Xll INTRODUCTION 



much more accurate measurement of a number of short Hnes, 

 or bases. Similarly, instead of determining direction by observ- 

 ing the position of a shadow at midday, or of a constellation in 

 the night sky, or even of a steady wind, use was made of 

 terrestrial magnetism through the magnetic compass, and 

 instruments were evolved which enabled horizontal angles to 

 be measured with great accuracy. Meanwhile the astronomers 

 showed that the earth is spherical, and that the position of any 

 place on its surface could be expressed by its angular distances 

 from the Equator (latitude) and a prime meridian (longitude), 

 though for many centuries an accurate and practical method 

 of finding longitude baffled the scientists. 



The application of these astronomical conceptions, and the 

 extension of the knowledge of the world through exploration 

 and intercourse, encouraged attempts to map the known 

 world — but this introduced another problem: how to map a 

 spherical surface on a flat sheet. The mathematician came to 

 the rescue again^ — with his system of projections, by which 

 some, but not all, spatial properties of the earth's surface can 

 be preserved on a single map. Then the astronomers dis- 

 covered that the earth is not a perfect sphere, but is flattened 

 slightly at the Poles; this introduced further refinements, such 

 as the conception of geodetic as opposed to astronomical 

 latitudes, into the mapping of large areas, and great lines of 

 triangulation were run north and south across the continents 

 to determine the true 'figure of the earth', and to provide 

 bases for their accurate mapping. 



Meanwhile, increasing demands were being made on the 

 map maker. The traveller or the merchant ceased to be the sole 

 user of maps. The soldier, especially after the introduction of 

 artillery, and the problems of range, field of fire, and dead 

 ground which it raised, demanded an accurate representation 

 of the surface features, in place of the earlier conventional or 

 pictorial delineation, and a solution in any degree satisfactory 

 was not reached until the contour was invented. This again 

 adds to the task of the surveyor who must run lines of levels 

 and sometimes go to the extent of pegging out the contour 

 lines on the ground. Then the archaeologist, the historian, and 

 much later, the modern geographer had their own special 



