CHAPTER XIII. 



RELATIVE MOTION AND UNIVERSAL GRAVITATION. 



275. IN the course of this book we have, in order to avoid 

 interruptions of the argument, made a number of statements of a 

 provisional character. Such, for example, were the statement in 

 Article 3 concerning the method of measuring time, the state- 

 ments in Articles 90, 91, and 94 concerning the relations between 

 weight, mass, acceleration due to gravity, and gravitational force 

 exerted by the Earth upon a body, and the statement in Article 

 88 that frames of reference can be chosen for which the Postulates 

 of Mechanics apply to natural bodies. We shall now reconsider 

 all these matters, and we shall find it convenient to begin with an 

 account of the motion known as the rotation of the Earth, and its 

 effects as observed in the cases of foiling bodies and pendulums. 



276. Rotation of the Earth. It is a fact of observation 

 that there is a relative motion of the Earth and stars by which 

 every star moves relatively to the Earth continually from East to 

 West, or, what is the same thing, by which any part of the Earth's 

 surface moves relatively to the stars continually from West to 

 East. This motion can be precisely described by saying that, 

 relatively to the stars, the Earth rotates about its polar axis ; the 

 magnitude of the angular velocity is such that the Earth turns 

 through four right angles in a sidereal day, and the sense is such 

 that the positive sense of the axis of rotation is from South Pole 

 to North Pole. We shall use the letter II to denote the angular 

 velocity of the Earth's Rotation. 



In the statement of the Law of Gravitation in Article 97 we 

 said that the forces between bodies in the solar system are 



