Figure 236 — Flow past a circular disk. 

 See Section 138, Case 2. 





s 









-^_^^^ 





X^'^^^^^ 



____^ 



c V^^^^ 





Axis of Symmetry a; 







Case 3. Motion of an Oblate SpheToid Perpendicular to its Axis of Symmetry. At ve- 

 locity y toward positive y, as in Figure 237, if ^ = ^^q on the ellipsoid, 



= A2/fcF(^2^1)l/2(i_^2)l/2 l^ot-1 ^--^jcoscu, 



[138v'] 



-cot-iCo 



^o(^o + l) 



yn^ 



[138w'] 



As e-*0 and <Cq-»°°, e h^-^Z/\, as appears from the series (l-e)~'=l + e /2 + . . . . and 

 the series for sin~^ e as obtained from Equation [33j]. As e ^ 1 and Cq^Oi '^2^^' '^hus 9S 

 equals for a disk, as it must. 



Toward infinity, li^r/k = r/ec and, using Equation [I38g'] and the series 



c 





1 1 



[138x'] 



2 o 1 /o COS oj 2 



— e^A.c^y — 



[138y'] 



approximately, which is the potential of a dipole with its axis parallel to y. As <^q->°o, and 

 e -* 0, since e^h^ -» 3/4, 4> -* c^ Fy/2r^, as for a moving sphere of radius c. 



364 



