the Uofato^y Motion of BoJieS, 



J" 



I 



It CberrD, y will be equal to the invariable quantity « J' 

 the projected track, a right line parallel to AD ; and the track 

 on the furface of the fphere, a lejjer circle in a plane parallel to 

 the plane of the great circle CD. 



If D/«" be::=C^?" the projeded track will be the right line AR, 



r 



andj/zr-^^ xa;; the track upon the furface of the fphere be- 

 ing the great circle CR. 

 " In all other cafes in this projection, the track will be an by' 



Co^c^TL)^ 



^erboU vAio^Q center is A, femi-axis Aa— — —z , and the 



; the right line AR being always an 



Other lemi-axis r: ;: 



ajypmtote. 



Fig. 4. When the track is projected on a plane ACD, to 

 which the radius AB Is perpendicular (the point D being the 



vertex as before) the equation thereof will hty~ — .— x ;;r - x~ ; 



a;^ meafjred from the center A upon AD, being ~ ^ (as before) ; 

 andjv, at right angles thereto = 7. This projection of the track 

 of the pole will therefore always be an elUpjis a b (or a circle } 

 whofe center is A ; femi-axis A a = ;« ; and the other femi-axis 



r=— ] yim: except ^ be = 3; in which cafe the proje£led track 



^ill be a right line a b parallel to AC. 



Fig. 5. Moreover, the equation of the track projeCled on the 

 plane ABC, to which the radius AD is perpendicular, will be 



y''— — y,n'' — x^\ x^ meafured from the center A upon AB, 



being =z)S; andjy, at right angles thereto, =y. The track of 

 the pole in this projedtion will therefore always be aii eUipfis 



U u 2 ab 



