g^k f/^(l~Ccot-i C), [138d'] 



^= -^^2^' /7«2 + i)(l-^2) / ^-1 ^_ J_), [I38e'] 



6^ = I cor 1 Co ^1 = sin-ie-eyi-e2 . [138f'] 



If e = 1, so that ^^ = 0, $?2 = ^/t?- As e-»0, and Cq-*'^, e^^^j"*^/^, as is easily verified by 

 using Equation [138x'] and the series, obtained from Equation [33k] and valid for any real 

 number ^ = 1, 



,1111 r n 



cot-i f = tan-i— = — - + [138g'] 



^ ^ 3^3 5^5 



Toward infinity, with use of the last series, 



^=T^2*^-T = T^V f^ 



/-2 3 



ipproximately, since k = ec. Thus the flow is that of a dipole. As f ^0 and e^gr^-^7>/%, 

 ^^ c^ U cos d/2T-^, as for a sphere of radius c; see Section 127. 



The velocity components in the coordinate directions are 5^ = and 



'(''^""i^Th"'-^} "'''■' 



?„■ -S,vl^-^\" ll-icor'{\. [13811 



On the a-'axis, n ^ - 1, x ^ - k C, q ^ \u\ and 



= .,^.,^.,.„r.^-_ii±,. ussi 



360 



