GENERAL CIRCULATION OP THE PACIFIC OCEAN 537 



where 



p = (14997110)^/^, 



q = y-^. (77) 



For the intermediate value o£ -q, these four roots vary continuously ex- 

 cept yS and 8 which change from complex conjugates to real as 77 

 increases from 7^ = 0.3 to ly = 0.4. 



Of course, there are 10 series of such four roots of 10 equations 

 (70), each varying with the parameter 77. 



The constants A, B, C and D can be, of course, expressed in terms 

 of a, p, y and S. Thus the solution Y becomes, when yS and 8 are com- 

 plex conjugates of the form 



P =: j^ p + qi; 8 = p — qi. (78) 



}' _ \\ -{- — - — e«(X— 1) — — - — e^(x— 1) 

 I a — y a — y 



_{. I e—y — 1 I e-P^ cos qX 



\a — y / 



+ (.-^e-.^-^^ - -^) .-P^ sin qX [y, 

 \«-y q q / f 



(79) 



y 



and, when a, j3, y, 8 are all real, 



[y IS a y — S I 



13 — 8 a — y P 



(80) 

 where Y^ is the particular solution given by (71), of the equation (70). 

 When rj increases y also increases. If we can neglect e-y, the ex- 

 pression (80) will be further simplified, and we have 



y _ J 1 4. — i — ga(\-i) _j_ e^^ — ey(\-i) 



I a — y /3 — 8 a — y 



-J^^'\^'- (81) 



Since Fp is given by (71) as 



the solutions of the equations (63) and (64) will tend to zero as rj in- 

 creases indefinitely. 



The values of the roots a, jS, y and 8 of each of the 10 equations 

 given by (63) and (64) were computed numerically and given in Tables 

 V-XIV. 



