Pacific Ocean Circulation — - Hid AKA 
199 
where 
p = (149971 10) \ 
(77) 
For the intermediate value of ?/, these four roots vary continuously except fi and 8 which 
change from complex conjugates to real as rj increases from 77 = 0,3 to rj = 0.4. 
Of course, there are 10 series of such four roots of 10 equations (70), each varying with 
the parameter rj. 
The constants A, B, C, and D can be, of course, expressed in terms of «, /3, 7 , and 8, 
Thus the solution F becomes, when (3 and 0 are complex conjugates of the form 
(3 = +P + qi; 8 = p - qi , (78) 
F = {l + 
7 «(X-i) 
e 
a — 7 
a — 7 
yO-i) , 
e + 
+ 
(— 
(-2- - l) e~ p> 
\ot — 7 / 
cos gA 
-T P + 7 A -pX • x l 
e . — - / e sin q\ ( . 
q qj * ) 
and, when a, (3 , 7 , 5 are all real, 
7 «(x_i) , J 5 . a 7 <5 _ 7 l 
«V*— 17 1 
e + 
a — 7 
« y(X— 1 ) 
0 
a — - 7 
+ 1 - 
a (3 - y -y\ px 
e r . e 
1 6—8 a — y ' /3 — 8 
(79) 
(80) 
. F, 
where F p is the particular solution given by (71), of the equation (70). 
When r i increases, 7 also increases. If we can neglect e~ y } the expression (80) will be 
further simplified, and we have 
F = 
7 «(X-l) 
e 
a — 7 
a t(x_ 1 ) 
e 
a — 7 
(81) 
Since Y p is given by (71) as 
= 
(c/b) 
the solutions of the equations (63) and (64) will tend to zero as rj increases indefinitely. 
The values of the roots a, (3 , 7 , and 5 of each of the 10 equations given by (63) and 
(64) were computed numerically and are given in Tables 5-14. 
Computation of the Currents 
In order to calculate the distribution of the currents at various levels, we had first to 
compute Fi(A; 77 ), F 2 (X; 97 ), ... , F i 0 (X ; 77 ) according to one of the expressions (79), (80), 
and (81) for 
X = 0.0000, 0.0025, 0.0050, . . . , 0.0500, 0.0550, 0.0600, . . . , 0.1000, 0.1100, 
0.1200, 0.1300, . . . , 0.2000 
and for 
7] = 0.0, 0.1, 0.2, . . . , 1.0, 2.0, 3.0, . . . , 10.0. 
