Over the surface of the ellipsoid itself, where ^ = ^ and is constant, the transverse 

 component q varies relatively in the same manner as over a sphere. Furthermore, around the 

 circumference in the 3a;-plane, where sin w = - 1, g is constant, since 



C 



^0 



1 , -0 

 In — 



C + 1 



e 1 1 + e \ 



A, F -—In . [137u'] 



' 1-.2 2 1-e 



The kinetic energy of the fluid, found from Equation [136h] in analogy with Equation 



[137f '] but with use of the integrals /^ (1 - f?) d^i = 4/3 and /^"'cos^ codco = n, is 



-1 



r = — 77 ph. ab^V^ 



/ e 1 1 + e \ 



[137v'] 



Case 4- Flow Past a Prolate Spheroid Perpendicularly to Its Axis of Symmetry. Let the 

 fluid at infinity flow at velocity V toward negative y or ^ = 0, oj ^ 77. Adding Vy for the 

 uniform stream, 



, 1/2 , 1/2 



1 + h. 



c 



C'-\ 



1 , c+1 



- — In 



2 <-l 



cos &j. [137w'] 



If a prime denotes values given by Equations [137p ', q ', r ']; from Equations [l37o,p,q], 



?^= ql- V d 



1 - 



1/2 



/■2 . 



. ^ - 1 



cos ca, q^^q^^Vt,^ ^^ ^ 



cos CD. [137x ' y '] 



q = q/ + V sin co. 



[137z'] 



Everywhere v = v' - V, and on all three axes q = \v\. 



On the ellipsoid itself, where C, = Cq ~ 1/^, ?/• = and 



2e^Aj F 



1/2 



\1 cos (D 



(1-eO (l-e^^) 



1/2 



' 9., = 



Se^A, F 



I - e' 



sin dj. 



[137a ",b"] 



where ^i - x/a. The same remarks concerning q apply here as in Case 3, except that here 

 around the circumference of the ellipsoid in the sec-plane q = \q \ where \qj\ is given by 



354 



