Sharma 



The above integrals were numerically evaluated at 241 points, in the range 

 X = - 207T (n/ 10 )4tt , for typical parameter values f = l , y = tt by the Romberg 

 method specifying an absolute accuracy of ±0.0005. The results are listed in 

 Tables 1 and 2. It may be noted that at the afterend of the cut the slope oscilla- 

 tions have decayed down to about 1 percent of their peak values (which is a real- 

 istic simulation of experimental accuracy), while the corresponding figure for 

 height is much higher (about 25 percent) as may also be expected. 



Table 1 

 List of Computed i^ (xlO"*) Values for a Submerged Sphere 

 (Parameters: r := i, f = i^ y = tt; Variable, x = 477 stepped -VlO 

 until -2O77) 



The slope data of Table 1 were analyzed to yield the amplitude spectrum 

 according to Eq. (15), truncating once at -x= iott and then at -x= lOn without 

 any correction for the residual terms. The resulting amplitudes bA(u) are 

 plotted vs transverse wavenumber u as curves 2 and 3 in Fig. 1 for the sake of 

 comparison with curve 1, the exact theoretical curve, which is of course known 

 a priori: 



ba(u) = (27a) 



and 



b/3(u) = bA(u) = Stts^ exp(-fs2)/(2s2- 1) . (27b) 



740 



