Map projection

“ Such is the conception of an accurate map which is an attempt to produce on a plain surface or sheet of paper, a horizontal projection of objects on the ground, which will show the relative positions of every detail on any desired scale with as little distortion as possible, and on which distances may be measured in any direction, and areas computed with a degree of accuracy only limited by the scale. ”

“ If the map is intended for statistical purposes to show areas, density of population, incidence of rainfall, of disease, distribution of wealth, &c., an equal-area projection should be chosen. In such a case an area scale should be given. At sea, Mercator’s is practically the only projection used except when it is desired to determine graphically great circle courses in great oceans, when the central projection must be employed. For conveying good general ideas of the shape and distribution of the surface features of continents or of a hemisphere Clarke’s perspective projection is the best. ”

“ The plane of projection is usually tangent to the ellipsoid at the center of the area being mapped. he analytical expressions that determine the elements of the projection. If the point of projection is at the center of the ellipsoid, a gnomonic map projection results; if it is at the point opposite the plane’s point of tangency a stereographic map projection; and if at infinity (the projecting lines being parallel to each other) , an orthographic map projection. Most map projections are not perspective. ”

“ Mercator's principal title to fame rests upon his invention of the method of drawing maps, which is known as Mercator's Projection. Under this system the map represents the earth as an unrolled cylinder, and the poles are remanded to infinity. The parallels of latitude and the meridians are drawn as straight lines, crossing one another at right angles. ”

“ The resulting projection is accurate near the central meridian, but as this is departed from the parallels increasingly separate from each other, and the parallels and meridians (except along the equator) intersect at angles which increasingly differ from a right angle. The real merit of the projection is that each particular parallel has for every map the same absolute radius, and it is thus easy to construct tables which shall be of universal use. This is especially valuable for the projection of single sheets on comparatively large scales. ”

“ The term “gnomonic” was applied to this projection because the projection of the meridians is a similar problem to that of the graduation of a sun-dial. It is, however, better to use the term “central,” which explains itself. The central projection is useful for the study of direct routes by sea and land. The United States Hydrographic Department has published some charts on this projection. False notions of the direction of shortest lines, which are engendered by a study of maps on Mercator’s projection, may be corrected by an inspection of maps drawn on the central projection. ”

“ Field sheets for topographical surveys should be on conical projections with rectified meridians; these projections for small areas and ordinary topographical scales—not less than 1/500,000—are sensibly errorless. But to save labour it is customary to employ for this purpose either form of polyconic projection, in which the errors for such scales are also negligible. In some surveys, to avoid the difficulty of plotting the flat arcs required for the parallels, the arcs are replaced by polygons, each side being the length of the portion of the arc it replaces. ”

“ In 1511 Bernard Sylvanus produced in his edition of Ptolemy a general map of the world, upon what has since been called the cordiform or heart-shaped projection, which, while giving the whole of the geographical features of the earth, was, from the curve and sweep of the parallels of both latitude and longitude, better adapted than anything that had preceded it to convey upon a plane surface a general idea of the earth's globular form. ”

“ For a long time mountains were supposed to be the limitations of rivers, and old maps represent them always as flowing along the valleys without ever passing through the mountain-chains that divide them; but geology is fast correcting the errors of geography, and a map which represents merely the external features of a country, without reference to their structural relations, is no longer of any scientific value. ”

“ RUSKIN'S MAPS
Reading the map is as great a pleasure to some people as reading a story-book. You will see them pore over the atlas for an hour together, going on dream-journeys. It is a cheap way of globe-trotting, and gets rid of the discomforts; only one must have imagination to turn the wriggling hair-lines into vistas of river scenery, and the woolly-bear shading into forested crests and peaks against the sunset. It needs a good deal of imagination to get over the ugliness of most modern maps; but why should maps be ugly? ”

“ Many a cartographer, burning with desire to draw a good map of a newly explored region, has been driven to despair by the inadequacy of the route surveys in his hands. Not a few of these surveys have been unworthy of reproduction in the books of the explorers who made them, and the best that could be done was to generalize their information on maps of comparatively small scale. ”

“ In spite of the fact that the requirements in history state that geographical knowledge will be tested by requiring the location of places and movements on an outline map, in spite of the fact that almost every set of questions for nine years has demanded map work, the papers of candidates have shown that instruction in geography, including the use of maps, has been signally neglected. ”

“ Commercial considerations are not to be overlooked; cheap and rapid methods of reproduction bring their temptations as well as their advantages to bear upon cartography. Their advantages are manifest; the map, whether as an adjunct to travel or as a graphic illustration of a great variety of subjects, has become a commodity of almost daily use. But in some countries, such as the United States, the standard of cartography generally is as low as that of the maps of the survey is high. ”

“ They can be made to represent anything that any map can, though their special province is the exhibition of general facts where minute details are negligible. In fact, the encumbering of a large map with a multitude of names and other data is the cardinal sin of the cartographer. The two broad classes of facts put upon maps are political and physical, and almost always in combination, as neither one has very much meaning without the other. ”

“ Each mountain peak cannot be shown, nor every indentation of coast-line, but the general trend or direction of mountain ranges and rivers, and more or less of geological structure can be portrayed in a conventional manner.
It is not difficult to chalk model with reasonable accuracy. The ability to do this, however, with any degree of rapidity as well as accuracy, implies, as has just been said, an adequate knowledge of the subject to be represented. No mere imitation, or acquisition of technique, or copying of maps, is educational, nor has it any vital relation to the true study of geography. ”

“ Rafn's fault was, however, no greater than that committed by the modern makers of so-called "ancient atlases"—still current and in use in schools—when, for example, they take a correct modern map of Europe, with parts of Africa and Asia, and upon countries so dimly known to the ancients as Scandinavia and Hindustan, but now drawn with perfect accuracy, they simply print the ancient names!! Nothing but confusion can come from using such wretched maps. The only safe way to study the history of geography is to reproduce the ancient maps themselves, as I have done in the present work. ”

“ What the ideal geographer, as cartographer, first of all tries to do is to devise a notation by which he and his fellow-geographers, by the inspection of a map of a given region, may get a simultaneous vision of the terrestrial phenomena which all the explorers and observers of that region have collectively seen. Now it must always be that however minutely observed and explored a region—even the most inhabited—may be, there is always something new to be observed, even in the shape and configuration of the surface, for these are always changing ”

“ Maps are the essential apparatus of Kultur, and every educated German is a geographer in a sense that is true of very few Englishmen or Americans. He has been taught to see in maps not merely the conventional boundaries established by scraps of paper, but permanent physical opportunities—'ways and means' in the literal sense of the words. His Real-Politik lives in his mind upon a mental map. The serious teaching of geography in German High Schools and Universities dates from the very beginning of Kultur. ”

“ Clearness and distinctness, every one must feel, are not the strong points of modern cartography, hence the use of sketch-maps: such as this of Spain, scribbled on a sheet of foolscap to keep him in mind of the graceful, swinging coastline and the proportions of the provinces.
The overloaded modern map is a work of reference—it is a dictionary, not a book. Ruskin felt that it was useless for educational or literary purposes, and he was continually trying to improve away the detail and to substitute graphic statistics. ”

“ Alphabetical printing is far from being the only use the Boston press is put to. The arithmetical, geometrical, and musical signs are as easily prepared; and there is an atlas which far surpasses any illustrations of geography previously devised. The maps made in Europe are very expensive, and exceedingly troublesome to prepare, the boundaries of sea and land being represented by strings glued on to the lines of a common map, pasted on a board. The American maps are embossed; the land being raised, and the water depressed ”

“ It is good for us all to know the position of New York and Rio and Calcutta on the map, without its being necessary for us to understand, far less to work out for ourselves, the observations and calculations which fixed their latitude and longitude. Knowledge of the map is a good thing in itself, though it is a very different thing indeed from the technical knowledge which enables a man to make a chart of an unknown region, or to explore and survey it. Furthermore, it is a form of knowledge far more generally useful. ”

“ Some kinds of apparatus have long been found in schools. Geography has long had the aid of maps, and no teacher would use a geography which was not furnished with a respectable atlas. But maps alone are not a sufficient apparatus in teaching geography. A globular revolving map of the world, a globe, and a cylindrical revolving Mercator's chart, will furnish important aid in explaining the globular, polar, and Mercator's projections of a map of the world. Astronomy and natural philosophy can no more be successfully taught without the use of machines, than can geography without the use of maps. ”

“ Such a parallel of the historic survey of the city to that of its underlying geological area is thus in no wise a metaphoric one, but one which may be worked out upon maps sections and diagrams almost completely in the same way—in fact, with little change save that of colours and vertical scale. The attempt to express the characteristic and essential life and thought of a given region in each period upon a series of maps is in fact the best method of understanding the everyday map at which we commonly look so unthinkingly. ”

“ As a work of art, graphically delineating the configuration of a district of surpassing beauty and variety of scenery, it will, perhaps, possess greater interest to the ordinary observer than any scientific value of accuracy and completeness could give it. If a person were called upon to construct an ideal map which should group together specimens of all types of topographical form and the conventional signs known to the draughtsman, he could hardly derive from his imagination a chart more comprehensive than this. ”

“ All a political map is, then, is a map which pays relatively [48] more attention to the human side of geography than to the physical, and so, as it were, looks at the face of the continent from the point of view of man rather than nature. ”

“ I once asked the agent of one of the largest map establishments in the United States. "Oh," he answered, "when we cannot get township details from local surveys, we sling them in anyhow." An error once taught from our geographies and maps will remain an error for a generation, and our text-book geographers will continue to repeat it, for they do not travel over the countries they describe, and rarely adopt the results of scientific investigation. The most unpopular study in the schools of the United States is that of the geography of our country. ”

“ When the Greek philosopher Anaxagoras said that man was born to contemplate the heavens, the sun, and the moon, he might have added also the earth and its formation in all its details, and enjoined on his disciples the necessity of representing the result of such contemplations by maps and charts. We require a map fully to understand the geography and chorography of a country; hence a study of the maps made by contemporaneous makers becomes the duty of the writer of New Netherland history. ”