DIFFRACTION OF R.VDIO \V WKS BY .\ P.\R.\BOLir CYLINDKR 481 



VALUES OF T -W }p 



Fig. 2.5 — ■ The amplitude of the crest wave may be obtained from these curves 

 and expressions (2.24). Here r = /i'/' ^ where \l/ is small. However p must be large 

 enough to make tZ-'p » 1. 



and this corresponds to a half-plane with its edge at the crest of the 

 cyhnder. t may be small even though we are considering | i/' [ to be large 

 enough to make (2.21) and (2.22) hold, i.e. large enough to make 

 1 ^ \p'~ >i> 1. Indeed, multiplying by lii^^ gives | t \p'' » ]i^^ which may 

 be achieved for small values of r by making p large enough. 



It follows from (2.22) and its analogue for vertical polarization that 

 the amplitudes of the crest waves are 



(hp) 

 (vp) 



(27rp)-^''^ A^'M ^(r) +1/t1, 

 (27rp)-^'^ /l^'M ^lA) + l/r|, 



(2.24) 



where the expression (2.9) for c{()) has l)een used. The last factors in 



(2.24) may be computed from Tabk; 2.1. They are plotted in Fig. 2.5. 



When we go deep down into the shadow where r is large and negati\'e 



