31 



application of this procedure gives ip (x) and ip (x) which are also graphed in 

 Figure 3- The sequence is stopped at ip (x) since \p has increased appreciably 

 over \p at x = -0 . 956 . 



3 



Hence, from [59 ]> we have the approximate distribution 



i 4 (x) = m^x) - -^(x) + ^(x) + ^(x)] 



m 



to which ip (x) is the corresponding error function. The distance An between 

 the stream surface for m (x) and the given profile is seen to be very small; 



4 



the largest error, \p = -0.00007 at x = -O.956, gives a An of about one per- 

 cent of the maximum ordinate. A graph of m (x) is given in Figure 4. For the 

 sake of comparison the curves for m (x) and the original Munk approximation 

 77f(x) are also shown. 



-1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 



Figure 4 - Comparison of Doublet Distributions m^x), m (x), 

 and Munk's Approximation y 2 / 2 * 



