538 EIGHTH PACIFIC SCIENCE CONGRESS 



10. Computation of the Currents 



In order to calculate the distribution of the currents at various 

 levels, we had first to compute F^ (A; tj), \\ (A; t]), . . ., Y^^ (A; -q) accord- 

 ing to one of the expressions (79), (80) and (81) for 



A = 0.0000, 0.0025, 0.0050, . . ., 0.0500. 0.0550, 0.0600, .... 

 0.1000,0.1100,0.1200,0.1300, . . ., 0.2000 

 and for 



t; = 0.0, 0.1, 0.2, . . ., 1.0, 2.0, 3.0, . . ., 10.0. 

 For larger values of 77, we have 

 a = + 1040.3075,7, 

 yS = — 1040.3075,7, 

 y = + (&/ 1082323) v^, 



8 = — (6/1082323)% (82) 



very accurately, while Y^ (rj) are all very small, so that ¥., (A; 77) will b€ 

 approximately given by 



y = \^-^'---e-.\^ (83) 



where y, and c are independent of 77. It will be more convenient to 

 leave (83) as it stands rather than to compute their values against ,7. 



These values of the ten functions 3^^ (A; ,7) may be then converted 

 into the functions N^, (A; ,7) by virtue of the formulas (67) and (68). 



Substitutions of the functions A/"i (A; ,7), A^'o (A; ,7), A/'g (A; ,7), • . ., 

 A'lo (A; ,7) into the equation (69) give the complete solution as 



^r 



(X. >'. z) = Y^ X ^■^'^- (y) J Q^- (^' V) cos ( ^^ j d-q. 



To evaluate the integral 



00 



(84) 



j^Ar„(A;,7)cos ( ^j)dr,, 



we have computed the functions N^ (A; ^7) for 



,7 =: 0.0, 0.1, 0.2, . . ., 1.0, 2.0, 3.0, . . ., 10.0 

 and the process has to be carried out numerically between ,7 == and 

 77 — 10.0. For larger values of 77, we may use the approximate for- 

 mula (83). 



Let the values of a function ^^(,7) for ,7 = 0, /i and 2h be Fq, F^, 

 and F2 respectively. Then the interpolation formula in this interval 

 of 77 will be given by 



F{-n) = Fo + 



- 3Fo + 4Fi — F3 / ,7 \ Fo - 2F, -+ F, 



""^/rj \ F,-2F^+F,/rj Y 



