50 



where 



C 



1+k i f 1 1 ■ / \ 



T~J Io y 2dx - 2 (b " a) ( m a +m b) 



fVdx--l(b-a)(f a+ f b ) 



•'a 



and k is the longitudinal virtual mass coefficient for the body. 



This approximation is used to obtain a sequence of successive approx- 

 imations by means of the iteration formula 



_ i(x) = mi(x)+ ^ (x) [j.£!!i!!! dt ] 



When a doublet distribution has been assumed, the velocity components at a 

 point (x, y) in a meridian plane are 



dt 



V r 5 r 3 ' 



v = 3y f ^-m(t)dt 

 and the pressure is. given by 



-2-= 1 - (u 2 + v 2 ) 



q 



where q is the stagnation pressure. 



The iterations are most conveniently performed in terms of the dif- 

 ferences between successive approximations to m(x), which also furnish, at 

 each iteration, a geometric measure of the accuracy of an approximation. 

 Simpler forms for the velocity components at the surface of the body are given 

 in terms of this difference or error function. 



Gauss' quadrature formulas are recommended for the numerical eval- 

 uation of the integrals. Two methods of carrying out the iterations are 

 given. The first employs a polar transformation and a graphical operation be- 

 tween successive iterations; the second is completely arithmetical and is 

 suitable for processing on an automatic-sequence computing machine. All of 

 these procedures are illustrated in detail by an example, in which the semi- 

 graphical method is employed. The accuracy of the method is analyzed; the re- 

 sults are compared with those obtained by the methods of Karman and Kaplan. 



