Geographical Maps and Sailing Charts. 249 



stand out with rather surprising stereoscopic effect, making the 

 figure appear much more real. It is believed that a careful 

 consideration of either of the figures here presented will serve 

 to convey a clear idea of the principles upon which the stereo- 

 graphic projection is based. 



Three kinds of stereographic maps come under considera- 

 tion : (1) projection upon the plane of the equator, when the 

 point of vision is at one of the poles; (2) projection upon the 

 plane of a meridian, when the point of vision is at some point 

 on the equator ; while (3) if the point of vision is at any posi- 

 tion other than the ones mentioned, the map may be considered 

 as made on a plane tangent to the sphere at the antipodal 

 point : such a map is said to be made upon the plane of the 

 horizon, and the latitude and longitude of the point of tan- 

 gency should be given. 



Important features of the projection are as follows : As shown 

 by figures 1 and 2, when a circle of a sphere passes through 

 the point of vision it is projected as a straight line on the map, 

 while all other circles are projected as circles* which appear 

 generally as portions of circular arcs on maps. This is a most 

 important feature, for no other lines can be more accurately 

 constructed than circles, and by making use of a few simple 

 mathematical principles it is possible to project a system of 

 parallels and meridians, the very foundation of a map, with 

 almost absolute accuracy. Angles are preserved, and the 

 stereographic is the only true projection which possesses this 

 important feature, although by methods of development maps 

 are produced (the so-called Mercator's projection, for example) 

 where angles are preserved. A given distance is represented 

 by varying lengths on different parts of a stereographic map, 

 but the distortion of distances is of a nature deserving most 

 careful consideration. Starting from the center of a hemi- 

 sphere, the distances from degree to degree become gradually 

 greater as the periphery is neared ; the rate of increase, how- 

 ever, is very slight at first. Within a radius of 90° from the 

 center the maximum variation is such that the distance from 

 the eighty-ninth to the ninetieth degree fails just a little of 

 being twice as great as from the center to the first degree. 

 This important subject of distortion will be considered more 

 fully in a later paragraph. In spite of distortion, however, 

 distances may be measured with facility and accuracy on stereo- 

 graphic maps, provided use is made of specially devised 

 Stereographic Protractors previously described by the writer.f 

 These may be of various forms ; one of which is represented, 

 much reduced, by figure 3, and the use of this and other forms, 



* This Journal (4), xi, pp. 8-13, 1901. 

 fLoc. cit., pp. 17-23. 



