302 NEWTON S PRINCIPIA. 



Bernoulli s second objection has more force, according 

 to our preceding investigation, the friction being 



and the arm of the lever at which this acts being r, we 

 have 



o dca . 



,3__ 8r . 



to be constant for all values of r, this gives 



= ~^ + e- 



If a sphere begin to rotate and communicate an angular 

 velocity to the surrounding fluid, the inner parts of the 

 vortex will move quicker than those without, and these 

 by friction will be continually communicating velocity to 

 those outer strata. The vortex created will, therefore, 

 always grow larger and larger, and the motion of the sphere 

 will be continuously transferred from the centre to the 

 circumference, until it is swallowed up and lost in the 

 boundless extent of space. Hence there must be some 

 active principle which may tend to communicate velocity 

 to the cylinder, otherwise it will move slower and slower 

 and finally lose all its motion. If any motion had been 

 communicated to the infinite fluid also, the friction of the 

 fluid and cylinder will never cease to retard or accelerate 

 that body until the whole fluid and cylinder revolve round 

 with the same angular velocity. This, therefore, ought to 

 be the state of the Cartesian vortex. But it is well known 

 that the planets do not describe their orbits in the same 

 time. 



Newton next argues that even if we grant the existence 

 of an active principle that will keep up the angular velo- 



