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.

Summary.

The following projections have been briefly described:—

Perspective  1. Cylindrical equal-area.
 2. Orthographic.
 3. Stereographic (which is orthomorphic).
 4. General external perspective.
 5. Minimum error perspective. (Clarke’s).
 6. Central.
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., 1⁄2 in., 1⁄4 in. and 1⁄10 in. Ordnance maps of Scotland and Ireland. The 1 : 800,000 map of the Cape Colony, published by the Surveyor-General.