66 U. S. COAST AND GEODETIC SURVEY. 



vertical projection of the line MM^ and rr' is the hori- 

 zontal projection of the same line. Prolong TT* tmtil it 

 intersects the line S'S at TJ' and erect the perpendicular 

 VR intersecting rV prolonged in i?. i? is the trace of the 

 line MM' on the horizontal plane, which is here the 

 primitive plane. RO is then the trace of the great circle 

 plane on the horizontal or primitive plane. This deter- 

 mines the points C and C, through which the projection 

 of the great circle must pass. A circle made to pass 

 through the points C, m, m', and C is the required pro- 

 jection. Note that m'm produced passes through the 

 point R, as it should. 



Problem 9, — To lay off on a great circle an arc of given 

 length from a given j)oint P: 



Determine the projection of the pole of the given great 

 circle projection. In figure 22 let K be the projection of 

 the pole of the great circle of which the arc SPRQN is the 



Projection; draw KP intersecting the primitive circle in 

 *'. Lay off the given arcP'Q' on the primitive circle and 

 draw KQ' intersecting the projection of the great circle 

 in Q; then PQ is the projection of the required arc. 



Problem 10. — ^The projection of a great circle and that 

 of a point being given, to construct the projection of the 

 great circle passing through the given point and perpen- 

 dicular to the given ^eat circle : 



Determine the projection of the pole of the given great 

 circle and then construct the projection of the great circle 

 passing through this pole and the given point; this is the 

 required projection. 



Problem 11. — To construct the projection of a great 

 circle which passes through a given point and which is 

 inclined at a certain angle z to the primitive plane: 



