200 
PACIFIC SCIENCE, Vol. IX, April, 1955 
For larger values of 77 , we have 
a | +1040.3075TJ, 
13 = -1040.3075t/, (82) 
7 = +C&/1082323) 1 , 
S (6/ 1082323) 1 
very accurately, while Y p (rj) are all very small, so that F 2 (A; 77 ) will be approximately 
given by 
Y = {l - e+> - ^ X } . A (83) 
where 7 , and c are independent of 77 . It will be more convenient to leave (83) as it stands 
rather than to compute their values against 77 . 
These values of the 10 functions F TO (A; 77 ) may be, then, converted into the functions 
N m (\; 77 ) by virtue of formulas (67) and ( 68 ). 
Substitutions of the functions iV+A; 77 ), N 2 (\; 77 ), N 3 (\; 77 ), ... , A^ i 0 (A; 77 ) into equation 
(69) give the complete solution as 
y, z) = 
To evaluate the integral 
(84) 
we have computed the functions N m (\; rj) for 
77 = 0.0, 0.1, 0.2, . . . , 1.0, 2.0, 3.0, . . . , 10.0 
and the process has to be carried out numerically between 77 = 0 and 77 = 10.0. For 
larger values of 77 , we may use the approximate formula (83). 
Let the values of a function F(rj) for 77 = 0 , h, and 2 h be F 0 , F\, and F 2 , respectively. 
Then the interpolation formula in this interval of 77 will be given by 
F{ 77 ) = F 0 + 
Then we have 
•2 h 
— 3 F () + 4Fi — F 2 ^77 j F 0 — 2Fi + F 2 ^77 
/ 
or 
F(rj) cos 
7 rz 
2 A 
t? j drj = 
= K f cos (+ * 
•so 
f- h ( TTZ \ , Fo - 2 F, + F 2 f 
J r,cos \2D z V dv + W / 
c/n •/() 
-3F 0 + 4Fi - F 2 
2 h 
77 cos 
(m)' 
dr\ 
(85) 
f F(n ) cos (+ dr, = (a, - 36, + d) . F„ + (4 61 - 2 Ci) . F, + ( 6 , + c) . F 2 
•so 
