, 1/2 



Toward infinity ^ -> r/k -» ~, {C - 1) -> ^and, from Equations [137y, z], 



approximately, 



2 o 1/2 cos oj 2 , 1 V 



= - A^/;F(l-;.2) __ .3. „3t. _Z- 



-C' 



3 1 



[137o'] 



since ^ = ae. The flow is again that of a dipole, but this time with its axis in the y direction; 

 and for small values of e agreement with the result for a sphere is obtained, since then 

 2 e^ A/3 -> 1/2. 



The velocity components in the coordinate directions are, from Equations [137o,p,q] 

 and Equations [137k, 1, m]. 



= A, y 



q^^n^ 



1 - 



/•2 . 



1/2 



1 ^ + 1 <2 _ 2 

 — C In - I cos CO, 



2 C-1 ^2_, 



[137p'] 



9.-h^V(i 



1/2 



e-1 



e -iJL^ j \c -^ 



C 1 C+i 



In I cos o). 



2 4-1 



[137q'] 



C 1 < + i 



§■ = Aj F I In — 1 sin a. 



C -I 



2 ^-1 



[137r'] 



On the axes the velocity is in the direction of i V and a - \v\. On the y-axis, cos w = - 1, 



1/2 



^ =0, y = - k{C - I) and 



?^=^i 

 On the ic-axis y. = - 1, x -- k C, and 



1^1 V'' //' n/?"^' 



k I Jf^ 



[137s'] 



V ^- h,V 



1 |a;| + A 



- In 



^2_^2 2 |a;|-A 



which represents the limit of + a as l/xl -♦ 1 while w = 0. On the 2-axis, u = 0, sin w = - 1, 

 2 = i A(C - 1) and 



V = + a 



3/-, 





^2^ + A;^ + A; 

 Jz^^n? - k 



[137t'] 



353 



