the Rotatory Motion of Bodies. zj $ 
the diftance r from the axis; and whilft it is fo revolving 
let the faid pole be urged to turn about a diameter of the 
/ / 
mid-circle vqs towards q, by an accelerative force f, and 
let fuch force continue to a<ft on th&fucceffive new poles 
tt at 
p, pf Sec. as they become fuch, always urging the fphere 
to turn about a diameter of the contemporary mid-circle, 
whilft the direction in which fuch perturbating force 
acts is regulated in the following manner. 
Conceive the faid revolving fphere to be furrounded 
by an immoveable concave fphere of the fame ra- 
t // at 
dius r. Then the momentary pole (/>,/>, />> 'Sec.)" will 
/ it i.i> 
always be found in fome curve pp? Sec. in the faid 
i it Hi 
concave fphere, and in fome curve ppp Sec. on the 
revolving fphere; which laft mentioned curve will conti- 
/ a tit 
nually touch and roll along the bther curve p pp Sec. on 
the immoveable fphere, the force f and the direction in 
which it a6ts varying in any manner whatever. Let f 
be invariable; then, it is obvious, the two curves fo 
touching each other will be circles ; and if great circles 
t / an tit nt 
p y, p y, p y, Sec. be deferibed on the furface of the im- 
moveable fphere whofe planes fliall be at right angles to 
,/ // /// . ✓ // ttf > 
the plane of the circle ppp Sec. the points q, q, q, Sec. 
N n 2 therein, 
