522 EIGHTH PACIFIC SCIENCE CONGRESS 



oceans, induced by the superincumbent, quasi-permanent wind system 

 (westerlies or trades), the equation of continuity as given by (5) will 

 not cause serious errors in the results. 



There may be some further question concerning the use of (5) for 

 the continuity equation. But, in treating the oceanographic data for 

 estimating geostrophic currents, we always assume 



1 dp 



■If — _i_ *■ 



2a}p sin (ji dy 

 1 dp 



2ti>p sin cj) dx ' 



provided the frictional terms are neglected. These expressions impiv 

 that geostrophic currents usually satisfy the equation (5), which shows 

 the absence of horizontal divergence. This means that the equation 



_1^ + -^ =0 



9x dy 



may be used without serious errors in treating the general circulation 

 of the oceans. 



On eliminating p bet^veen the two ecjiiations of (1) by cross- 

 differentiation, we have 



\dy'- a.x^ / ^ 3z L dz \dy dz /J 



d 



+ 2a)p -7- (sin</,)t; = (6) 



'^ dy 



when we take the equation of continuity (5) into account. This equa- 

 tion may also be regarded as expressing the condition that a function p 

 (pressure) should exist on a level z as an exact differential with respect 

 to X and y. And the validity of equation (6) suggests the possibility 

 of determining the pressure in any level 2 as a function of x and y. 



Now suppose the coefficients of mixing Ai and A,,^ are both inde- 

 pendent of z, and put 



(2^-1). 



where 



s = 1 



and assume, in accord with Stokes, 



d'u 2 XTA (25— l)7rZ r^dHi (25—1)77^ 



dz^ h ^ 2h J(^ dP 2/» 



* = 1 



