All-101 83 



result of the interaction of centripetal acceleration and 



gravity, onto the plane. We shall, therefore, neglect the 



small difference between the true equilibrium surface and 



the sphere. 



The apparent gravity, g, in (1) acts perpendicular 



to the spherical surface. V/e shall now consider g to act 



perpendicular to the equilibrium surface. V/e must then 



drop the term Q-r sin Q cos from the equation since, in 



reality, this force combines with g acting normal to the 



spherical surface, to give rise to a resultant normal to the 



equilibrium surface. Finally, g = g' - ^(i Q^r^sin Q) is 



r <c 



assum.ed constant. The final result of the approxilnate trans- 

 formation is to map the equilibrium free surface of the 

 ocean onto the x-y plane, with the apparent force of gravity 

 acting normal to this plane. 



