337 

 r3 = o, ¥4 = 0,... Yi = 0, 



or 



/6(J.-l)e. + 5,fl 



^ V 2(5Z)-3) ^ ^^ 



and, therefore, 



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

 revolution having the ellipticity 



5gD + 6(Di- l)ei 

 2(5Z)-3) 



" 3. If the difference between the elHpticities of the spheroid 

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

 presented by £, vpe shall have 



5qD- 2(5D-3Di)ei , , 



'" 2(5Z)-3) ■ ^''' 



This expression shows, that when 5Z) > 3Z)i, e will decrease 

 when e\ increases. In the actual case of the earth we should 

 have £) = 2Z)i nearly, and consequently 



(55'-7ei)Z)i 



£ = 



{pD - 3) 



5(7 



£ cannot be negative, and if it become zero, e\ = — . But 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 -r^r-rr' T1"S quantity is, however, too 

 ^ 404. b 



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



