A New Net for a World Map

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The aim of this net is to obtain a showing all the important habitable lands of the earth, with a true representation of area and a minimum distortion of shape. The stimulus to the search was Figure 3 in Mackinder's Britain and the British Seas, a diagram which is of great value in enabling one to visualize some important facts in the relative positions of the major areas of land and of the oceans, but does not appear to be drawn on any exact projection. The same may be said of the map widely used on posters by the former Empire Marketing Board, which is an impressionistic sketch rather than a map. I have endeavoured many times in the past thirty years to devise an exact net on which such a could be drawn. The solution given here occurred to me in August of 1948. I propose first to describe the construction of the new map-net for two cases; and then to note the chief features of the maps, and some of the uses to which they may be put. On Map I, which shows the simplest case, the net is centred on the North Pole. For the hemisphere round the centre of construction, the northern hemisphere, the net is the normal azimuthal (or zenithal) equal area pro? jection first contrived by J. H. Lambert, and described in many textbooks. Its bounding circle is, of course, the equator. The new feature is seen in each of the sectors which project from this hemisphere; for each an axis (a central meridian) is chosen in relation to the land areas to be shown. The meridians used are: for South America, 6o? W.; for South Africa, 300 E.; for Australia and New Zealand, 1350 E. The parallels in these sectors are arcs of circles concentric with those in the central (northern) hemisphere and are spaced at intervals from the equator equal to those of the corresponding parallels in that hemisphere. Along each parallel so obtained the meridians are spaced at distances from the axis equal to the corresponding distances in the central hemisphere. These distances are to be measured along the are of the parallel in each case. Thus the mesh a'b'c'd' in the South African sector is equal in area to the mesh abed within the circle, between the same meridians and at the same distance from the equator (see Map I). These two meshes represent equal areas on the globe though they are not identical in shape. Every mesh in the sector is similarly related to its corresponding mesh within the circle. Hence the sector net retains the desired property of being equalarea. In each sector the meridians converge towards the South Pole and the central meridian crosses the equator as a straight line perpendicular to it. All the other meridians change direction on crossing the equator; they are not straight lines and do not cut the parallels at right angles. Therefore the net in the sectors is not azimuthal. It is an arbitrary net on which the dis? tortion of shape increases with distance from the axis. The South Polar regions are shown by plotting round the position of the South Pole, at the end of each sector, an equal area azimuthal net for a radius of 300. The enclosing circle is the parallel of 6o? S. latitude and is