  Complicating the matter further was the publication in 1689 of Leibniz's “Essay on the causes of celestial motions,” which offered a vortex theory in which “a planet moves with a double motion composed of the harmonic circulation of its fluid deferent orb, and the paracentric motion, as if it had a certain gravity of attraction, namely an impulsion towards the Sun” [L,  132].[16] Leibniz further concluded that when the body “is carried in an ellipse (or another conic section) with a harmonic circulation, and the centre both of attraction and of circulation is at the focus of the ellipse, then the attractions or solicitations of gravity will be directly as the squares of the circulations, or inversely as the squares of the radii or distances from the focus” [L, 137]. So, within a year and a half of the publication of the Principia a competing vortex theory of Keplerian motion had appeared that was consistent with Newton's conclusion that the centripetal forces in Keplerian motion are inverse-square. This gave Newton reason to sharpen the argument in the Principia against vortices.