Newton's errors with the rotational motion of fluids (Q1806801)

In propositions 51 to 53 of book II, section IX of the Principia, Newton considers the motion that is caused by the rotation of a cylinder or a sphere in a uniform and infinite fluid. According to the author, Newton's errors in this treatment of the rotational motion in fluids (which were first pointed out by G. Stokes in 1845) are due to the failure of neglecting angular momentum. It is shown that Newton's approach gives the same result as the modern method of tackling this problem, if angular momentum is taken into account. The paper ends with an outline of Newton's arguments against Descartes' vortex theory of planetary motion.