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# Special Purpose Projections

## projection, meridians, scale, parallels, map, arcs, central and scales

SPECIAL PURPOSE PROJECTIONS These projections are devised for simplicity of drawing and not for any special properties. The most useful projection of this class is the globular projection. This is a conventional rep resentation of a hemisphere in which the equator and central meridian are two equal straight lines at right angles, their intersection being the centre of the circular boundary. The meridians divide the equator into equal parts and are arcs of circles passing through points so determined and the poles. The parallels are arcs of circles which divide the central and extreme meridians into equal parts. This is a simple and effective projec tion, well suited for conveying ideas of the general shape and position of the chief land masses.

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 i :5oo,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. This method is especially suitable for scales of i :125,000 and larger, but it is also sometimes used for smaller scales.

Among projections which have not been described may be mentioned the circular orthomorphic (Lagrange's) and the rectilinear equal-area (Collignon's) and a considerable number of conventional projections, which latter are for the most part of little value.

The choice of a projection depends on the function which the map is intended to fulfil. If the map is intended for statistical purposes to show areas, density of population, incidence of rain fall, of disease, distribution of wealth, etc., an equal-area pro jection 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 general ideas of the shape and dis tribution of the surface features of continents or of a hemi sphere Clarke's perspective projection is a good one. For exhibiting the progress of polar exploration the polar equidistant projection should be selected. For special maps for general use on scales

of :I,osoo,000 and smaller, and for a series of which the sheets are to fit together, the conical, with rectified meridians and two standard parallels, is a good projection. For topographical maps, in which each sheet is plotted independently and the scale is not smaller than I :5oo,000, either form of polyconic is very con venient.

Projections may be devised to fulfil a special purpose. Thus, Mr. J. T. Craig invented a projection the special property of which is that, from every point on the map, the true bearing of Mecca can be accurately measured. He called this the Mecca Azimuthal Projection (see J. T. Craig, Map Projections, Survey of Egypt publication, Cairo, 19°9). Another example of a projection which was devised to be used for a special purpose is the Two Point Equidistant Projection. In this projection, having chosen two points on the sphere (or spheroid), the distances on the map from these two points, to all other points, are true to scale. So that, if the chosen points are the beginning and ending points of a journey, such a projection will enable the traveller to ascertain accurately, by direct measurement the distances that he is from his starting point or his goal (Ordnance Survey Pro fessional Paper no. 5).

The Projection of the International Map of the World on the i :i,000,000 scale is a slightly modified form of simple polyconic. Each sheet is 4° in latitude by 6° in longitude, and each sheet is plotted independently. The upper and lower parallels have the radius v cot lat., where v in each case is the normal terminated by the minor axis. Instead of the central meridian (which is a straight line) being exactly to scale, the meridians 2° to the east and west of it are true to scale; the object of this device is to reduce the maximum error. Along the limiting parallels the degrees of longitude are marked off in their true lengths to scale, and the meridians are straight lines joining the appropriate points on the limiting parallels. The meridians themselves are divided equally, and the inner parallels join the appropriate points on the meridians. The largest scale error is about 1/127o (La Carte du Monde au Millionieme, Association Francaise pour l'Avancement des Sciences, 1910.