360 Pen field — Use of the Stereographic Projection for 



be enormous if the commerce of the world, which is now car- 

 ried in ships, followed great circles, whenever it is advantage- 

 ous to do so, instead of rhumb courses as indicated by the 

 Mercator charts now in general use. To be sure, many experi- 

 enced navigators practice great circle sailing, and have fol- 

 lowed the ocean pathways for so long a time that they are 

 thoroughly familiar with them : with stereographic charts and 

 protractors, however, their problems would be still less com- 

 plicated ; in fact, the practical workings of the stereographic 

 charts and accompanying protractors are so simple that any 

 intelligent person would soon learn to use them, and great 

 circle sailing would, if anything, be made even easier than 

 rhumb sailing. 



On figure 24: considerable land is shown in the upper left 

 hand corner of the chart, and places located there are rather 

 far from the center, where distortion is considerable. In spite 

 of this, however, distances such as from New York to Chi- 

 cago, Boston to Washington, D ninth to St. Augustine, or 

 across the ocean from New York to Paris, were measured with 

 accuracy by means of the protractor, the error amounting in 

 one case to three miles, but averaging less than one and one- 

 half miles. 



Comparison of the Stereographic with the Polyconic Pro- 

 jection. — Reasons for making this comparison are because of 

 the interest of the polyconic projection as being the one 

 employed by the United States Coast and Geodetic Survey, 

 which department is responsible for most of the official maps 

 issued by our government ; and also because it has been 

 claimed that, of all methods of map projection, the polyconic 

 is the most accurate for limited areas. It is further claimed, 

 as one of the advantages of the polyconic projection, that 

 parallels on the maps are of the same length as on a sphere of 

 corresponding dimensions, which is true, but when the several 

 cones are flattened out, or, what amounts to the same, when 

 the parallels are plotted on a flat surface, the curves do not 

 remain parallel, as on a sphere, but diverge as they depart 

 from the central meridian. 



One of the simplest ways to make a comparison between 

 two maps is to draw them both to scale on one sheet, and the 

 result of doing this with the stereographic and polyconic pro- 

 jections is shown in figure 27, the full lines having been traced 

 from the writer's stereographic map, figure 21, page 3±8, and 

 the dashed lines from the IT. S. Geological Survey map referred 

 to on page 273. The outline of the United States is stereo- 

 graphic. The central meridian is a straight line, and the 

 spacing of this for a distance of 12° from the center is nearly 

 the same on both maps. Other meridians are circular arcs on 



