128 S. L. Pei) field — Stereographic Projection. 



would appear not as circular arcs, but as the irregular curves 

 x' and y\ figure 24, showing marked deviation from circular 

 arcs in the lower left-hand portions of the chart. 



It is impossible to represent the areal relations of a hemi- 

 sphere upon a plane without sacrificing some features. In the 

 stereographic projection, plates II and III, distances between 

 the meridians and parallels become smaller as they approach 

 the center. Distances and areas on stereographic maps must 

 therefore be magnified in proportion as the distances between 

 the meridians and parallels become smaller. The gradual con- 

 traction of areas, as the center of a stereographically projected 

 hemisphere is approached, is not altogether a drawback, for 

 it should be part of a person's education to understand that, in 

 making a map on a fiat surface, some contraction or magnifica- 

 tion of areas must appear on certain portions of the map. 

 Doubtless most geographical relations can be appreciated best 

 by beginners by studying a sphere or globe. Serious difficulties, 

 however, are encountered in making accurate drawings and meas- 

 urements on a spherical surface; hence to be able to plot all 

 the relations of a sphere easily, quickly, and accurately on a flat 

 surface is a great advantage, an advantage, moreover, which the 

 stereographic projection alone possesses. 



It would seem as though the distorted and inaccurate globu- 

 lar representation, now universally employed- by geographers, 

 should give place to the accurate stereographic projection. It 

 is safe to assume that few teachers in our academies and high- 

 schools have exact ideas concerning the kinds of projection 

 employed in map construction. By making use of comparatively 

 simple wire models* it should be possible to give not alone to 

 teachers, but to scholars of from twelve to sixteen years of age, 

 a sufficient knowledge of the essential features of the stereo- 

 graphic projection to enable them to appreciate the meaning 

 and significance of meridians and parallels as projected on a flat 

 surface, plates II and III. 



If scholars were supplied with stereographic charts, corre- 

 sponding to plates II and III, and were taught to locate places 

 from their longitudes and latitudes, the more skillful of them, 

 at least, would soon be able to construct quite accurate maps, 

 better than those now existing in our school geographies, and 



* The writer has in mind models such as are used in teaching crystallography. 

 Wire circles could be arranged and soldered so as to represent meridians, parallels, 

 and arcs of circles in auy desired position. It does not take many wire circles to 

 give to such models the effect of a sphere. By running wires or threads from 

 certain fixed points on the circles to the south pole, for example, the fundamental 

 conception of the stereographic projection. — the projection to a pole on the surface 

 of a sphere — can be demonstrated. Where the wires or threads intersect the 

 plane of the equator, determine the position of the points in stereographic pro- 

 jection. Great and small circles could be thus projected, and if properly worked 

 out with not too much detail, the models would be very effective. 



