the Rotatory Motion of Bodies . 285 
Moreover, referring to our obfervation in art. 8. let 
u-e be to — x p pr (the value of v) as c tod, u being 
1 i . cd b z — r 2 , , 
greater than e ; or let e—u be to — x pr— j y as ctoa^u being 
lefs than e: whence, in both cafes-, we fhall have the 
( f r ^ If- \ 
yx — ) for the value of u-e; and: 
f }f 
eonfequently u, in both cafes, will be = e + — x prpry • 
Conceive now a fpherical furface without matter, 
having the fame center and radius as the equator de, to 
be carried about with the revolving fpheroid; and fup~ 
pofe a fphere, whofe radius is r, to revolve about an 
axis pen with the angular velocity e r and, whilft it is 
lb revolving, let an accelerative force (f) equal to 
T*?TP or r x v+T 2 5 according as a is lels or greater 
than r, urge the pole />, and the fucceffive momentary 
poles as they become fuch, to turn about a diameter of 
the contemporary mid-circle in the manner exprelfed in. 
, , . f 1 r 2 -b z cd r z — b z 
art. o. u being to v as e + to — x y-yy or as e + 
-x -r-^p to — x prp-p. , according as a. is lefs, or greater 
than r. Then will the motion of the furface of this 
fphere be exactly the fame as the motion of the faid 
fpherical furface carried about with the revolving 
fpheroid 
