* is?] Relativ: .'\fotion .- fhe Snap / the Earth 233 



187. The variation of the tin,c of oscillation of a 

 pendulum in different parts c" .ne earth, discovered by 

 Richer in 1672 (chapter vm $161), indicated that the 

 earth was probably not a sy iere. Newton pointed out 

 that this departure from the >pherical form was a conse- 

 quence of the mutual gravitation of the particles making 

 up the earth and of the earth's rotation. He supposed a 

 canal of water to pass from the pole to the centre of the 

 earth, and then from the centre to a point on the equator 

 (BO a \ in fig. 72), and then found the condition that these 

 two columns of water OB, o A, each being attracted towards 

 the centre of the earth, should balance. This method 

 involved certain assumptions as to the inside of the earth, 

 of which little can be said to be known even now, and 

 consequently, though Newton's general, result, that the 

 earth is flattened at the poles and bulges out at the equator, 

 was right, the actual numerical expression which he found 

 was not very accurate. If, in the figure, the dotted line is 

 a circle the radius of which is equal to the distance of the 



those bodies. If, for example, we look at Newton's First Law of 

 Motion (chapter vi., 130), we see that it has no meaning, unless we 

 know what are the body or bodies relative to which the motion is 

 being expressed ; a body at rest relatively to the earth is moving 

 relatively to the sun or to the fixed stars, and the applicability of the 

 First Law to it depends therefore on whether we are dealing with its 

 motion relatively to the earth or not. For most terrestrial motions 

 it is sufficient to regard the Laws of Motion as referring to motion 

 relative to the earth ; or, in other words, we may for this purpose 

 treat the earth as "fixed.'' But if we examine certain terrestrial 

 motions more exactly, we find that the Laws of Motion thus interpreted 

 are not quite true ; but that we get a more accurate explanation of 

 the observed phenomena if we regard the Laws of Motion as referring 

 to motion relative to the centre of the sun and to lines drawn from it 

 to the stars; or, in other words, we treat the centre of the sun as a 

 " fixed " point and these lines as " fixed " directions. But again when 

 we are dealing with the solar system generally this interpretation is 

 slightly inaccurate, and we have to treat the centre of gravity of the 

 solar system instead of the sun as " fixed." 



From this point of view we may say that Newton's object in the 

 Principia was to shew that it was possible to choose a certain point 

 (the centre of gravity of the solar system) and certain directions 

 (lines joining this point to the fixed stars), as a base of reference, 

 such that all motions being treated as relative to this base, the Laws 

 of Motion and the law of gravitation afford a consistent explanation 

 of the obseived motions of the bodies of the solar system. 



