All-101 20 



The rectangular coordinate system is oriented with the 

 origin in the southwest corner of the ocean and v/ith the equili- 

 brium surface in the x-y plane. 



A number of assumptions were made in the reduction of 

 the four equations valid on a spherical earth to the four equa- 

 tions given above« These assumptions are listed here for the 

 convenience of the reader v;ho does not wish to go through the 

 detail in Appendix 1, 



(1) In the radial component of the equations of motion^ 

 the acceleration terms and the viscous terms are 

 neglected in comparison to g, the gravitational accel- 

 eration. In essence, we assume hydrostatic pressure » 



(2) All terms involving radial velocity are neglected in 

 the remaining t\Jo equations of motion on the supposi- 

 tion that the radial velocity is very small compared 

 to the lateral velocities. 



(3) The variation of the radial distance, r, over the 

 depth of the ocean is neglected and v;e write r ^ R, 

 the mean radius of the earth, 



(Actually, tho radial distance varlos by about 1/1000 

 of its total length.) 



ih) Terms which are divided by R are neglected in compar- 

 ison v;ith all other terms, 



(5) The region considered must not lie close to the north 

 pole since some terms which have been neglected 



* In Appendix 3. this assumption is discussed in more detail. 



