PER LA STORIA DELLA TEORLA. DELLE SUPERFICIE GEOIDICHE 1031 



" of the line u along vliich it acts. Then J \]du must be added 

 " to the potential in the equation of fluid equilibrium of Art. 73. 



. • . [^ i^ = V + ^ r\l — \x^) -f I U(/?^ = const. at the surface (1). 

 " Putting iv^ = w — 2" and substituting for V from Art. 91; 



(A) const = 7" + (' ~ 1) (i ~ ^' ) "^ + 



+ ^^(i-Mr-ffuc^t.. 



" Now when the small force U is neglected 



^=1 + 6^1 

 r 



" Hence, neglecting small quantities of the second order and 

 " dividing by E, and multiplying by a, 



const = ^ + ^ (t ~ ^') +UU^w; 

 . • . — = Constant. + ^ |li* — ^ 1 U e? m. 



" Comparing this with the value of -^ when U is neglected, 

 "' we bave 



1 dr 



" Now — ^ is the tangent of the angle between r and 

 "" the normal = tang. ip suppose. 



(1) tv è la velocità angolare della Terra; fJ = cos 9, 6 l'angolo che r 

 fa coll'asse z di rotazione. 



