C w ] 
higher Proportion than the Velocities requifite to 
carry Bodies in Circles about the fame Centre, the 
Velocity in the lower Part of the Curve may exceed 
the Velocity in a Circle at the fame Diftance, and 
thereby become fufficient to carry off the Body again. 
But while the Diftance decreales, if the Velocities in 
Circles increafe in the fame or in a higher Propor- 
tion, than the Velocity in a Traje&ory can increafe, 
the Body muft either continually approach toward the 
Centre, if it once begin to approach to it, or recede 
continually from the Centre, if it once begin to 
afeend from it 5 and this is the Cafe, when the cen- 
tripetal Force increafes as the Cube of the Diftance 
decreafes, or in a higher Proportion. But though, in 
fuch Cafes, the Body approach continually towards the 
Centre, we are not to conclude, that it will always 
approach to it till it fall into it, or come within any 
given Diftance 5 for it is demonftrated afterwards in 
Art. 879 and 880. that it may approach to the Centre 
for ever, in a Spiral that never defeends to a given 
Circle deferibed in the fame Plane, and that it may 
recede from it for ever in a Spiral that never arifes to 
a given Altitude. An Example of each Cafe is given 
when the centripetal Force is inverfely as the Fifth 
Power of the Diftance. 
When theTraje&ory is deferibed in a Medium , let 
z be to a given Magnitude as the centripetal Force is 
to the Force by which the fame Traje&ory could be 
deferibed in a Void ; and if the Area be fuppofed to 
flow uniformly, the Refiftance will be in the com- 
pound Ratio of the Fluxion of z> and of the Fluxion 
of the Curve 5 and the Denfity of the Medium (flip- 
poling the Refiftance to be in the compound Ratio 
Y y ©f 
