Figure of the Earth. 489 



This is the sun's effect. The moon's effect must be added 

 to this. The mean place of the moon is in the ecliptic, and 

 if the action of the moon be taken to be the same as that of 

 a similar body always in the ecliptic at the moon's distance 

 the error will be small. 



Let 8, E, M denote the sun's, earth's, and moon's masses ; 

 d s , d u the sun's and moon's distances from the earth: then 



Moon's effect ®k 



Sun's effect S^ 



*l 



E-f-M 



M d l 



M 



M + E S 



d s 



1 



1 (Moon's Period) 2 



82_ _JL_ 



(Earth's Period) 2 



1 /365^ 2 



= 2-18 about. 



Hence the effective moment of momentum created by the 

 combined action of the sun and moon 



.= 3*18 xf 7r 2 Bn sin *(-931). 



If I is the moment of inertia of the earth and co, as before, 

 its angular velocity of rotation, this effect turns the earth's 

 axis through 



3-18 x-fAB sin *(-931) ,. 



- f radians. 



lco 



But the earth's axis describes a cone of semi-vertical angle 

 a in 26,000 years. Hence the angle turned through by the 

 earth's axis in one year is 



27rsina 



26000 ' 



Therefore '93 1 x 3*18 X 1 7r 2 Bn sin a _ 2 7r sin a 



26000 * 



