GENERAL CIRCULATION OF THE PACIFIC OCEAN 523 



then we have, by substitution from (2) , (3) and (8) , 



-X' 



and (9) becomes 



= 2^iT ~A — - —nr^ — "^^i^^'J) r cos 



(10) 

 Similarly we have 



(11) 



az2 ^ \ h A, 



» = 1 



where 



V = y^ v,{x,y) COS ^J (12) 



» = 1 



Substitutions of (7), (10), (11) and (12) into (6) and (5) give 



/a^ 8^t/, \ _ (25— 1)V J, /du, dv^\ 



\dy^ ~' cx^ ) 4h^ \'dy ~ dx / 



COS,;!, 2 /a-, dr, \ 



+ 2ojp -— -t;, + -— ( ,7— — ;, 1=0 



i? /j VcV ox / 



?y 

 where R is the radius of the earth, and 



(13) 



—— +~-=0. (14) 



dx dy 



Equation (14) gives a set of functions ■^e(^^}') such that 



u. ~ ~ — ; Vn = — 'z — (15) 



^ dy dx ^ ^ 



and (13) becomes 



/ 8^^s 3"^, \ (25— l)-7r-^, /o'^^, £--$-, \ 



'^^Ve'c^ "^ dy^ ) ~ 4^2 \ ax- "^ a))^ / 



OS^ d^, 2 /07x C7y \ 



cos 



