214 



A Short History of Astronomy 



[Cn. IX. 



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 VIIL, 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 condiiions a body 

 can revolve with uniform 

 speed 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. Conse- 

 quently by Galilei's First 

 Law (chapter vi., 

 . 130, 133), if left to 

 itself and uninfluenced by any other body, it would con- 

 tinue to move with the same speed and in the same 

 direction, i.e. along the line A a, and consecjuently 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 



FIG. 70. Motion in a circle. 



