THEORY OF POLYGON IC TROJECTIOXS. 



41 



The parallels and meridians form, then, an orthogonal net 

 of circles. 



(ds - dp\ 



a cos ^ 



cos a cos ip 

 (sin a + sin ip) 



X 



cos X + cos a COS ip + sin a cos X sin <p 1 + sin a sin <^ 

 1+sin a sin <;^ + cos a cos \ cos (p (sin a + sin ipY- 



^ 1 



1 + sin a sin (p + cos a cos X cos <p 



h 



p a cos <^ 



1 



dX 



sin a + sin ip 



sm a + sm ip 1 + sm a sm (p + cos a cos X cos <p 



^ 1 



"" 1 + sin a sin cp + cos a cos X cos <p 



/ao' 



Fig. 10.— Stcreographic horizon projection of a hemisphere— horizon of Paris. 



