will 
-280 Mr, landen’s new theory of 
If u be negative the arc pr whofe fine is ^===e 
be greater than 90°. 
8. The motion of the fphere according to the regula- 
tion in the preceding article is one motion compounded 
of the primitive motion of the fphere and the motion 
generated by the action of the force f. But conceiving 
the velocity of the point Q_to arife from an 
impulfe given to it whilfl: the fphere revolved about an 
axis of which Qjwas an immoveable pole before fuch im- 
pulfe, and about which the mid-circle correfponding to 
that primitive axis revolved with the angular velocity 
-e.ecn u ( a ) 
and confidering that the force f, continually 
aching at right angles to the momentary direction of the 
point Q_and to the plane of the faid mid-circle, only ferves 
to alter the pofition of the faid primitive axis ; we may, 
by the help of what is done above, explain the motion 
which the fphere will have, during the adlion of the 
force F, fo as to retain in our ideas the two primitive mo- 
tions (one about the axis qo, and the other about a dia- 
meter at right angles to that axis) as remaining diftindt 
and unaltered. 
(a) Denoting this by c and the velocity of Qpy d, y/ d + d 1 is e, agree- 
.able to art. j , 
Fig- 
