526 EIGHTH PACIFIC SCIENCE CONGRESS 



meter 2a) sin ^ varies with y. This is a quite natural consequence when 



we consider the relation <i,= -_, where R is the mean radius of the 



R 

 earth, and y is counted zero on the equator. 



For these reasons, we can represent the Pacific approximately as 



a square ocean bounded by x = 0, x = a and }' = ± — , in which 



Y = coincides with the equator (Fig. 1). Here a is a mean east- 

 west extent of this ocean and approximately equals 120° of longitude 

 or 27r/3 in radians. This means that the northern and southern bound- 



2—7? 



axies of this ocean are given by v = ± — '~ — or the parallels of 60° N 



o 

 and S. 



To solve the equation (28), assume 



V 



^i(->^. >'; r;) = ^M^(>') N^{x;r,), 



(30) 



^\here m = 1, 2, 3, and A'',„(.\', r/) are functions of .\ which are 



to be determined later, while M^{y) are of the forms: 



M.^()') = cos -^cos___ for m: odd 

 za 2a 



■n-y . m-rry 

 COS -_ — sin - for m : even , 



2fl 2a 



(31) 



Since these functions and their }'-derivatives vanish along y = ±: — , (30) 



and its v-derivatives will also vanish alonsr y = ± — . This makes the 

 function -^(x^y.z) satisfy the condition (22) along the northern and 



southern boundaries y = ± _ . 



2 



5. Stresses of Winds over the Pacific Ocean 

 Dr. Munk kindly furnished me with his unpublished data of the 

 distribution of the wind-stresses over the Pacific Ocean north of 5° S. 

 From these data, the most probable distribution of the wind-stresses was 

 found to be zonal and determined as 



r^ (d,) = + 0.045544yVf; (<^) — 0.262308M^ {<f>) 

 + 0.022902M'3 (<^) + 0.069493Ai^ (<^) 



— 0.036900m{ (<^) + 0.011560M'J,^) dyne/cm= (32) 



where <^ is latitude so that 6 = y/R and M'^ (^) stand for 

 d d 



d^ ^^ ' dy 



