Geographical Maps and Sailing Charts. 363 



"The above perspective projections, in their applications to 

 astronomy and geography, are usually confined to the repre- 

 sentation of a hemisphere, and but rarely to smaller surfaces. 

 For the purposes of land and sea charts on a large scale and 

 consequently of quite limited extent, they are not well suited, 

 for one or more reasons : they are generally laborious of con- 

 struction tuhen embracing limited areas, and cannot be made 

 to satisfy any special conditions which they do not already 

 possess, but which may be of paramount importance, or they 

 may possess certain features which are not desirable on the 

 chart. We thus come to the construction of maps and charts 

 by so-called development. These are of comparatively modern 

 origin, whereas the preceding three principal perspective pro- 

 jections were all known to the ancients." 



The writer has taken the liberty of italicizing two of the 

 statements of the foregoing paragraph to which decided excep- 

 tions are taken, in so far as they relate to the stereographic 

 projection. It may be stated, however, that the conclusion 

 arrived at on page 12 of the survey publication just referred 

 to, that their "investigation tends to commend the harbor, 

 coast and sailing charts of the Coast Survey to the fullest con- 

 fidence of the geographer as well as of the mariner," is wholly 

 justifiable, provided the charts do not cover too large an area. 

 In an example cited of an area about like that of New York 

 State, but plotted on a somewhat larger scale than the writer's 

 map, page 353, it is stated* that " for so short a distance as 

 three or four hundred miles and in latitudes below 45°, the 

 error in distance, as compared with the arc of a great circle, is 

 generally less than two-tenths of a mile." By reference to 

 page 35i, it may be seen that a like conclusion was obtained by 

 the present writer from the actual measurement of distances 

 on his stereographic map of New York State with a millimeter 

 scale. 



In conclusion, it may be stated that for an area as large as 

 the United States the stereographic projection is better than 

 the polyconic, and for smaller areas the same must hold true, 

 although the differences between the two projections may then 

 be scarcely appreciable. The stereographic projection is as 

 good for one part of a sphere as another, which is not true of 

 the polyconic projection : the latter, for example, would not 

 be at all suitable for a map of the polar regions. Other advan- 

 tages of the stereographic projection are that distortion is 

 symmetrical about the center, or point of tangency, and by 

 means of a stereographic protractor great circle courses may be 

 indicated, and measurement of distances made, with exactness. 



* Methods and Results, loe. cit., page 12. 



Am. Jour. Sci.— Fourth Series, Vol. XTII, No. 11.— May, 1902. 

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