Diffraction of Waves by a Semi-infinite Screen. 661) 



Transferring to parabolic coordinates, f, 77, given by 

 # + iy = (£ + iv) 2 > tne equation (V1 2 + ^' 2 )</> =0 gives 



Bl 2 P~ I (fcosa + ^sin*) — 



+ (f sin a -77cos«)|--|= 0. . (2) 

 This equation is found to have a solution 



u = /(ag+brj) if a = cos-~, b = sin-, 

 in which case the equation to determine /becomes 



/"-4^(fcos| + i7sin|)/ = 3 ... (3) 



2 V' 5 rff = „. ... (4) 



In the same way we find 



f* 5 cos - — ^ sm s o 7 -7^2 



„=C + D 2 2 , ? rf?. .... (5) 



Therefore for the whole potential we have 



+ *-*'{ O + DfV^r} • • (6) 



(<£; included in A), where for brevity we have written 



x cos a + y sin «+ ci = ft, a; cos a — ?/ sina + c£ = 7, "} 



f cos ^4- 17 sin- = G> b f cos- — qsm- = g> 2 , 



and the lower limit zero has been introduced, for definiteness, 

 into the integrals. 



§ 3. It now remains to satisfy the boundary and other 



