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held by Kepler, the actual velocity itself required preservation by force. Thus he looked for tangential forces, as in the accompanying figure (4). But according to the Newtonian law, apart from some force the planet would move for ever with its existing velocity in a straight line, and thus depart entirely from the sun. Newton, therefore, had to search for a force which would bend the motion

round into its elliptical orbit. This he showed must be a force directed towards the sun, as in the next figure (5). In fact, the force is the gravitational attraction of the sun acting according to the law of the inverse square of the distance, which has been stated above.

The science of mechanics rose among the Greeks from a consideration of the theory of the mechanical advantage obtained by the

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