62 V. S. COAST AND GEODETIC SURVEY. 



In figure 22 construct the projection of the great circle 

 passing through P and Q, the projections of the two given 

 points, by the method of problem 7. Draw NS the diam- 

 eter determined by the intersections of this great circle pro- 

 jection with the primitive circle and draw the perpendicu- 

 lar diameter WE. This diameter is then the line of meas- 

 ures. Locate the projection of the pole of SRN by drawing 



IT 



SRT and by laying off TU=^7 and by then drawing S U, 



thus locating K, the projection of the pole. Draw KP and 

 KQ and prolong them to intersect the primitive circle in 

 P' and Q\ respectively; then P' WQ^ is the great circle arc, 

 between the given points of which P and Q are the projec- 

 tions. ZP' and KQ^ are the projections of circles passing 

 through the point of projection and through the pole of the 

 great circle of which SPQN is the projection. But the 

 point of projection is the pole of the primitive circle; hence 

 the planes that determine the projections KP^ and KQ^ 

 cut off equal arcs on the great circle, whose projection is 

 SPQN and the primitive circle. Therefore, the arc P'Q' 

 is equal to the arc of which PRQ is the projection. 



This problem can be solved, together with that of deter- 

 mining the projection of the great circle passing through 

 the projections of the two given points in the following 

 manner: 



