64 



U. S. COAST AND GEODETIC SURVEY. 



Now, in figure 24 let NESW be the primitive circle and 

 let WE be the Hne of measures ; also let m and m' be the 

 projections of the given points. Take On' = Om' and 

 On = Om; draw Sn' to intersect the primitive circle in p^ 

 and Sn to intersect it in p. On mm^ construct the tri- 

 angle Dmm% having mD = Sn and m'D = Sn'; prolong 

 Dm^ to q^, making m'g'' = 7i/^', and prolong Dm to q, mak- 

 7riq = np, Then gg;' is the chord distance between the 

 given points, and this chord being laid off anywhere on 



^'-^>? 



Fig. 24.— Projection of great circle tlirough two points and length of arc between them 

 on stereographic projection. 



the primitive circle will give the great-circle-arc distance. 

 The triangle Dqq^ is evidently the triangle EMM' of 

 figure 23 turned on mm' as an axis into the plane of the 

 projection or into the primitive plane. Prolong mm.' and 

 qc[' until they intersect at i?, and draw RO intersecting the 

 primitive circle in C and C, A circle made to pass 

 through (7, m, m', and C , is the required projection of the 

 great circle through the points M and M' of the sphere. 



