2.82 Mr. landen’s new 'theory of 
It is obfervable, that the laft mentioned velocity will, 
according to this regulation of the motion, be to the 
primitive angular velocity about the axis of which ojs a 
pole, as v to e—u, or as v to u-e, according as u is lefs or 
J 
greater than e\ that is, according as the arc pQ_is lefs or 
greater than 90°. 
9. From what has been faid it follows, that denoting 
the two primitive angular velocities 
e.e r s: u 
e — d + v z 
and 
ev 
—»l +v 
(fpecified in the preceding article) by c and d 
refpe&ively, the radius (fig, 5.) of the circle ppp See. 
dr 
(or fine of the arc pq=pq_, Sec.) will be = — ; the radius 
4 it iii * Ji 
of the circle ppp 8ec. (or fine of the arc pr=pr, Sec.) = 
— t a great circle oaffing through the, 
primitive poles o and eg, on the revolving fphere, will 
turn from the pofition oRCgwith the velocity^ meafured; 
at the mid-circle,, or with the velocity — ■ 
meafured at the fixed point r ; whilft thofe poles deferibe, 
i // W 
with the velocity d, circles parallel to ppp See. the 
radius (k) of each of the circles (fig. 6.) fo deferibed 
2 being 
