GENERAL CIRCULATION OF THE PACIFIC OCEAN 



533 



This equation has five real roots. Let them be 

 ii' ^3. ^5. ii and ^9 

 and, corresponding to them, equations (52 will give five sets of ^i, l^, 



. . ., Is, or 



1' 3' 5' 7' 9 C^"*) 



These five sets of roots and multipliers Ts will give Y^ and F^ as 



^m = ^r^i + ^T^3 + ^T^5 + ^T^T + ^"^£9 



(777 = 1, 3, 5, 7, 9) (55) 



and the corresponding five equations 

 D(Y ) + ^ Y + E =0 



(m = 1, 3, 5, 7, 9) (56) 



for Fi^ Fg, . . ., Fg. They are no longer simultaneous, and not diffi- 

 cult to solve. The same, of course, applies to even sets, too. 

 Practically, the equation corresponding to (53) is 



For even series we have, coiTesponding to (57), (58) and (59), 



7 — y +16 — 12 +8 — 4 



— •8 43 — y + 24 — 16 +8 =0 

 + 12 — 24 111 — y + 24 — 12 



— 16 +32 — 48 211.— y +16 

 + 20 — 40 +60 — 80 343 — . 



