he argued, because experts know how to measure distances on a Mercator map, and amateurs can quickly master the graduated bar scale printed on many Mercator charts. Although Lambert and Mercator frameworks are equally efficient for contact piloting, the latter is superior for reading angles, plotting positions, planning courses, and referencing heavenly bodies as landmarks in celestial navigation.
According to Bryan, the Lambert framework’s single apparent advantage involved radio bearings, which follow great circles, not rhumb lines. On large-scale maps neither projection needs a correction because straight lines approximate great circles. Medium-scale Lambert projections are also immune because at scales of around 1: 1,000,000 the difference between a straight line and a great circle is barely noticeable. But small-scale Lambert charts require a cumbersome correction, much more complex than the corresponding adjustment for a small- or medium-scale Mercator chart. Furthermore, the Lambert projection’s medium-scale advantage is largely spurious because in radio navigation the pilot is following a signal, not a map. Better to use one map—a Mercator map—for plotting all navigation data.
Bryan cited endorsements of the Mercator by the Royal Air Force, which considered it the only suitable projection for aeronautical charts, and the International Aeronautical Conference, which in 1919 had approved it as the standard projection for route maps and general aviation maps. Neither recommendation satisfied the Coast and Geodetic Survey and the air force, which collaborated on the 1: 1,000,000- scale World Aeronautical Chart (WAC), published on a Lambert conformal conic framework with two standard parallels strategically positioned for low distortion across each sheet. The air force’s concern for radio navigation eclipsed the navy’s traditional reverence for the Mercator map.

Buy an aeronautical chart these days, and you’ll most likely discover its projection is a locally secant Lambert conformal conic, which readily satisfies the International Civil Aviation Organization’s flexible requirement for “a conformal projection on which a straight line approximates a great circle.” But for areas north of 80° N or south of 80° S, the projection will probably be the polar stereographic, an appropriate substitute for both a locally secant Lambert chart, which is highly similar, and a Mercator chart, which is virtually useless near the poles. A polar gnomonic projection might seem the logical choice, but charting experts consider the polar stereographic’s correct angles more useful than the gnomonic’s perfectly straight great circles.

Although most cartographic genres have confronted radical technological change, few have had to adjust as rapidly and frequently as aeronautical charting. Early in the last century, when slow, low-altitude flying was the norm, pilots were content with any topographic map showing features readily visible from the air. Increased airspeeds, higher flying altitudes, and better navigation instruments called for more specialized charts focusing on airports, key landmarks, radio beacons, vertical obstructions, and restricted areas. Jet aircraft able to leap several thousand miles in a single flight demanded charts covering greater distances at smaller scales. Automatic piloting, instrument landing, LORAN (Long Range Navigation), satellite tracking, helicopters, ultralights, gliders, and a host of FAA (Federal Aviation Administration) restrictions added to the complexity and altered the appearance of aeronautical charts. Keeping the charts up to date became far more important than debating the relative merits of simi­larly suitable conformal projections.

Although weather maps are even more complex and varied than aeronautical charts, meteorologists resolved their search for appropriate map projections more quickly and decisively, through a single international group, the International Meteorological Organization’s Commission on Map Projections, which met in Salzburg in 1937. Because meteorologists treat the atmosphere as a phenomenon to be studied, not an obstacle to be traversed, rhumb lines are irrelevant. Far more pertinent are lines describing wind flow and differences in pressure and temperature. Distance is important but angles are more so, especially the angles between isobars and wind arrows and the angles formed where isobars and isotherms intersect meridians and parallels. Accurate depiction of relative direction calls for conformality, which makes the Mercator projection appropriate for tropical areas, close to the tangent parallel at the equator. Similarly, the commission endorsed a conformal polar map based on the polar stereographic projection secant at 60' and a mid-latitude map based on the Lambert conformal conic projection secant at 30' and 60'. For a whole-world map, the commission turned to the Mercator projection, with the caveat that a pair of polar stereographic projections, one for each hemisphere, might be a suitable alternative.

 

Standardization is important because national weather organizations reap enormous benefits by sharing data with one another, but as the Salzburg report noted, the requirements shouldn’t be rigid. For example, researchers exploring upper-level wind velocity might need a polar stereographic map extending well below the Arctic Circle (fig. 6.8). Recognizing the value of flexibility, the commission also endorsed a set of equal-area projections for climatological data, to help viewers compare relative sizes of climatic regions and relate them conveniently to existing equal-area maps of vegetation, soils, and agriculture. The commissioners called for cylindrical, conic, and polar equal-area projections with standard lines identical to their conformal counterparts, but stopped short of endorsing a specific whole-world equal-area projection.

The U.S. Weather Bureau, which had supplied the commission’s president, responded promptly, but with no apparent fanfare, by replacing its polyconic map of the United States with a Lambert conformal conic framework. For small-scale newspaper weather charts and similar publications, it’s unlikely anyone outside the bureau noticed the change. Visual differences between conic projections offering low distortion can be subtle.                                                                       

 

 

 

 

 

 

 

 

 

 

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