3 il 
the Rotatory Motion of Bodies . 
If C be~ D, y will be equal to the invariable quantity n ; 
^he projected track, a right line parallel to AD ; and the track 
oil the furface of the fphere, a lefier circle in a plane parallel to 
$he plane of the great circle CD. 
If Dm 1 be — Ca z the projected track will be the right line AR„ 
b 
and yr=-- ; x # ; the track upon the furface of the fphere be- 
ins; the great circle OR. 
u o 
In all other xafes in this projection, the track will be an by- 
t 
j, 
, and the 
la whofe center is A, femi-axis A a 
C a a- [)rr~ 
B 
Ca x oo D m M 
-axis 
c 
; the right line AR being always ah 
-ajypmtote. 
Fig. 4. When the track is projected on a plane ACD, to 
which the radius AB is perpendicular (the point D being the 
D 
vertex as before) the equation thereof will beqfxr — x m 
x 1 
a*, meafured from the center A upon AD, being = 0 (as before) ; 
und y, at right angles thereto s y. This projection of the track 
■of the pole will therefore always be an ellipfis a b (or a circle J 
whofe center is A ; femi-axis Aa*«; and the other femi-axis 
D 
c 
x m : except c be == h ; in which cafe the projected track 
will be a right line a b parallel to AC, 
Fig. 5. Moreover, the equation of the track projected on the 
;j)lane ABC, to which the radius AD is perpendicular, will be 
D 
y z ~ — Xn z — x z ; x, meafured from the center A upon AB, 
■being = £; and jy, at right angles thereto, — y. The track of 
the pole in this projection will therefore always be an ellipfis 
U 11 2 ab 
