Appendix II 351 



them unchanged, and lengthening the whole section, or a part of it, 

 three hundred times. This would give the true average slopes of 

 the continents and oceans. 



445. Maps. The plan or map of a room is simply an exact drawing 

 of the outline of the floor, and the spaces occupied by each article of 

 furniture, drawn so that one inch or any other definite length on the 

 paper corresponds to one foot on the floor. The ratio of the lengths 

 is called the scale of the map ; thus the scale of a map in which 

 one inch represents one foot is I : 12 ; the maps of counties on the 

 Ordnance Survey of the United Kingdom are drawn on the scale of 

 six inches to one mile, or I : 10,560 ; those of the country generally, 

 in which one inch stands for one mile, are on the scale of I : 63,360 ; 

 Plates IX. and X. represent the British Islands on the scale of 

 I : 7,500,000; and Plates I II. -VI II., etc., show the Earth on the 

 scale of I : 200,000,000 along the equator. In the case of the plan 

 of a room, the map, if increased twelve times in length and breadth, 

 would make a carpet accurately fitting the floor, with spaces marked 

 for the furniture to rest on ; but if the map of the British Islands 

 were magnified 7,500,000 times each way, it would not fit the 

 country exactly, because the Earth's surface is curved, and a flat 

 sheet cannot lie smoothly on a curved surface without being folded 

 or stretched. In the case of the Earth as a whole, this difficulty of 

 representing the whole surface in its true form and proportions is 

 much greater. The surface of the sphere cannot be spread out flat, 

 and many devices termed projections are adopted to represent it 

 with as little distortion as possible. On Mercator's projection, shown 

 in Plates I. and II., the parallels of latitude are shown as straight 

 lines, the equator being unbent from a ring into a rod, so that we can 

 see all round it at one glance. The other parallels are not only unbent, 

 but stretched to the same length as the equator, so that the meridians 

 become parallel straight lines, and, in latitude 60, are just twice as 

 far apart as they should be. In order to preserve the correct out- 

 line of the land, and to make the directions measured on the map 

 correct, the parallels are not placed equidistant, but stretched out 

 toward the poles, the degrees of latitude increasing in length in the 

 same proportion as the degrees of longitude. Thus different parts 

 of the map are on different scales ; one square inch including Green- 

 land, for example, represents only one-tenth of the area which one 

 square inch including India comprises. It resembles a cylindrical 

 projection, which may be supposed to be drawn on a great sheet 

 wrapped round the globe, as shown in Fig. 66. Mercator's projec- 



