APP. B.] 



APPENDIX 



517 



B. — In Graduating a Chart on the Gnomonic Projection, 



To show that the angle of half couvergency laid off from the rectangle 

 intersects the opposite meridian on the parallel, and also that the further 

 subdivisions of the convergoucy intersect their respective meridians on the 

 same parallel. 



Fig. ii8. 



From K and H, the grariuating positions, draw the true bearings, lines 

 K P, P G, which are meridians and will meet at P, the pule of the 

 projection, making the angle K P C, or the Convergency. 



Make H C = difference of latitude of H and K. Then P C will equal P K. 



Join K 0, bisect it in D, and join P D, the central meridian. Lay off 

 K G perpendicular to K P. 



Then /_ K G is the half convercrency ; 

 For in A P D K . . . D K P = 90 - D P K, 

 and as F K P is drawn = 90; 



...... DKP = 90- DKF: 



.'. D P K = D K F. 

 But D P K = 1 K P C the convergency ; 



. • . D K F or C K G = 5 convergency. 



Q. E. D. 



