Scale (map)

“ On such a scale the 1/100th part of an inch represents a distance of very nearly nine feet on the ground and consequently however accurate the map might be in its projection, as an image showing the relative positions of all objects of importance on the ground, the scale is clearly too small for the measurement of areas for valuation purposes, and it is but a reproduction of the larger cadastral map. ”

“ 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 materials required are at least three copies of the same map, drawn to such scale as may be suitable to the magnitude of the operations to be represented. If the scheme is one for small numbers of troops, maps of large scale are essential, as small features of the ground largely influence the action of small bodies, and it is only on large-scale maps that the real influence of small features can readily be appreciated. Conversely, with large bodies, maps on a diminished scale are convenient. A great amount of detail is necessary in all, maps drawn for military purposes ”

“ 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 degree of fineness and lightness should be such that when the detail is finely but firmly outlined, the reference lines and points may not be visible, except on a close inspection of the surface.
To plot secondary reference lines, as, for example, a number of offset lines, apply the scale so that its edge may be parallel to and almost over the pencil trace of the primary line and its zero point coincident with the point at which the line begins. Care must always be taken to place the zero of the scale at the beginning of the line, and not at the end of it. ”

“ 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. ”

“ Scales of Construction. —Scales of construction are intended to afford means of measuring more minute quantities than scales of distances. Of the former there are two kinds, known respectively as the Diagonal and the Vernier scale. The diagonal is the more frequently employed. Its construction involves no peculiar difficulty, as it consists simply of an ordinary scale of distances, with the addition of a number of parallel lines crossed by other parallel lines drawn diagonally from the smaller points of division. An example will best show the construction and mode of using this scale. ”

“ 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. ”

“ For instance, a series of projections may be constructed for zones, each having a range of 10° of latitude, from the equator to the pole. Treating the earth as a sphere and using the above formulae, the series will possess the following properties: the meridians will all be true to scale, the area of each zone will be correct, the scale errors of the limiting parallels will all be the same, so that the length of the upper parallel of any zone will be equal to that of the lower parallel of the zone above it. ”

“ This, again, is a perspective projection, namely, the Stereographic. In this, though all small parts of the surface are represented in their correct shapes, yet, the scale varying from one part of the map to another, the whole is not a similar representation of the original. The scale, σ = 1⁄2c sec2 1⁄2z, at any point, applies to all directions round that point.
These two last projections are, as it were, at the extremes of the scale; each, perfect in its own way, is in other respects objectionable. We may avoid both extremes by the following considerations. ”

“ 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. ”

“ VI. A map drawn by this rule will have the following properties:
1. The intersections of the meridians and parallels will be rectangular.
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2. The distances north and south will be exact; and any meridian will serve as a scale.
3. The parallels thro’ z and y, where the line Rr cuts the arc Ll, or any small distances of places that lie in those parallels, will be of their just quantity. At the extreme latitudes they will exceed, and in mean latitudes, from x towards z or y, they will fall short of it. ”

“ The engraver or the lithographer will supply such matter in proper form according to specifications. For direct reproduction, however, as by photolithography or zinc etching, the lettering must either be carefully drawn with pen or printed from type on slips, which are pasted on the drawing.
GRAPHIC SCALES FOR MAPS.
A bar scale for miles or feet should be given on every map, and if the map is of international interest the metric scale should be given just beneath the scale of miles or feet. The accepted designs for these scales are shown in figure 7. ”

“ 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 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. ”

“ When reducing by scales, it is obviously not essential to use the same scale as that to which the original is made; the dimensions on one scale may be readily transferred to any other, and the student will do well to make himself familiar with the operation. ”

“ It is obvious that if a scale of feet showing inches diagonally be required, twelve equidistant parallel lines must be drawn instead of eight as in the foregoing example where furlongs are required. The diagonal scale possesses the important advantages of accuracy and distinctness of division which render it very suitable as a scale of construction. Another practical advantage is that it is less rapidly defaced by use than the other kinds, in consequence of the measurements being taken on so many different lines. ”

“ A map drawn on the scale of 400,000 miles to the inch would need to be 1,100 miles long to take in both the earth and the nearest fixed star. On such a map the earth would be one-fiftieth of an inch in diameter—the size of a small grain of sand. ”

“ The larger work occupied thirty-two years, and was accomplished with complete success. The map in 25 sheets on the scale of 1/100000 was published at intervals between 1842 and 1865, and is an admirable specimen of cartography. ”

“ In the case of general maps on a smaller scale, the orographic features must be generalized by a skilful draughtsman and artist. One of the best modern examples of this kind is Vogel’s map of Germany, on a scale of 1 : 500,000.
Selection of Names and Orthography.—The nomenclature or “lettering” of maps is a subject deserving special attention. ”

“ Any physical quantity whose field can be described by a single numerical value at each point in space. A scalar quantity is distinguished from a VECTOR quantity by the fact that scalar quantity possesses only magnitude, where as, a vector quantity possesses both magnitude and direction.
scale, n. 1. A series of marks or graduations at definite intervals. A linear scale is a scale graduated at uniform intervals; a logarithmic scale is graduated in the logarithms of uniformly-spaced consecutive numbers. 2. The ratio between the linear dimensions of chart, map drawing, etc. ”

“ The symbols shown, however, will cover all the ordinary requirements of miscellaneous mapping. Though the plate shows more than one symbol for some features the symbol most commonly used is given first and should be preferred. The center of each symbol should mark the location of the feature symbolized. Symbols are not always platted with sufficient care. On small-scale maps they are difficult to locate and unless great care is taken in platting them they are likely to be several miles out of place. All symbols should be located precisely where they belong. ”

“ 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. ”

“ Every map is a sketch, which is corrected by the geometric location of a greater or less number of points. Assuming entire accuracy in the location of the points, that is, assuming that the errors of location of the points are not perceptible upon the map, the measure of accuracy of the map consists in the number of these geometric locations per unit of surface, per square inch, if you will, of the map. The greater the number of these locations the greater the accuracy of the map, but however numerous they may be the map itself is a sketch, the points located being simply mathematical points. ”

“ We read how the truths have appealed to his own consciousness. It stands where the relief map itself stands, as representing the delineator’s own mental image of such structure.
There are no lines drawn in this map that contradict or confuse the meaning; all is direct, truthful and clear in statement of fact. Each line has its own particular meaning. If represents direction. Applied to land surface, a vertical line means a perpendicular mountain or side wall of plateau, horizontal lines indicate level areas, and oblique lines a sloping surface. ”

“ 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 artist when inspired with his subject masses his material in boldly and each stroke counts for the thing he wants to say—it tells of the direction of surface, or edge of mass, or detail.
In the new map, the representation of solidity and land continuity as mass, with no hard and fast limitations of land and water, such as the outlines so prominent in the old reference maps, is a noticeable feature. ”

“ 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. ”