Ohlateness of a Rotating Planet. 703 



The attraction on a particle at its equator is 



the second term being the centrifugal force, 

 where T= the period of the spin. 



8. The pressure due to a small part dp of the polar canal 

 at the point p is 



— Vpdp, 



where P = 4?r/>^-- — ^ - -J, 



and the pressure due to the whole canal at the point 



= -§Fpdp=-iFp 2 + C. 



We determine C by the condition that at h the pressure 

 ceases. 



Consequently, 



-*P/ + C = or C=^P6 2 , 

 and therefore at the centre, where jt? = 0, the pressure is 



=\w. 



Similarly for the equatorial canal, if 



Q = 2tt / > Vl-e^— ^- — e , )- T , 



the pressure at the centre = ~ Qa 2 . 



Since these must be equal for equilibrium, we have 



P6 2 = Qa 2 , 



or ~Pb a ( . 



Qa~6 ; W 



but P& is the force at the pole and Qa is the force at the 

 equator. These then are to each other as 



