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than the gravitational pull at the surface of the Earth. Many years later, Newton wrote that he had found the comparison to 'answer pretty nearly', but it would appear that at the time he was slightly disappointed in the lack of quantitative agreement, and so turned his mind to other studies, in particular his researches into optics. It should also be emphasized that at this time Newton still adhered to the Cartesian vortex theory, so what he had actually demonstrated was that, in the whirlpool of the terrestrial vortex, the endeavour of bodies to move out of their circular orbits varied, at least approximately, as the inverse square of the distance from the Earth. Thus, while this statement clearly is important, Newton was still a long way from any concept of universal gravitation and had not yet formulated his dynamics in terms of central forces and tangential inertia.

The year 1679 was a crucial one in the development of Newton's thought on planetary motion. By this time Newton had come to appreciate the many inadequacies in the vortex theory and had freed himself of much of the restrictive Cartesian baggage. He was unwilling still (like most other astronomers) to accept Kepler's second law as being true, since it had no firm mechanical foundation. The area law was, however, becoming more well known, particularly through the works of Nicholas Mercator - a Danish mathematician who lived in London - and it was clear that whatever the correct law, it had to give results close to those produced by the area rule. Newton recognized that planetary orbits certainly were approximately elliptical, but did not believe there was sufficient empirical evidence to be certain of their exact elliptical nature. The catalyst for the fundamental change in Newton's thought was an exchange of letters with Robert Hooke.

During the latter half of the seventeenth century, there was much discussion in England concerning the precise nature of planetary orbits and the relation

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