in a very indistinct form certainly—that the motion of a planet is to be explained, not by a force acting in the direction in which it is moving, but by a force directed towards the sun, that is about at right angles to the direction of the planet's motion. Huygens carried this idea much further—though without special reference to astronomy—and obtained (chapter viii., § 158) a numerical measure for the tendency of a body moving in a circle to recede from the centre, a tendency which had in some way to be counteracted if the body was not to fly away. Huygens published his work in 1673, some years after Newton had obtained his corresponding result, but before he had published anything; and there can be no doubt that the two men worked quite independently.
171. Viewed as a purely general question, apart from its astronomical applications, the problem may be said to be to examine under what conditions a body can revolve with uniform speed in a circle.
Fig. 70.—Motion in a circle.
Let a represent the position at a certain instant of a body which is revolving with uniform speed in a circle of centre o. Then at this instant the body is moving in the direction of the tangent a a to the circle. Consequently by Galilei's First Law (chapter vi., §§ 130, 133), if left to Itself and uninfluenced by any other body, it would continue to move with the same speed and in the same direction, i.e. along the line a a, and consequently would be found after some time at such a point as a. But actually it is found to be at b on the circle. Hence some influence must have been at work to bring it to b instead of to a. But b is nearer to the centre of the circle than a is; hence some influence must be at work tending
