where

Suppose, further, that

where

We wish to demonstrate that

Let

Note, from Equations (12.192) and (12.194), that

It follows from Equations (12.191), (12.193), (12.197), and (12.198) that

Equations (12.199) and (12.201) imply that

and

Furthermore, Equation (12.200) yields

Multiplying by , integrating over the ocean, and making use of the boundary condition (12.204), we obtain

(12.201) |

Here, is the surface of the Earth that is covered by ocean, and . It follows that is a constant. Thus, Equations (12.202) and (12.203) imply that , and, hence, that Equations (12.195) and (12.196) are valid.