aves 



670 Mr. W, G. Bickley on the infraction of PF, 



conditions by finding suitable values o£ the constants A, B, 

 G, and D. For points i'ar to the left {% negative), 77 is great 

 compared with f. Here (j> — ></>;, so that, using the first 

 terms of the asymptotic expansions of the integrals, we get 



1 = A + iBA/.^A = O-iD^/jp. (8) 



For the boundary conditions on the plane, where 77 = 0, 

 we may have two cases : 



Case I. <p = 0. Then 







A + C = 0, B + D = 0, 



. . . 



. (9) 



giving, with (8) above, 







A=-C = i, B=-D=v 



m-H 



(10) 



Case II. |^ = 0. Then 



A-C = 0, B-D = 0, . . . (9') 



giving, with (8), 



A = G=i, B = D = \/ 2 ^e~ i ^. . (10') 

 So both cases may be included in 



HF,-^{i + 2 X /^j>^^[]; (ID 



I e rf?-i^/.^, .... (12) 



1/ -co 



*=v / 5!j'_?' K '""j:r , « ■ <«) 



or, since 



