MaestreZlo and Linden 



i|j(x,y,z) = - -^ \ \ dx' dy' G(x,y,z|x',y',0)LW(x',y') (8) 

 where 



pOO pOO i[a(x-x')+)S(y-y') + C(z-z')] 

 G(T I T^) = \ \ da d|3 ^ p 



which is found in Appendix A to be for supersonic flow. 



(9) 



ZTTi e 



Vm^-1 Vu^ - R^ 



outside the Mach cone 



and for subsonic flow. 



G(T|7^) = -i^L=- ^ r===- (10) 



Vl-M^ Vu+R^ 



except in this case, K = k/Vl - M and u = {x-x')/Vl-M . If LW 

 had been evaluated as 



A 



(k - aM)W 

 then Eq, (8) would read 



4;(x,y,z) = - -V \ \ dx' dy' W(x',y')L G(x,y , z | x' ,y ' ,0)(1 1) 

 4-n "^0 '-'0 



* 

 This equation is formally correct if L G is interpreted as a distri- 

 bution, which is to say that one partially integrates to obtain Eq. (8), 



Now using Eq. (8) 

 P2(x,y,z) = - ipoCl_i|j(x,y,z) 



= i£o^ r C dx' dy' G(x,y, z|x',y',0)|l.|^W(x',y') 

 4Tr2 Jo Jo 



(12) 



488 



