1 Submitted Title: Rewriting the History of Mapping Submitted Abstract ...
Submitted Title: Rewriting the History of Mapping Submitted Abstract: The paper will demonstrate how ArcView can be used backwards. While in most cases, you know the projection that a map is using, I will show how you can use ArcMap 8.3 to find out what projection the map maker was using. The availability of the Mercator projection this past fall has made inquires into the early history of cartography and the pre-history of Mercator's projection possible. Three tools in ArcMap 8.3 have enormous potential for the history of cartography: the georeferencing function, the projection changing function, and the Geostatistical Analyst extension. Together these tools have the potential to change the way historians of cartography think about maps. Historians have had a limited number of tools—most often comparing individual locations on historical and modern maps. Questions of the scale developed on historical maps, the type of projection used, all have drawn the interest of historians of cartography, but they have lacked means to resolve any of these issues successfully. Using ArcMap for the first time we can address the question of scale on an historical map—not simply for the entire map but for different segments of a map. The projection changing function of ArcMap allows us to precisely assess the long puzzling question of the projection or lack thereof. Finally GeoStatistical Analyst provides more precise tools than have previously been available to illustrate the sources of distortion in historical maps For this presentation we are interested in re-examining the history of nautical charts leading up to the development of Mercator’s projection in 1569. The tradition of sea charts began in the Mediterranean at the end of the thirteenth century, and most sea charts over the next three hundred years redrew the Mediterranean in varying degrees of detail. But beginning in 1441, however, map makers had to draw brand new coastlines— those of West Africa, for the Portuguese pilots who were the first to sail through the bottom third of the North Atlantic Ocean. What principles did they use in constructing their maps? What scale did they use? Were they experimenting with projections? Students of maps have raised these questions for generations, without being able to reach any conclusions. The mapmakers have left us only their drawings; and hence we must look to the drawings themselves in order to understand the techniques of drawing nautical charts. Because mapmakers had no prior source of information on the west coast of Africa, we know they had to employ their existing techniques to a brand-new area. We have selected three different maps from the period before 1569 to analyze several dimensions of the process of creating new sea charts prior to Mercator. All three maps cover the portions of the African coast uncovered by Portugal’s Atlantic voyages. The second and third maps were drawn by Portuguese cartographers, those with the most detailed and direct knowledge of the African coastline and that of Brazil. Therefore the series of maps—each constructed approximately thirty years apart—offers a preliminary glimpse of how changes in nautical charts were occurring as previously uncharted coasts of the world became identified. The first map by Gracioso Benincasa, drawn in 1468,
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extends from Cap Blanc in the north (in what is now Mauritania) through the present day nations of Senegal, The Gambia, Guinea Bissau, Guinea, and ending on the islands named for the turtles that once resided in large numbers off the coast of Sierra Leone. The second map by Jorge de Aguiar in 1492 extends beyond the region covered in the Benincasa map through the Gulf of Guinea, and extending northward along Europe’s western coast as far north as the Netherlands and the British Isles. A final map by Gaspar Viegas in 1527 covers this area plus seacoasts on both sides of the Atlantic. The first tool we have found useful is ArcMap’s Georeferencing tool. By importing a high-resolution digital image of the 1468 Benincasa map, we are able to align the historical map with the current map using a series of locations. Because many of the points along the West African coastline retain the names by which they appear on the fifteenth-century map, the task of identifying the points was relatively easy. Out of 41 named positions on the earliest map, we were able to identify 36 contemporary positions. It is at this point that the georeferencing tool begins to make its usefulness known, allowing us to go beyond the comparison of names and locations. First, we georeferenced the historical map using two known points. (The larger number of identifiable locations allowed us innumerable possibilities for selection of which we will provide a few.) The example, shown in figure 1, shows the sharp distortions that appear in the historical map—using a variety of different control points. Using Cape Blanc and the Turtle Islands (Figure 1A), the coastline from Cape Verde and Dakar southward are immensely wrong. Taking two points in the northern part of the map, Cap Blanc and the Gambia River (Figure 1B) solves the problem of the misplaced Dakar, but places the endpoint of the map, the Turtle Islands hundreds of miles to the west of their actual location. The same phenomenon occurs in reverse when we chose control points to the south (Figure 2C and 2D). The southern part lines up correctly but the coast of Mauritania is again too far out into the Atlantic Ocean. The control points provide us concrete evidence on the map’s distortion. But how then can we use ArcMap to analyze the differences? The most useful tool in this respect is the Geostatistical Analyst extension, which allows us to spatially explore, analyze, and display anomalies in the map. Here we will provide an example of how the Geostatistical Analyst improves our ability to visualize and understand the sources of distortion in historical maps. After trying a number of different techniques to see what created the distortion between Benincasa’s map and the contemporary map, we were eventually able to establish that irregularities of scale accounted for the greatest amount of distortion. Taking 28 of the points along the coast, we were able to establish that the scale ranged from a low of 1,724 in southern Mauritania to highs around 3,000,000 at the broad open deltas of the Gambia and Rio Curubal. Figure 3 shows the variation in scale in a bar graph, while Figure 4 shows the distortion using Geostatistical Analyst. Here the immense difference in scale at the two river deltas appears as the red peaks, while the smaller variations in scale appear in wavy blue, green, and yellow shapes. Thus Benincasa’s map shows no consistency in scale, as the Geostatistical Analyst demonstrates. Using the Geostatistical Analyst as a guide, we grouped the map into first six and then seven sections that had the same scale. Going from north to south along the coast, the first and the third section had the same scale, while the second, fourth, and fifth section had a similar scale (between 55 and 60 percent of the first and third sections). The
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final two sections of the map had wildly different scales. The sixth section was nearly half again as large, while the final section was nearly three times smaller than the first two. While inequalities of scale accounted for one source of the distortion in Benincasa's map, we were interested in discovering whether other sources of distortion might remain. To do so, we needed to eliminate the differences in scale among the separate sections of the map. We then electronically enlarged or reduced (depending on the error) the erroneously scaled sections so that they fit along a single scaled coast of Africa. We then attempted to look for the next source of distortion by aligning these segments with the coastline of Africa. To show how this process worked, we provide an example from the northern part of the Benincasa map. Examining the region from Cape Blanc to Cape Verde, we see that about halfway down this stretch of coast, the line on the original map veers out into the Atlantic. And at this point the mouth of the Guinea River on the Benincasa map lies at a great distance from the actual location of the mouth of the river. Figure 5. We then electronically cut the map where it diverged from the current coastline, and using AutoCad rotated that section of the map until it perfectly aligned with the coastline. After rotating the map that first segment lines up perfectly with the African coast, and the mouth of the Guinea River on the Benincasa map is exactly where it should be. Following this same process for each of the succeeding sections of the map, we were able to identify seven differently rotated sections of the map. As it turned out each of the separate sections of the map were all rotated by the same measure--12.25 degrees. The uniformity in the angle of distortion, however, was not matched by parallel uniformity in the direction of the rotation. The resulting map has three different segments that are rotated 12.25 degrees to the northeast; two segments rotated 12.25 degrees to the northwest, and two segments that are exactly aligned along the north south axis. Figure 6. Because the angle of rotation proved identical, it suggests that the error had a single source. The angle is close to smallest angle of distortion that a compass can measure—11.25 degrees.) Therefore the compass readings seemed to be responsible for the second major source of distortion in the map. Once changing by the smallest measurable compass angle the Benincasa map aligned correctly with the coast of Africa. However, the question of what may have caused the compass errors still remains. Several earlier studies have attempted to attribute large angles of rotation on portulan charts to geomagnetic influences. However such studies have been hampered by their need to rely on gross characteristics of the map—and have been unable to analyze the distortion on such a detailed local level. Here we show no single pattern of geomagnetic distortion, but rather a random, seemingly arbitrary pattern of shifts over relatively short distances. Furthermore the amount of the shift is greater than that which seems to have been the pattern for this region of the Atlantic coast. The degree of inclination for this region of Africa appears to have ranged historically between 8 and 10 degrees, less than the amount of distortion on the different sections of the map. Since the Benincasa map was a compilation of information from multiple voyages down the coast of Africa, the source of error may have been incorrectly calibrated compasses. A single voyage reporting back with a slightly incorrect compass reading would have provided consistently distorted information for an entire segment of the map.
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The skill of the pilots in reading compasses may also have varied during different voyages. A pilot who consistently read the compass wrong would also have reported back consistently erroneous information for the segment of the coast he was exploring. Human or mechanical error seems more likely to have caused the pattern of variation than underlying geophysical conditions. The final major advance that ArcMap opens up to historians of cartography is the long-standing puzzle concerning the existence of projections on nautical charts. Historians have argued for and against the existence of such projections, but have lacked a tool to settle the question more definitively. At this point ArcMap’s ability to change projections on the fly (as well as the central meridians and parallels of a projection) becomes particularly useful. The rapid projection change feature allows us to take a map that has been georeferenced using two control points—and test a variety of different projections in order to find out which, if any of the projections best fits the data on the map. In that way the question of whether a projection fits the data or not, becomes transformed into the more manageable question—which (if any) of the projections fit the historical map—and how well do they fit the projection. Perhaps the most important step in testing the projection is preserving the integrity of the original map; keeping it free of distortion, because understanding the sources of the distortion in early nautical charts remains the goal of the project. Hence we had to take particular care in preventing the electronic distortion of the maps. To safeguard against such a possibility we took two separate steps. First we limited georeferencing points to two. Introducing a third or fourth control point often stretched the map electronically, and not providing an accurate picture of the map, inadvertently stretching the original map (a phenomenon often called “rubber sheeting.”) Second we relied upon the measure of angular distortion. Unlike earlier techniques, angular distortion does not require making any additional assumptions. Other techniques for examining distortion have required assuming latitude, longitude or a grid in order to gauge the accuracy of points. Since we have no evidence that map makers actually utilized latitude and longitude coordinates (let alone grids) evaluating these early maps in this fashion introduces facts that are not yet in evidence in order to make conclusions about the nature of the distortion in the maps. Angular distortion measures the relationship between the points without needing to introduce anachronistic assumptions. We examine the process of angular distortion abstractly in Figure 7. If A and B are control points (figure 7A) when we georeference the control points we wind up with an angle of distortion. That angle is the difference between the line AB and A1B1 (figure 7B). If we were to add additional control points (C, D) then the shape of the map becomes distorted, turning the circle into an ellipse (Figure 7C). While angular distortion visually establishes the degree of inexactitude in earlier maps, it does not establish the sources of this distortion. For this we have to turn to other ArcMap tools. After examining nearly the entire repertoire of ArcMap’s projections, we concluded that no projection fit Grazioso Benincasa’s map of 1468. However we decided to take the two other nautical charts from the period prior to Mercator, to see if projections became used as greater areas of the earth’s coastline became mapped. To examine the possibility of projections in larger scale nautical maps we
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examined the two later Portuguese maps, Jorge de Aguiar’s 1492 map of the Mediterranean and African coast through the Gulf of Guinea and Gaspar Viegas’ chart of the Portuguese Atlantic 35 years later. Both predate Mercator’s famous drawing by 42 and 77 years respectively. While neither large map used Mercator’s projection, less than a quarter of a century after Benincasa’s awkwardly composed map, projections do seem to be used for large-scale nautical charts of not only the Atlantic coast of Africa, but the northern European coast as well. Analyzing the Portuguese cartographer Jorge de Aguiar’s 1492 chart of Europe, the Mediterranean, and most of Africa, we first introduced measures of angular distortion in a grid across the map. We then tried a variety of different projections. The first figure shows one of the oldest projections—the gnomic. The lack of fit between the 1492 drawing and the projection is apparent in the vast difference between the projected and the sketched location of the West African coast. At roughly the latitude of the Madeira Islands the projection would have the map extending farther to the west. Figure 8 We then tried the Mercator projection itself. While fitting better than the gnomic projection, serious discrepancies appeared on the northern edge of the map. The Brittany coast and the English channel aligned poorly with the projection, appearing far to the south of where they should have been had a Mercator projection been used. Since the distortion in the Mercator projection appears towards the northern edge of the map, we tried a different version of the Mercator. The Mercator projection is based upon a cylinder wrapped around the equator, we decided to shift the orientation of the cylinder from the east-west equatorial direction to a north south direction. This shift in orientation is the modern transverse-Mercator. However, the resulting overlay was equally unsatisfactory. England and the Brittany Coast appeared at nearly the latitude we would have expected, but the African coast no longer fits with the projection. Figure 9 Finally we turned to another of the older projections, the equidistant conic. However, here we encountered an unexpected surprise. As we changed the standard parallels for the equidistant conic projection to improve the fit between the map and the projection we eventually came to the point where the two parallels were identically spaced north and south of the equator. When the parallels are spaced thus, then the projection is cylindrical or equirectangular. This projection seemed to fit best of all. The English Channel and the Brittany coast line up fairly well, and the longitudinal dimension of the Black Sea appears almost exact. The Mediterranean fits exceedingly well, with only a slight westward swing of the southern Italian peninsula. The coast of Africa also lines up fairly well with the projection, the only difference being a slight northward compression of the coast south of Cap Blanc. Figure 10. While the visual evidence of the fit between the projections and the coastlines appears in the overlays just shown, a second legitimate question is how to quantify those differences. Here again the potential for mathematical analysis made possible by ArcMap, makes this process relatively easy. We can quantify the coordinate system by measuring the distance between the actual position of a point in the present day and its position on an historical map using the similarity transformation to find the root mean square error. (The similarity transformation neither rescales the axes nor does it introduce any skew.) In the case of the Aguiar map we took a sample of 637 locations distributed along the coasts, and calculated the root mean square error for the cylindrical projection as 72 kilometres. For a map drawn in 1492, this error rate seems excellent.
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To pinpoint the precise location of the sources of error, we created a three dimensional image of the error sources in the cylindrical projection. The illustration of the error rate distribution shows the regions of greatest error to lay at the north and southern limits of the Atlantic coast. The Mediterranean and Black Sea areas on the map align extremely well with the projection, and the Iberian coasts (unsurprisingly) align nearly perfectly. Figure 11. But Aguiar’s map was created just before knowledge of the world was about to make an enormous leap. On the way to Asia, Columbus accidentally encountered the Caribbean Islands. Spain and Portugal then signed an agreement dividing the unexplored zones of the world along a north south axis in the Atlantic Ocean. As Spanish explorers founded in the Caribbean, Portuguese navigators set off in search of their Atlantic possessions. Ten years later, they had defined the northeastern coast of Canada, and a major segment of the coast of Brazil. While the original Portuguese maps of their possessions in the Atlantic disappeared, we have an authentic Portuguese example that Gaspar Viegas created in 1527 showing the African coastline along with the Portuguese Atlantic possessions. In analyzing this map, we decided to show how the introduction of a third control point creates angular distortion in the projection. First we tried the conic projection, and the angular distortion appears in the compass roses—the roses appear unmistakeably flattened. Figure 12. An unlikely projection, but one useful for demonstration purposes is the Robinson projection also with three control points. Rather than an east-west distortion, this projection causes a north south distortion. In the next illustration we see slightly different distortions. Figure 13. The Mercator with three points also distorts the map in a north south direction, as does the cylindrical equidistant. Finally we employ the transverse Mercator first with three and then with two points. Figure 14. While the three point transverse Mercator produces a slight angular distortion in the north-south direction, the transverse Mercator does not. And while the two point transverse Mercator fits the entire West African coast extremely well. The shape of the Brazilian coast follows that of the projection, although the entire continent lies several degrees south of where it belongs. Why might a transverse Mercator be a reasonable choice? Since Portuguese ships travelled the Atlantic in those years principally between the western coast of Africa and eastern coast of Brazil, on their way to India, centering a projection on the Atlantic Ocean makes a great deal of sense. Having the sphere on which the projection was centered lie tangent to the central area of Portuguese navigation also seems relevant. Creating such a projection would accurately show the direction for ships to travel between the Portuguese possessions on either side of the Atlantic on their way to India. And as we all know today, the Mercator projection remains the best method for creating nautical charts. Since no Dutch or Low Countries ships were plying the Atlantic at the time Mercator produced the nautical projection that bears his name, his information had to come from Spanish or Portuguese sources. Perhaps along with the information came the information on how to construct nautical projections. But that remains for another time. This series of maps shows a previously unsuspected development in the history of projections—their apparent absence of projections in the early years of exploration of the African coast, and the experimentation first with cylindrical projections around 1492, and
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finally with what may have been Mercator projections by 1527. Using these three tools from ArcMap--georeferencing, changing projections, and Geostatistical Analyst we have gained wealth of information about the ways in which nautical charts were constructed in the years before the first official Mercator projection appeared—and a better understanding of the challenges map-makers faced as they began the daunting task of charting regions never before seen from ships. Using these most modern of tools, the maps reveal information about their construction that mere visual inspection--even with a microscope fails to reveal. While we may never learn how the earliest map-makers worked, we should be able to pinpoint when cartographers learned to create uniform scales for large coastlines, as well as when and how they first began to use projections on nautical charts. All of these contributions will be made possible by using the tools available in ArcMap and the Geospatial Analyst.
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Acknowlegements: Rice University GIS/Data Center (GDC) Think Tank Fellows: Eva Garza, Brendan Mulcahy and Joe Kellner. Layout by Joe Kellner. Financial support from Kamran Khan, Rice University. Maps: Benincasa, 1468 – British Library. Jorge de Aguiar, 1492 – Beineke Library, Yale University.
Authors: Patricia Seed, Department of History, Rice University, P.O. Box 1892, Houston, TX 77251, (713) 348-2198, [email protected] German Díaz, GIS Specialist, Fondren Library, P.O. Box 1892, Houston, TX 77251, (713) 348-2595, [email protected],
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extends from Cap Blanc in the north (in what is now Mauritania) through the present day nations of Senegal, The Gambia, Guinea Bissau, Guinea, and ending on the islands named for the turtles that once resided in large numbers off the coast of Sierra Leone. The second map by Jorge de Aguiar in 1492 extends beyond the region covered in the Benincasa map through the Gulf of Guinea, and extending northward along Europe’s western coast as far north as the Netherlands and the British Isles. A final map by Gaspar Viegas in 1527 covers this area plus seacoasts on both sides of the Atlantic. The first tool we have found useful is ArcMap’s Georeferencing tool. By importing a high-resolution digital image of the 1468 Benincasa map, we are able to align the historical map with the current map using a series of locations. Because many of the points along the West African coastline retain the names by which they appear on the fifteenth-century map, the task of identifying the points was relatively easy. Out of 41 named positions on the earliest map, we were able to identify 36 contemporary positions. It is at this point that the georeferencing tool begins to make its usefulness known, allowing us to go beyond the comparison of names and locations. First, we georeferenced the historical map using two known points. (The larger number of identifiable locations allowed us innumerable possibilities for selection of which we will provide a few.) The example, shown in figure 1, shows the sharp distortions that appear in the historical map—using a variety of different control points. Using Cape Blanc and the Turtle Islands (Figure 1A), the coastline from Cape Verde and Dakar southward are immensely wrong. Taking two points in the northern part of the map, Cap Blanc and the Gambia River (Figure 1B) solves the problem of the misplaced Dakar, but places the endpoint of the map, the Turtle Islands hundreds of miles to the west of their actual location. The same phenomenon occurs in reverse when we chose control points to the south (Figure 2C and 2D). The southern part lines up correctly but the coast of Mauritania is again too far out into the Atlantic Ocean. The control points provide us concrete evidence on the map’s distortion. But how then can we use ArcMap to analyze the differences? The most useful tool in this respect is the Geostatistical Analyst extension, which allows us to spatially explore, analyze, and display anomalies in the map. Here we will provide an example of how the Geostatistical Analyst improves our ability to visualize and understand the sources of distortion in historical maps. After trying a number of different techniques to see what created the distortion between Benincasa’s map and the contemporary map, we were eventually able to establish that irregularities of scale accounted for the greatest amount of distortion. Taking 28 of the points along the coast, we were able to establish that the scale ranged from a low of 1,724 in southern Mauritania to highs around 3,000,000 at the broad open deltas of the Gambia and Rio Curubal. Figure 3 shows the variation in scale in a bar graph, while Figure 4 shows the distortion using Geostatistical Analyst. Here the immense difference in scale at the two river deltas appears as the red peaks, while the smaller variations in scale appear in wavy blue, green, and yellow shapes. Thus Benincasa’s map shows no consistency in scale, as the Geostatistical Analyst demonstrates. Using the Geostatistical Analyst as a guide, we grouped the map into first six and then seven sections that had the same scale. Going from north to south along the coast, the first and the third section had the same scale, while the second, fourth, and fifth section had a similar scale (between 55 and 60 percent of the first and third sections). The
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final two sections of the map had wildly different scales. The sixth section was nearly half again as large, while the final section was nearly three times smaller than the first two. While inequalities of scale accounted for one source of the distortion in Benincasa's map, we were interested in discovering whether other sources of distortion might remain. To do so, we needed to eliminate the differences in scale among the separate sections of the map. We then electronically enlarged or reduced (depending on the error) the erroneously scaled sections so that they fit along a single scaled coast of Africa. We then attempted to look for the next source of distortion by aligning these segments with the coastline of Africa. To show how this process worked, we provide an example from the northern part of the Benincasa map. Examining the region from Cape Blanc to Cape Verde, we see that about halfway down this stretch of coast, the line on the original map veers out into the Atlantic. And at this point the mouth of the Guinea River on the Benincasa map lies at a great distance from the actual location of the mouth of the river. Figure 5. We then electronically cut the map where it diverged from the current coastline, and using AutoCad rotated that section of the map until it perfectly aligned with the coastline. After rotating the map that first segment lines up perfectly with the African coast, and the mouth of the Guinea River on the Benincasa map is exactly where it should be. Following this same process for each of the succeeding sections of the map, we were able to identify seven differently rotated sections of the map. As it turned out each of the separate sections of the map were all rotated by the same measure--12.25 degrees. The uniformity in the angle of distortion, however, was not matched by parallel uniformity in the direction of the rotation. The resulting map has three different segments that are rotated 12.25 degrees to the northeast; two segments rotated 12.25 degrees to the northwest, and two segments that are exactly aligned along the north south axis. Figure 6. Because the angle of rotation proved identical, it suggests that the error had a single source. The angle is close to smallest angle of distortion that a compass can measure—11.25 degrees.) Therefore the compass readings seemed to be responsible for the second major source of distortion in the map. Once changing by the smallest measurable compass angle the Benincasa map aligned correctly with the coast of Africa. However, the question of what may have caused the compass errors still remains. Several earlier studies have attempted to attribute large angles of rotation on portulan charts to geomagnetic influences. However such studies have been hampered by their need to rely on gross characteristics of the map—and have been unable to analyze the distortion on such a detailed local level. Here we show no single pattern of geomagnetic distortion, but rather a random, seemingly arbitrary pattern of shifts over relatively short distances. Furthermore the amount of the shift is greater than that which seems to have been the pattern for this region of the Atlantic coast. The degree of inclination for this region of Africa appears to have ranged historically between 8 and 10 degrees, less than the amount of distortion on the different sections of the map. Since the Benincasa map was a compilation of information from multiple voyages down the coast of Africa, the source of error may have been incorrectly calibrated compasses. A single voyage reporting back with a slightly incorrect compass reading would have provided consistently distorted information for an entire segment of the map.
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The skill of the pilots in reading compasses may also have varied during different voyages. A pilot who consistently read the compass wrong would also have reported back consistently erroneous information for the segment of the coast he was exploring. Human or mechanical error seems more likely to have caused the pattern of variation than underlying geophysical conditions. The final major advance that ArcMap opens up to historians of cartography is the long-standing puzzle concerning the existence of projections on nautical charts. Historians have argued for and against the existence of such projections, but have lacked a tool to settle the question more definitively. At this point ArcMap’s ability to change projections on the fly (as well as the central meridians and parallels of a projection) becomes particularly useful. The rapid projection change feature allows us to take a map that has been georeferenced using two control points—and test a variety of different projections in order to find out which, if any of the projections best fits the data on the map. In that way the question of whether a projection fits the data or not, becomes transformed into the more manageable question—which (if any) of the projections fit the historical map—and how well do they fit the projection. Perhaps the most important step in testing the projection is preserving the integrity of the original map; keeping it free of distortion, because understanding the sources of the distortion in early nautical charts remains the goal of the project. Hence we had to take particular care in preventing the electronic distortion of the maps. To safeguard against such a possibility we took two separate steps. First we limited georeferencing points to two. Introducing a third or fourth control point often stretched the map electronically, and not providing an accurate picture of the map, inadvertently stretching the original map (a phenomenon often called “rubber sheeting.”) Second we relied upon the measure of angular distortion. Unlike earlier techniques, angular distortion does not require making any additional assumptions. Other techniques for examining distortion have required assuming latitude, longitude or a grid in order to gauge the accuracy of points. Since we have no evidence that map makers actually utilized latitude and longitude coordinates (let alone grids) evaluating these early maps in this fashion introduces facts that are not yet in evidence in order to make conclusions about the nature of the distortion in the maps. Angular distortion measures the relationship between the points without needing to introduce anachronistic assumptions. We examine the process of angular distortion abstractly in Figure 7. If A and B are control points (figure 7A) when we georeference the control points we wind up with an angle of distortion. That angle is the difference between the line AB and A1B1 (figure 7B). If we were to add additional control points (C, D) then the shape of the map becomes distorted, turning the circle into an ellipse (Figure 7C). While angular distortion visually establishes the degree of inexactitude in earlier maps, it does not establish the sources of this distortion. For this we have to turn to other ArcMap tools. After examining nearly the entire repertoire of ArcMap’s projections, we concluded that no projection fit Grazioso Benincasa’s map of 1468. However we decided to take the two other nautical charts from the period prior to Mercator, to see if projections became used as greater areas of the earth’s coastline became mapped. To examine the possibility of projections in larger scale nautical maps we
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examined the two later Portuguese maps, Jorge de Aguiar’s 1492 map of the Mediterranean and African coast through the Gulf of Guinea and Gaspar Viegas’ chart of the Portuguese Atlantic 35 years later. Both predate Mercator’s famous drawing by 42 and 77 years respectively. While neither large map used Mercator’s projection, less than a quarter of a century after Benincasa’s awkwardly composed map, projections do seem to be used for large-scale nautical charts of not only the Atlantic coast of Africa, but the northern European coast as well. Analyzing the Portuguese cartographer Jorge de Aguiar’s 1492 chart of Europe, the Mediterranean, and most of Africa, we first introduced measures of angular distortion in a grid across the map. We then tried a variety of different projections. The first figure shows one of the oldest projections—the gnomic. The lack of fit between the 1492 drawing and the projection is apparent in the vast difference between the projected and the sketched location of the West African coast. At roughly the latitude of the Madeira Islands the projection would have the map extending farther to the west. Figure 8 We then tried the Mercator projection itself. While fitting better than the gnomic projection, serious discrepancies appeared on the northern edge of the map. The Brittany coast and the English channel aligned poorly with the projection, appearing far to the south of where they should have been had a Mercator projection been used. Since the distortion in the Mercator projection appears towards the northern edge of the map, we tried a different version of the Mercator. The Mercator projection is based upon a cylinder wrapped around the equator, we decided to shift the orientation of the cylinder from the east-west equatorial direction to a north south direction. This shift in orientation is the modern transverse-Mercator. However, the resulting overlay was equally unsatisfactory. England and the Brittany Coast appeared at nearly the latitude we would have expected, but the African coast no longer fits with the projection. Figure 9 Finally we turned to another of the older projections, the equidistant conic. However, here we encountered an unexpected surprise. As we changed the standard parallels for the equidistant conic projection to improve the fit between the map and the projection we eventually came to the point where the two parallels were identically spaced north and south of the equator. When the parallels are spaced thus, then the projection is cylindrical or equirectangular. This projection seemed to fit best of all. The English Channel and the Brittany coast line up fairly well, and the longitudinal dimension of the Black Sea appears almost exact. The Mediterranean fits exceedingly well, with only a slight westward swing of the southern Italian peninsula. The coast of Africa also lines up fairly well with the projection, the only difference being a slight northward compression of the coast south of Cap Blanc. Figure 10. While the visual evidence of the fit between the projections and the coastlines appears in the overlays just shown, a second legitimate question is how to quantify those differences. Here again the potential for mathematical analysis made possible by ArcMap, makes this process relatively easy. We can quantify the coordinate system by measuring the distance between the actual position of a point in the present day and its position on an historical map using the similarity transformation to find the root mean square error. (The similarity transformation neither rescales the axes nor does it introduce any skew.) In the case of the Aguiar map we took a sample of 637 locations distributed along the coasts, and calculated the root mean square error for the cylindrical projection as 72 kilometres. For a map drawn in 1492, this error rate seems excellent.
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To pinpoint the precise location of the sources of error, we created a three dimensional image of the error sources in the cylindrical projection. The illustration of the error rate distribution shows the regions of greatest error to lay at the north and southern limits of the Atlantic coast. The Mediterranean and Black Sea areas on the map align extremely well with the projection, and the Iberian coasts (unsurprisingly) align nearly perfectly. Figure 11. But Aguiar’s map was created just before knowledge of the world was about to make an enormous leap. On the way to Asia, Columbus accidentally encountered the Caribbean Islands. Spain and Portugal then signed an agreement dividing the unexplored zones of the world along a north south axis in the Atlantic Ocean. As Spanish explorers founded in the Caribbean, Portuguese navigators set off in search of their Atlantic possessions. Ten years later, they had defined the northeastern coast of Canada, and a major segment of the coast of Brazil. While the original Portuguese maps of their possessions in the Atlantic disappeared, we have an authentic Portuguese example that Gaspar Viegas created in 1527 showing the African coastline along with the Portuguese Atlantic possessions. In analyzing this map, we decided to show how the introduction of a third control point creates angular distortion in the projection. First we tried the conic projection, and the angular distortion appears in the compass roses—the roses appear unmistakeably flattened. Figure 12. An unlikely projection, but one useful for demonstration purposes is the Robinson projection also with three control points. Rather than an east-west distortion, this projection causes a north south distortion. In the next illustration we see slightly different distortions. Figure 13. The Mercator with three points also distorts the map in a north south direction, as does the cylindrical equidistant. Finally we employ the transverse Mercator first with three and then with two points. Figure 14. While the three point transverse Mercator produces a slight angular distortion in the north-south direction, the transverse Mercator does not. And while the two point transverse Mercator fits the entire West African coast extremely well. The shape of the Brazilian coast follows that of the projection, although the entire continent lies several degrees south of where it belongs. Why might a transverse Mercator be a reasonable choice? Since Portuguese ships travelled the Atlantic in those years principally between the western coast of Africa and eastern coast of Brazil, on their way to India, centering a projection on the Atlantic Ocean makes a great deal of sense. Having the sphere on which the projection was centered lie tangent to the central area of Portuguese navigation also seems relevant. Creating such a projection would accurately show the direction for ships to travel between the Portuguese possessions on either side of the Atlantic on their way to India. And as we all know today, the Mercator projection remains the best method for creating nautical charts. Since no Dutch or Low Countries ships were plying the Atlantic at the time Mercator produced the nautical projection that bears his name, his information had to come from Spanish or Portuguese sources. Perhaps along with the information came the information on how to construct nautical projections. But that remains for another time. This series of maps shows a previously unsuspected development in the history of projections—their apparent absence of projections in the early years of exploration of the African coast, and the experimentation first with cylindrical projections around 1492, and
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finally with what may have been Mercator projections by 1527. Using these three tools from ArcMap--georeferencing, changing projections, and Geostatistical Analyst we have gained wealth of information about the ways in which nautical charts were constructed in the years before the first official Mercator projection appeared—and a better understanding of the challenges map-makers faced as they began the daunting task of charting regions never before seen from ships. Using these most modern of tools, the maps reveal information about their construction that mere visual inspection--even with a microscope fails to reveal. While we may never learn how the earliest map-makers worked, we should be able to pinpoint when cartographers learned to create uniform scales for large coastlines, as well as when and how they first began to use projections on nautical charts. All of these contributions will be made possible by using the tools available in ArcMap and the Geospatial Analyst.
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Acknowlegements: Rice University GIS/Data Center (GDC) Think Tank Fellows: Eva Garza, Brendan Mulcahy and Joe Kellner. Layout by Joe Kellner. Financial support from Kamran Khan, Rice University. Maps: Benincasa, 1468 – British Library. Jorge de Aguiar, 1492 – Beineke Library, Yale University.
Authors: Patricia Seed, Department of History, Rice University, P.O. Box 1892, Houston, TX 77251, (713) 348-2198, [email protected] German Díaz, GIS Specialist, Fondren Library, P.O. Box 1892, Houston, TX 77251, (713) 348-2595, [email protected],
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