Pacific Ocean Circulation — Hid AKA 
193 
E 
D] 81 d*N m 
,2tt 2 ’ 16tt 4 jR 4 * d\ A 
7] 2 9 d 2 N m 
8 ’ 47r 2 i? 2 * dy 2 
3 Vs 
2 w 
3 
dN m 
d\ 
E(-— — 
i V 8 R 2 
D l 
2tt 2 
A A 
• ^ 
iv» + A . At, 
pco 
0. (41) 
In order that this relation should be always valid, the coefficients of M m (</>) must vanish. 
Thus, we have 
D] d*N n 
R 2 <ZX 4 
32tt 2 1 d\ 2 
9 V3 t/iV, 
4 tt 2 <7X 
?(■ 
i * 
8 «i 
il + 
1 
H E « m T i — 0 (42) 
poo i 
where T { is given by (34). 
It may be anticipated from (39) and (40) that the values of $ % m are larger than that of 
a l m for any corresponding set of values of i and m. But the ratio 
D± = tSAi 
R 2 poo R 2 
is of the order of 10 4 for the usual value of Ai (= 10 8 ), so that we may neglect the terms 
of Pm in the coefficients of 2V* in (42). Then (42) becomes 
81 D ? d?N m 9 2 d 2 N m 
32 R 2 ' d \ 4 32?r 2 ^ d\ 2 
9 V3 dN m 
4tt 2 d\ 
8 i poo i 
(43) 
Determination of the Values of 
The coefficients of in the expansions of 
the higher terms being neglected. 
For the ocean under consideration, we have 
d 2 M ri 
d<$> 2 
were evaluated as far as Mio((f>), 
Mi (<t>) = - 1 2 r {M 1 (0) + 8M 3 (0) - 6M i (<j>) + 4 M,f0) ~ 2 M 9 (0)}, 
M 3 '(0) = l*{-3 MM) + 20 M 2 (0) + 18M 5 (0) - 12 M 7 (0) + 6 M»(0)}, 
= -A{+5Mx(0) - 15M 3 (0) + 6WW + 2OM,(0) - 1OM 9 (0)}, 144) 
M"(0) = -*{-7Mi(0) + 21M 3 (0) - 35M 5 (0) + 148M V (0) + 14M 9 (0)}, 
M 9 '(0) = -Al+OM^) - 27 M 3 (0) + 45M 5 (0) - 6 3M,(0) + 257M 9 (0)} 
and 
M" (0) = -% { 7M 2 (0) + 16 Mi (0) - 12 Mi (0) + 8 Ms (0) - 4 M 10 (0) }, 
Mi (0) = -%{:;■-* M 2 (0) + 43 M 4 (0) + 24 M 6 (0) - 16 Ms (0) + 8 M w (0) }, 
Mg' (0) = -%{ + 12M 2 (0) - 24 Mi (0) + 1UM 6 (0) + 24 Ms (0) - 12 Mu (0) }, (45) 
M's' (0) = -%{ -16 M 2 (0) + 32 Mi (0) - 48 Me (0) + 211 Ms (0) + 16 M 10 (0) }, 
M" (0) = -% { 20 M 2 (0) - 40 M 4 (0) + 60 Me (0) - 80 Ms (0) + 343 M 10 (0) }. 
Substituting (44) and (45) into equation (43), and evaluating the numerical values of 
their coefficients with R = 6.3712 X 10 8 cm., poo — 0.000075 sec -1 and 
Ai = 3.08 X 10 7 c.g.s. , (46) 
