general shape and position of the chief land masses; it is better for this purpose than the stereographic, which is commonly employed in atlases.
|(From Text Book of Topographical Surveying, by permission of the Controller|
of H.M. Stationery Office.)
|Fig. 27.—Plane Table Graticule, dimensions in inches, for a scale|
of 4 in. to 1 m.
Projections for Field Sheets.
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. This method is especially suitable for scales of 1 : 125,000 and larger, but it is also sometimes used for smaller scales.
Fig. 27 shows the method of plotting the projection for a field sheet. Such a projection is usually called a graticule. In this case ABC is the central meridian; the true meridian lengths of 30′ spaces are marked on this meridian, and to each of these, such as AB, the figure (in this case representing a square half degree), such as ABED, is applied. Thus the point D is the intersection of a circle of radius AD with a circle of radius BD, these lengths being taken from geodetic tables. The method has no merit except that of convenience.
The following projections have been briefly described:—
|Perspective||1. Cylindrical equal-area.|
|3. Stereographic (which is orthomorphic).|
|4. General external perspective.|
|5. Minimum error perspective. (Clarke’s).|
|Conical||7. Conical, with rectified meridians and two standard parallels (5 forms).|
|8. Simple conical.|
|9. Simple cylindrical (a special case of 8).|
|10. Modified conical equal-area (Bonne’s).|
|11. Sinusoidal equal-area (Sanson’s).|
|12. Werner’s conical equal-area|
|13. Simple polyconic.|
|14. Rectangular polyconic.|
|15. Conical orthomorphic with 2 standard parallels (Lambert’s, commonly called Gauss’s).|
|16. Cylindrical orthomorphic (Mercator’s).|
|17. Conical equal-area with one standard parallel.|
|18. Conical equal-area with two standard parallels.|
|19. Projection by rectangular spheroidal co-ordinates.|
|Zenithal||20. Equidistant zenithal.|
|21. Zenithal equal-area.|
|22. Zenithal projection by balance of errors (Airy’s).|
|23. Elliptical equal-area (Mollweide’s).|
|24. Globular (conventional).|
|25. Field sheet graticule.|
Of the above 25 projections, 23 are conical or quasi-conical, if zenithal and perspective projections be included. The projections may, if it is preferred, be grouped according to their properties. Thus in the above list 8 are equal-area, 3 are orthomorphic, 1 balances errors, 1 represents all great circles by straight lines, and in 5 one system of great circles is represented correctly.
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 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. For exhibiting the progress of polar exploration the polar equidistant projection should be selected. For special maps for general use on scales of 1/1,000,000 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 1/500,000, either form of polyconic is very convenient.
The following are the projections adopted for some of the principal official maps of the British Empire:—
Conical, with Rectified Meridians and Two Standard Parallels.—The 1 : 1,000,000 Ordnance map of the United Kingdom, special maps of the topographical section, General Staff, e.g. the 64-mile map of Afghanistan and Persia. The 1 : 1,000,000 Survey of India series of India and adjacent countries.
Modified Conical, Equal-area (Bonne’s).—The 1 in., 1 in., 1 in. and 1 in. Ordnance maps of Scotland and Ireland. The 1 : 800,000 map of the Cape Colony, published by the Surveyor-General.
Simple Polyconic and Rectangular Polyconic maps on scales of 1 : 1,000,000, 1 : 500,000, 1 : 250,000 and 1 : 125,000 of the topographical section of the General Staff, including all maps on these scales of British Africa. A rectilinear approximation to the simple polyconic is also used for the topographical sheets of the Survey of India. The simple polyconic is used for the 1 in. maps of the Militia Department of Canada.
Zenithal Projection by Balance of Errors (Airy’s).—The 10-mile to 1 in. Ordnance map of England.
Projection by Rectangular Spheroidal Co-ordinates.—The 1 : 2500 and the 6 in. Ordnance sheets of the United Kingdom, and the 1 in., 1 in. and 1 in. Ordnance maps of England. The cadastral plans of the Survey of India, and cadastral plans throughout the empire.
Authorities.—See Traité des projections des cartes géographiques, by A. Germain (Paris, 1865) and A Treatise on Projections, by T. Craig, United States Coast and Geodetic Survey (Washington, 1882). Both Germain and Craig (following Germain) make use of the term projections by development, a term which is apt to convey the impression that the spherical surface is developable. As this is not the case, and since such projections are conical, it is best to avoid the use of the term. For the history of the subject see d’Avezac, “Coup d’œil historique sur la projection des cartes géographiques,” Société de géographie de Paris (1863).
J. H. Lambert (Beiträge zum Gebrauch der Mathematik, u.s.w. Berlin, 1772) devised the following projections of the above list: 1, 15, 17, and 21; his transverse cylindrical orthomorphic and the transverse cylindrical equal-area have not been described, as they are seldom used. Among other contributors we mention Mercator, Euler, Gauss, C. B. Mollweide (1774–1825), Lagrange, Cassini, R. Bonne (1727–1795), Airy and Colonel A. R. Clarke. (C. F. Cl.; A. R. C.)
MAPLE, SIR JOHN BLUNDELL, Bart. (1845–1903), English business magnate, was born on the 1st of March 1845. His father, John Maple (d. 1900), had a small furniture shop in Tottenham Court Road, London, and his business began to develop about the time that his son entered it. The practical management soon devolved on the younger Maple, under whom it attained colossal dimensions. The firm became a limited liability company, with a capital of two millions, in 1890, with Mr Maple as chairman. He entered parliament as Conservative member for Dulwich in 1887, was knighted in 1892, and was made a baronet in 1897. He was the owner of a large stud of race-horses, and from 1885 onwards won many important races, appearing at first under the name of “Mr Childwick.” His public benefactions included a hospital and a recreation ground to the city of St Albans, near which his residence, Childwickbury, was situated, and the rebuilding, at a cost of more than £150,000, of University College Hospital, London. He died on the 24th of November 1903. His only surviving daughter married in 1896 Baron von Eckhardstein, of the German Embassy.