MERCATOR, ORTELIUS, AND THEIR SUCCESSORS 115 



of small areas is preserved (i.e. the projection is conformal). 

 This property combined with that of representing loxodromes 

 as straight lines, makes it extremely useful for representing 

 small areas. 



For large sections of the globe, it has obvious incon- 

 veniences. Owing to the 'waxing latitudes', the scale increases 

 progressively from Equator to Pole, and to measure distances 

 is not a simple operation. (The length of a degree of longitude 

 is zero at the poles, whereas on Mercator's projection it is 

 theoretically the same as at the Equator.) Mercator therefore 

 placed on his map two lengthy notes, explaining how, given 

 two of the following elements, difference of latitudes, difference 

 of longitudes, direction, and distance, it was possible to 

 determine the other two. The main difficulty was in the 

 determination of distance owing to the variation in scale. This 

 he solved by the principle of similar triangles. The triangle 

 given by the bearing between the two points on the chart, 

 whose distance was to be determined, and their difference in 

 latitude was constructed proportionally on the Equator. The 

 length of the required line was then measured off in equatorial 

 degrees, and the result obtained by multiplying the figure 

 thus obtained by the appropriate number of miles, one degree 

 being taken to equal fifteen German miles, sixty Italian, or 

 twenty French miles. 



It was many years before Mercator charts were generally 

 adopted by seamen, who preferred rule of thumb methods. 

 There was some complaint that on the original world chart 

 the coastlines were not clearly shown, but it is difficult to 

 believe that this in itself led to its early neglect. The theoretical 

 construction of the projection was not clearly set out until 

 Edward Wright published his 'Certaine errors in navigation' 

 in 1599. Until charts of relatively small areas were constructed 

 on its principle, its merits would not be recognized by navi- 

 gators. By the end of the century, such charts were beginning 

 to be drawn, but it was not until nearly a century after its 

 invention that Sir Robert Dudley produced a collection of 

 charts, all of which were on this projection, in his 'Arcano del 

 Mare', 1646. At the end of the century the famous navigator, 

 John Narbrough, could still write: 



