the Rotatory Motion of Bodies. 
rv 
; and it follows, that 
ev 
*79 
, , , , , , ( = — ) will be 
equal to the velocity of the point q_, and likewife of its 
oppolite point (o^ in the furface of the fphere. It alfo 
follows, that k, the radius of each of the circles defcribed 
by thofe points, during the action of the force f will be 
, rev 
equal to -7== — .. 
V u z -{-v x xv e — + v z 
By what is done it appears, that during the aflion of 
the force F, the motion of the revolving fphere will be 
/ it ni 
regulated by the circle ppp Sec. thereon (whofe radius is 
^3=== = ■■ = — continually touching and rol- 
* 2 S 
r f 
i n nt 
ling along the immoveable circle ppp 8ec. (whofe ra- 
dius is 
— - = ~r r ? fo that the velocity of the 
y/u 1 + Vi +*!£/ 
point of contrail be = v = — . Conlidering the point Q_as 
t it m 
always urged from the points p, p, p, 8ec. and confe- 
quently its oppolite point (o) towards thofe points, it is 
neceflary to obferve, that according as u is lefs or greater 
than e, the arc pq^ (whofe fine is — wilt be lets 
or greater than 90° ; and the point (o) oppolite to q_ 
on the furface of the fphere will accordingly be at a, 
i 
greater or lefs diftance than 90° from p. 
If 
