All- 101 21 



previously become infinite at the pole. In our prob- 

 lem the ocean is confined to a region lying southof 

 latitude 70°. 

 (6) An appropriate interpretation of the results as applied 

 to the spherical earth must be made, keeping in mind 

 that the boundaries have been distorted. If we con- 

 sider a rectangular ocean in the plane , the appropri- 

 ate mapping onto the sphere v;ould preserve the con- 

 stant east-west length. Such a mapping is not conform- 

 al since angles are not preserved. (In the case of a 

 Mercator projection, on the other hand, angles are 

 preserved, but the east-west distance is distorted.) 



Let us consider the simplified equation of vertical 

 motion (3)« In integrated form, this equation is 



r>^ 



pdz (3»a) 



P = g 



where r] measures the deflection of the free surface from its 

 equilibrium position and the scale of p is chosen in such a 

 manner that p = Oonz=T], Now, the density is a function of 

 temperature and salinity. In our treatment of the problemj how- 

 ever, we wish to avoid the analytical difficulties introduced 

 by including, explicitly, the energy equation and an equation of 

 state. We propose instead to account for the thermodynamics of 

 the problem empirically by prescribing a density distribution 

 which roughly conforms to observation'". In particular, we 



* In Appendix 3 it is shov/n that a specification of the density 

 distribution and the assumption of hydrostatic pressure are 

 not necessary for the steady problem. 



