$ 1 8?, 189] The Shape of the Earth : Precession 235 



(chapter n., 42), but had remained a complete mystery 

 ever since. 



If the earth is a perfect sphere, then its attraction on 

 any other body is exactly the same as if its mass were all 

 concentrated at "its centre ( 182), and so also the attraction 

 on it of any other body such as the sun or moon is 

 equivalent to a single force passing through the centre o of 

 the earth ; but this is no longer true if the earth is not 

 spherical. In fact the action of the sun or moon on the 

 spherical part of the earth, inside the dotted circle in 

 fig. 72, is equivalent to a force through o, and has no 

 tendency to turn the earth in any way about its centre ; 

 but the attraction on the remaining portion is of a different 

 character, and Newton shewed that from it resulted a 

 motion of the axis of the earth of the same general 

 character as precession. The amount of the precession as 

 calculated by Newton did as a matter of fact agree pretty 

 closely with the observed amount, but this was due to the 

 accidental compensation of two errors, arising from his 

 imperfect knowledge of the form and construction of the 

 earth, as well as from erroneous estimates of the distance 

 of the sun and of the mass of the moon, neither of which 

 quantities Newton was able to measure with any accuracy.* 

 It was further pointed out that the motion in question was 

 necessarily not quite uniform, but that, owing to the unequal 

 effects of the sun in different positions, the earth's axis 

 would oscillate to and fro every six months, though to a 

 very minute extent. 



189. Newton also gave a general explanation of the tides 

 as due to the disturbing action of the moon and sun, the 

 former being the more important. If the earth be regarded 

 as made of a solid spherical nucleus, covered by the ocean, 

 then the moon attracts different parts unequally, and in 

 particular the attraction, measured by the acceleration pro- 

 duced, on the water nearest to the moon is greater than 



* He estimated the annual precession due to the sun to be about 

 9", and that due to the moon to be about four and a half times as 

 great, so that the total amount due to the two bodies came out about 

 50", which agrees within a fraction of a second with the amount 

 shewn by observation ; but we know now that the moon's share is 

 not much more than twice that of the sun. 



