aY,= 



337 



or 



"^-" V 2(5£>-3) ^ ^^ 



and, therefore, 



This is an expression for the radius of a spheroidal surface of 

 revolution having the ellipticity 



5qD + 6(Di- l)gi 

 2(5Z)-3) 



" 3. If the difference between theellipticities of the spheroid 

 bounding the fluid, and that bounding the solid mass, be re- 

 presented by £, we shall have 



_ 5qp-2(5 D-3Di)ei ,. 



'" 2{5D-3) 



This expression shows, that when 5D > 3Du £ will decrease 

 when ei increases. In the actual case of the earth we should 

 have D = 2Di nearly, and consequently 



{5q - l ei)Di 

 ' ^ {oD- 3) ■ 



oq „ 

 t cannot be negative, and if it become zero, a = -y. liut q 



being the ratio of centrifugal force to gravity at the equator, 

 and, therefore, its value being — , we should have the ellip- 

 ticity finally attained by the earth, from the action of super- 

 ficial causes, equal to ^^. Tins quantity is, however, too 

 small to be admissible, and, consequently, the above result 



