PER LA STORIA DELLA TE0RL4. DELLE SUPERFICIE GEOIDICHE 1029 



" In the case of the Ocean the forces are the centrifugai 

 " force, the attraction of the general mass of the Earth, and 

 " these three disturbing forces W, Mi and Mj which I have 

 " been calculatìng (1). 



" Let tu be the angular velocity of the earth round its 

 " axis, 6 the latitude of any point of the surface, r its distance 

 " from the earth's centro, a the semiaxis major of the mean 

 " meridian. Then uu^^c and yiì^y is the centrifugai force parai] el 



" to X and ij, z beeing the earth's axis, and -r-uj^a^cos^G is the 



" corresponding part of the above equation. Let V be the po- 

 " tential for the earth's mass, supposed a perfect spheroid of 

 " equilibrium differing little from a sphere ; E the earth's mass. 



" Then V differs from -^ only by a small variable quantity 



" depending upon the ellipticity: let it equal — (1-f-U). Substi- 



" tuting these and the three disturbing forces the equation of 

 " the surface now becomes 



const = — (1 -|- U) -|- ^ uj^a^cos'6 -|- 

 + ^W rf \ — j Mi (^ t^ — j Ma d u (2) 

 " between the several limits, as already explained, or 

 const = -^ (1 -[- U) + -o" "J^«^ cos'è -\- Lg ; 



.-. const= f- 1 1 +U + ^?:^5^) +L ^ (3). 



(1) Le forze W, M,, Ma, calcolate in paragrafi precedenti, rappresentano 

 l'azione del mare, e delle due parti in cui l'autore divide la regione 

 montuosa. 



(2) X ed « sono quantità che valgono a determinare la posizione del 

 punto considerato. 



(3) g e la gravità. 



