Yim 



The limit ji -* +0 then leads to the following real expression 



Pg;(x)/Po= -{l+sgn(x)}/2 -11^ 



;n(x) C exp (- 



^ Jq 1 + 



IVl) 



dw 



- {1 - sgn (x)} cos (kox). 



(D8) 



which is indeed continuous at x = although the wave slope ^^ 

 becomes infinite at that point. This is evident in the accompanying 

 Figure (see Curve 1) , but does not show up on the scale used by the 

 author in his Fig. 1 . 



Fig, Dl, Comparison of Wave Profiles for a Line Sink and 

 a Pressure Step 



On the other hand, one can also approach the problem as the 

 limiting case of a submerged line source as the submergence tends 

 to zero. The velocity potential for a line source of strength m 

 (that is, output 2Trm per unit length of line) on the line x = 0, z = - f 

 is found to be 



<j>(x,z) = m 



In // x^+(z+f)^ l ^ 2mk C'" exp{k(z-f + ix) } . . 



^7ix2+(z.f)^/ +2mko)^ _^__-_ dk, (D9) 



602 



