708 Prof. P. Lowell on the Limits oj the 



At the centre, therefore, 



MM., 



u= — — — where w = 0. 



p b ' 



Similarly the pressure from an equatorial canal is 

 M 4tt 2 



} /M 4tt 2 \ , 



, M , 2tt 2 o , n 



and the pressure at the centre 



_M M 2tt 2 . LV 2 



— - — - + -mr-P — t,tt a , where p=Q; 



whence, since the two pressures are equal, 



M M M M , 2tt 2 . 2tt 2 . 



M 



It might seem at first as if the term — vitiated any 



solution. For becoming infinite when p=0we have in our 

 equation infinite terms side by side with finite ones from which 

 no conclusion could be drawn. 



17. But let us look into this more closely. As the radius p 

 of the kernel contracts to its limit zero, the ratio of the centri- 

 fugal force to the equatorial attraction itself decreases to zero, 

 since the one force depends on p directly, the other on its 

 inverse square. In consequence the polar and the equatorial 

 forces tend to equality as they severally tend to infinity. At 

 the limit the terms so introduced therefore cancel each other. 

 The kernel in fact becomes perfectly spherical. 



M 

 Transferring these terms - to the same side of the 



equation, we have V 



M_M_M_M 27T 2 9 

 p p ~ a b + T 2 a ' 



2-7T 2 



since the term T^rp 2 at the limit =0. 



As p tends to zero, the left side eventually becomes 

 M _ M _ 



