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his pupils, Toricelli or Viviani, who were allowed to visit him in his last two or three years; it was kept by them for some time, and then published surreptitiously in Holland. Not that there is anything in it bearing in any visible way on any theological controversy; but it is unlikely that the Inquisition would have suffered it to pass notwithstanding. I have appended to the summary preceding this lecture (p. 160) the three axioms or laws of motion discovered by Galileo. They are stated by Newton with unexampled clearness and accuracy, and are hence known as Newton's laws, but they are based on Galileo's work. The first is the simplest; though ignorance of it gave the ancients a deal of trouble. It is simply a statement that force is needed to change the motion of a body; _i.e._ that if no force act on a body it will continue to move uniformly both in speed and direction--in other words, steadily, in a straight line. The old idea had been that some force was needed to maintain motion. On the contrary, the first law asserts, some force is needed to destroy it. Leave a body alone, free from all friction or other retarding forces, and it will go on for ever. The planetary motion through empty space therefore wants no keeping up; it is not the motion that demands a force to maintain it, it is the curvature of the path that needs a force to produce it continually. The motion of a planet is approximately uniform so far as speed is concerned, but it is not constant in direction; it is nearly a circle. The real force needed is not a propelling but a deflecting force. The second law asserts that when a force acts, the motion changes, either in speed or in direction, or both, at a pace proportional to the magnitude of the force, and in the same direction as that in which the force acts. Now since it is almost solely in direction that planetary motion alters, a deflecting force only is needed; a force at right angles to the direction of motion, a force normal to the path. Considering the motion as circular, a force along the radius, a radial or centripetal force, must be acting continually. Whirl a weight round and round by a bit of elastic, the elastic is stretched; whirl it faster, it is stretched more. The moving mass pulls at the elastic--that is its centrifugal force; the hand at the centre pulls also--that is centripetal force. The third law asserts that these two forces are equal, and together constitute the tensio
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