DIFFRACTIOX OF RADIO WAVES BY A PAKAROLIC C^LINnFR 427 



E(iiuitions (2.14) and (2.15) hold only in the region of the crest of 

 the cylinder and for large h. Under these conditions x + 7/8 is very 

 nearly ecfual to the distance along the surface measured from the crest 

 of the cylinder. 



An expression equivalent to the one for ./„ in (2.15) has been derived 

 and tabulated by V. Fock. 



Series for ^oJ and ./, which converge for positive (shadow) values of 

 7 are given by equations (6.17) and (6.24). When 7 is large and negative 

 ihe application of the method of steepest descent to integrals (6.16) 

 and (6.23) leads to 



roJ^ -(.T/A)e-'^fi + zy47' + 



(2.17) 



in which x/h = 2yh~^ ^. 



Table 2.2 gives values of h}'^^oJ exp {ix) and /„ exp {ix). The values 

 of J for 7 > were computed from the series, and the ones for 7 ^ 

 w^ere obtained by numerical integration of (2.14). The entries for J^ 

 were taken from the more extensive table given by Fock. In order to 

 express his results m our terms it is necessary to use the fact that the 

 radius of curvature at the vertex of the parabola is 2h. A change in the 

 sign of i is also necessary because the time enters Fock's work through 

 exp { — icct) instead of exp (iwt). The values shown were checked for 

 7 > b}' the series and for 7 ^ by numerical integration of (2.15) 



Fock's table shows that by the time 7 has reached —2 the value of J„ 

 exp (ix) has become 1.982 at an angle of +1-45 degrees. This is close to 

 the limiting value of 2 predicted at 7 = — co by (2.17). 



It will be noted that, for large values of h, J is smaller than Jv by 



