Map scale

“ The Measurement of Areas is easily effected if the map at our disposal is drawn on an equal area projection. In that case we need simply cover the map with a network of squares—the area of each of which has been determined with reference to the scale of the map—count the squares, and estimate the contents of those only partially enclosed within the boundary, and the result will give the area desired. ”

“ The former method, usually called the “natural scale,” may be described as “international,” for it is quite independent of local measures of length, and depends exclusively upon the size and figure of the earth. Thus a scale of 1 : 1,000,000 signifies that each unit of length on the map 630 represents one million of such units in nature. The second method is still employed in many cases, and we find thus:—
In cases where the draughtsman has omitted to indicate the scale we can ascertain it by dividing the actual length of a meridian degree by the length of a degree measure upon the map. ”

“ The decimal scale has also been adopted for the United States’ Coast Survey, the smallest publication scale of which is 1⁄30000; this is also the scale of the new map of France.
In choosing a scale, regard must be had alike to the purposes for which the drawing is intended, and to the nature and the amount of detail required to be shown. Thus a larger scale is required in plans of towns than in those of the open country; and the smaller and more intricate the buildings, the larger should the scale be. ”

“ 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. ”

“ It is sometimes necessary to cut away the contour card; for, as has been already explained, a map is more or less generalized, and a contour is frequently carried across a ravine, instead of following it up, as it would do if the map were on a larger scale. Such generalizing is of course perfectly proper in a map, but, with the same scale, we expect more detail in a model. The modeler must have judgment enough and skill enough to read between the lines, and to undo the generalizing of the topographer and draughtsman, thus supplying the material omitted from the map. ”

“ It is that on which the ordnance survey map of Scotland on the scale of 1 in. to a mile is constructed, and it is frequently met with in ordinary atlases. It is ill-adapted for countries having great extent in longitude, as the intersections of the meridians and parallels become very oblique—as will be seen on examining the map of Asia in most atlases.
If φ0 be taken as the latitude of the centre parallel, and co-ordinates be measured from the intersection of this parallel with the central meridian, then, if ρ be the radius of the parallel of latitude φ, we have ρ = cot φ0 + φ0 − φ. ”

“ Topographical maps and plans are drawn on a scale sufficiently large to enable the draughtsman to show most objects on a scale true to nature. [2] Its information should not only be accurate, but also conveyed intelligibly and with taste. Exaggeration, however, is not always to be avoided, for even on the British 1 in. ordnance map the roads appear as if they were 130 ft. ”

“ The degree of generalization in the geologic and other detail to be shown on a map usually involves a corresponding degree of generalization in its base. Absolutely true generalization means the same degree of omission of detail for each kind of feature. If a base map on a scale of 1 mile to 1 inch, prepared with the usual detail, were placed before a camera and reduced to a scale of 16 miles to 1 inch, the lines representing the smaller tributaries of streams and the smaller water bodies, as well as many other features, would probably be so greatly reduced in length as to be illegible. ”

“ The great value of the modern topographical map is becoming, however, universally acknowledged, and every highly civilized nation has either completed or has in preparation sectional topographical maps of its domain on such a scale as is warranted by its financial condition and its state of development. Thus there is now being accumulated a vast library of geographical and to some extent geological information, of which the student of geology must be prepared to make use. ”

“ If the surface of the map is everywhere equally valuable it is clear that an arrangement by which errors of scale are larger towards the pole than towards the equator is unsound, and it is to be noted that in the case quoted the great bulk of the land is in the north of the map. ”

“ 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. ”

“ My 'Handbook of the Stars' has been prepared to aid the student in the construction of such maps.
In selecting maps it is well to be able to recognise the amount of distortion and scale-variation. This may be done by examining the spaces included between successive parallels and meridians, near the edges and angles of the maps, and comparing these either with those in the centre of the map, or with the known figures and dimensions of the corresponding spaces on a globe. ”

“ The surveys for this map were begun in 1905. The maps are based upon the cadastral plans (1 : 1000) , thoroughly revised and connected with the triangulation of France and furnished with contours at intervals of 5 m. by precise measurement. These minutes are published on a scale of 1 : 10,000 or 1 : 20,000 for mountain districts, while the scale of the general map is 1 : 50,000. Each sheet is bounded by parallels and meridians. The hills are shown in brown contours at intervals of 10 m. and grey shading in chalk (Berthaut, La Carte de France, 1750-1898; Paris, 1899) . ”

“ Article 9 The State establishes a nationwide unified geodetic coordinate system, plane coordinate system, vertical system, geocentric coordinate system and gravimetric system, and defines the classification of orders and classes and precision of the national geodetic survey, as well as the national basic scale map series and their basic precision. ”

“ 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. ”

“ Measurement of Distance.—The shortest distance between two places on the surface of a globe is represented by the arc of a great circle. If the two places are upon the same meridian or upon the equator the exact distance separating them is to be found by reference to a table giving the lengths of arcs of a meridian and of the equator. In all other cases recourse must be had to a map, a globe or mathematical formula. Measurements made on a topographical map yield the most satisfactory results. Even a general map may be trusted, as long as we keep within ten degrees of its centre. ”

“ 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 work is in every respect accommodated to the present advanced state of geographical knowledge, and whether on the ground of Accuracy, Beauty of Execution, or Cheapness, the Publishers invite a comparison with any other work of its class. The General Index, an addition without which no Atlas can be deemed complete, contains no fewer than 60,000 Names, with their Latitude and Longitude, and the Number of the Map in which they will be found.
"We are now in possession of an 'Atlas' which comprehends every discovery of which the present century can boast. ”

“ The lines should preferably run across the long axis of an area, not parallel to it, and the predominating trend or general direction of the areas of one geologic formation on a map should decide the direction of the lines for all areas of that formation on the same map, even if the rule must be violated on some of the minor areas.
An effort should always be made to produce a pattern that is subordinate in strength to the main lines of the base map on which it is drawn. In black and white maps, as in colored maps, unlike patterns should be placed next to each other. ”

“ 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. ”

“ A finished map border is used or omitted according to the kind of map prepared. Diagrammatic maps and maps on which no parallels and meridians appear do not need finished borders. On a map that shows complete areal geologic or other coloring, such as a map in a Survey geologic folio, the border lines tend to destroy the simple effect of the whole map. On a map that is not completely colored and on all very large maps borders are really necessary. ”

“ 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. ”

“ It is well to remember, however, that since a mile or minute of latitude has a different value in every latitude, there is an appearance of distortion in every Mercator chart which covers any large extent of surface. For instance, an island near the pole, will be represented as being much larger than one of the same size near the equator, due to the different scale used to preserve the accurate character of the projection. ”

“ 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. ”

“ If the geology be other than of the very simplest character—and this will generally be true of mountainous regions—it is not only necessary to fix the geographical positions of rock masses, but their elevations as well. In other words, the map must not only be a plan, but special elevations must be represented, known as geological sections. The most satisfactory representation—and this will be essential for all difficult areas—will be one which shows not only special elevations, but the topographic relief of every point in the area. ”

“ 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. ”

“ Much the same may be said of the dikes of cooled magma which have been injected along preëxisting fractures.
The base of the geological map.—Modern topographic maps form an important part of the library of the serious student of physiography; they are the gazetteer of this branch of science. Every civilized nation has to-day either completed a topographic atlas of its territory, or it is vigorously prosecuting a survey to furnish maps which represent the relief with some detail, and publishing the results in the form of an atlas of quadrangles. ”

“ The topographical survey of a country is defined by Sir A. Scott Waugh to imply ‘the measurement and delineation of the natural features of a country, and the works of man thereon, with the object of producing a complete and sufficiently accurate map. Being free from the trammels of boundaries of properties, the principal lines of operations must conform to the features of the country, and objects to be surveyed.’
The only safe basis for the topographical survey of a country is a system of accurate triangulation. ”