The linear scale of maps can obviously be used only in the case of maps covering a small area, for in the case of maps of greater extension measurements would be vitiated owing to the distortion or exaggeration inherent in all projections, not to mention the expansion or shrinking of the paper in the process of printing. As an extreme instance of the misleading character of the scale given on maps embracing a wide area we may refer to a map of a hemisphere. The scale of that map, as determined by the equator or centre meridian, we will suppose to be 1:125,000,000, while the encircling meridian indicates a scale of 1:80,000,000; and a "mean" scale, equal to the square root of the proportion which the area of the map bears to the actual area of a hemisphere, is 1:112,000,000. In adopting a scale for their maps, cartographers will do well to choose a multiple of 1000 if possible, for such a scale can claim to be international, while in planning an atlas they ought to avoid a needless multiplicity of scales. _Map Projections_ are dealt with separately below. It will suffice therefore to point out that the ordinary needs of the cartographer can be met by conical projections, and, in the case of maps covering a wide area, by Lambert's equal area projection. The indiscriminate use of Mercator's projection, for maps of the world, is to be deprecated owing to the inordinate exaggeration of areas in high latitudes. In the case of topographical maps sheets bounded by meridians and parallels are to be commended. The meridian of Greenwich has been universally accepted as the initial meridian, but in the case of most topographical maps of foreign countries local meridians are still adhered to--the more important among which are:-- Paris (Obs. nationale) 2° 20´ 14´´ E. of Greenwich. Pulkova (St Petersburg) 30° 19´ 39´´ E. " Stockholm 18° 3´ 30´´ E. " Rome (Collegio Romano) 12° 28´ 40´´ E. " Brussels (Old town) 4° 22´ 11´´ E. " Madrid 3° 41´ 16´´ W. " Ferro (assumed) 20° 0´ 0´´ W. of Paris. The _outline_ includes coast-line, rivers, roads, towns, and in fact all objects capable of being shown on a map, with the exception of the hills and of woods, swamps, deserts and the like, which the draughtsman generally describes as "ornament." Conventional signs and symbols are universally used in depicting these objects. [Illustration: FIG. 1.]