[ 45J ] 
Corollary II. 
Therefore the centrifugal Force does not diminifh 
in the Plane of the Equator in the inverted Ratio of 
the Squares of the Diftances from the Centre ; for 
iince FS=.fs\ F.f:.s.S. But the Points being 
fuppofed equal on both Sides, their Sums are as the 
Circumferences, and one has s.S. :: d. F), which 
gives F.f \ ; d.i), inftead of ; ; dd. F> F). 
Corollary III. 
Therefore Keplers Rules cannot be obferved in 
the Vortex^ or at ieaft in the Plane of its Equator ; 
for fince F.f\ :d.F> i by putting in the Place of F,f, 
their Values, we (hall have iid.F), and there- 
fore u and T>^.d^ wTT.tt. whereas we ought 
to have V>ui \V d.<\/ D and d^ \:TT.tt* 
Remark. 
There is here a Finejfe of the Cartejians to be 
obferved. Thefe Gentlemen confider only the 
librium of the fpherical Layers of the VorUXy and 
from the Equality of their central Forces they deduce 
Keplers Laws, as well as they can. 
Bur it is manifeft, that whatever becomes of the 
Equality of Force in different fpherical Superficies of 
the Vortex, there muft be an iiyFquilibrium in the 
Plane of the Equator 5 becaufe it is in this Plane that 
the Planets move j and if there had not afluaily been 
an ^_yEquilibrium between its Points, they would 
foon place themfelves there, by reafon that Fluids 
always 
