On the a;-axis x = - k(, and, from the limit of -^ as /i->- 1 with oj = 0, 



- \X\ fC \X\ 



V = -h^V Icot"^ -— -— 



^ ^ k x^ +k^ 



[I38d"] 



On the 2-axis /x = 0, sin w = i 1, s = i ^(C +1) , and 



^ = x?.„ = -^9^ sin 



_j _^ k^Jz'^-k^ 



[138e"] 



Over the surface of the ellipsoid itself, on which <C = Cq and is constant, the relative 

 variation of q is similar to that over a moving sphere. Furthermore, around the circumference 

 in the transverse or 2a;-plane, the velocity q is uniform, since |sin co\ - 1, and, using Equa- 

 tions [I38z, a '], 



= \qj-h^v[sin-^ e-e^fl^^j 



[138f"] 



The kinetic energy of the fluid, found by the method employed in obtaining Equation 



[137f'], is 



T ^—nph^c^V^ /l-e^ |sin-i e-e^l-e^ j. [138g"] 



Case If,. Flow Past an Ohlate Spheroid Perpendicular to its Axis of Symmetry. Let the 

 fluid at infinity flow toward negative y at velocity, V. Then, adding Vy in <?S, 



2^i\i/2 n_„2Ni/: 



= kV{C + l)'^^ (l-li^) 



1 + A cofi C- 



C'-l 



cos CO. [138h"] 



If a prime denotes values given by Equations [138z ', a ", b "], 



1-^^ 



2 \l/2 



e.,^ 



C^ + i ^1/2 



q^=q^-Vd— cosco,q^ = q^+VJ- cos c, [138i ", j "] 



366 



