Pacific Ocean Circulation — Hidaka 
195 
Multiply each of the five equations in (50) by l\, l 3 , h, l 7 , and / 9 , respectively, and add 
together; we have then 
D(hN 7 + l s N s + hN 5 + 1 7 Nt + kN») 
+ (C\h -p Cih -p C\h -p Cih -p Cih) Ni 
+ (Clh + Clh + Clh + Clh + Clh) N 3 
+ (Clh + Cjfj + Clh + Clh + Clh) N 3 
+ (Clh + Clh + Clh + Clh + Clh) Nt 
-f- (C9/1 -p Clh “P Clh “P Clh “P Czh) N 3 
-p (I1E1 ~p hEz -p /5-E5 ~p hE 7 -p /9-E9) = 0 . 
Now let 
Clh + Clh + Clh + Clh + Clh = hi, 
C 3 h + Clh ~p Clh + Clh + Clh = hi, 
Clh + Clh + Clh + Clh + 
Clh 
hi, 
and eliminate h, I3, ■ ■ ■ , U', we have then 
Cl-i Cl 
Cl Cl-i 
cl cl 
cl cl 
cl cl 
cl cl 
cl cl 
cl-i cl 
cl cl-i 
cl cl 
cl 
cl 
cl 
cl 
cl-i 
0 . 
(51) 
(52) 
(53) 
This equation has five real roots. Let them be £ 1 , £ 3 , £ 5 , £7, and £9 and, corresponding 
to them, equations (52) will give five sets of l lf l 3 , . . . , 1 9 , or 
A, il i\, A, il 
f r- 
h, h, 
ll 
A, It l 
A, ll 
ll, ll, ll A, 
7 9 ; 9 7 9 7 9 
hi hi hi hi 
ll; 
ll; 
ll 
(54) 
These five sets of roots and multipliers V s will give Y m and F m as 
Y m = ITN ! + IT Ns + IT Ns + ITN 7 + IT Ns ■, 
F m = IT El + iTEs + ITEs + ITE 7 + ITEs 
( m = 1, 3, 5, 7, 9) 
(55) 
and the corresponding five equations 
D( Y m ) + £ w T m + E m = 0 (56) 
(m = 1, 3, 5, 7, 9) 
for Fi, F 3 , . . . , F 9 . They are no longer simultaneous, and are not difficult to solve. The 
same, of course, applies to even sets, too. 
