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., ½ in., ¼ 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. _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., ½ in. and ¼ in. Ordnance maps of England. The cadastral plans of the Survey of India, and cadastral plans throughout the empire.