17 



long as An, decreases on the average, and is terminated when the error begins 

 to increase and grows to an unacceptable magnitude at some point along the 

 body. The strong similarity between these remarks and the discussion follow- 

 ing Theorem 2 of Reference 17 should be noted. 



There is also a strong similarity between the iteration formula of 

 Reference 17 whose convergence was thoroughly discussed, and the present equa- 

 tion [56]. An essential difference between the iteration formulas is that the 

 former employs the iterated kernel of the integral equation, the latter does 

 not, so that the convergence theorems of Reference 17 are not applicable. Nev- 

 ertheless, it is proposed to use the form in [56] (or the equivalent iteration 

 formula [58]), for the following reasons: 



a. The labor of numerical calculations would be greatly increased by 

 iterating the kernel, and even then only convergence in the mean would be 

 guaranteed (Theorem 4 of Reference 17) • 



b. The physical derivation of Equation [56] indicates that at least the 

 first few approximations should be successively improving. 



c. The successive approximations are monitored so that the sequence can 

 be stopped when the error is as small as desired or, in the case of initial 

 convergence and then divergence, when the errors begin to grow. 



VELOCITY AND PRESSURE DISTRIBUTION ON THE SURFACE 



When an approximate doublet distribution m, (x) has been obtained, 

 the velocity components u, v can be computed from the corresponding stream 

 function [18] 



~'»m,(t) 



^3 — dt - ■=■ 



[61] 



^U,y) = y 2 lj"3 



from which, in accordance with Equations [5] and [6], 



u = i + f'fizf _i_\ m, (t)dt [62] 



I \ r 5 r 3 ' i 



and 



t-x 



v- 3y f — m 1 (t)dt [63 



J a r 



