THEORY OF POLYGON IC PROJECTIONS. 



139 



projections of the parallels intercept upon this cii'cnmf erence 

 and upon the projection of the central meridian lengths 

 proportional to the corresponding arcs of the globe. 



In figui^e 38 let APA'P^ be a cu-cmnf erence the radius of 



which OP is equal to hJ it will reprdsent the principal 

 meridian. Let PP^ be the central meridian of the map 



P' 



Fig. 38.— Geometrical relations of Foumier's projection. 



and let AA' be the Equator. If we take OP equal to ^^ 

 and if we make the angles AOJJ and A'OV also equal to v?, 

 the circumference passing through the throe points V, B, 

 J]' wiU be the projection of the parallel of latitude <p. By 

 taking OG equal to X and constructing a half ellipse havmg 

 for vertices P, G, and P' we shall obtain the projection of 

 the meridian of longitude X. Let M be the point where it 



