MaestveZIo and Linden 



and 



r.n. ^rr-^g '-tf^^"^'" («4'''(f)''=(^)] 



-00 -00 



T(K) 



-"[^r(f).s(D]) 



The computation of the integral rmnrs rnay be simplified by- 

 deforming the contour on the O'-plane. Due to the manner in which 

 the Fourier transform was chosen, the integrand, except the term 

 T(k), is single-valued and analytic in the lower half-plane. The 

 contour will, thus, be deformed in this half- plane. This deformation 

 is determined by the analytic properties of the function T(k), 

 Eq. (19a). 



T(a,P)Mc^' + p¥--^' 



2 . 2, ,2. 



J 



B" 



Po^(l -f_^) 



^ Vk^ + (M^ - l)c^^ - ZkMor - ^ 

 This function is two- sheeted with square- root type branch points at 



kM ± Vk^ "r (M^ - 1)P^ 

 M^ - 1 



The sheet associated with the positive value of the square root will 

 be termed the physical sheet, since it corresponds to outgoing radi- 

 ation. 



The function has ten zeros on the two sheets, four zeros on 

 each sheet with the same values, corresponding to resonances of the 

 plate and the other two zeros are located near the branch points on 

 one of the two sheets, independent of each other. 



It is convenient to make the following substitutions 

 = Po. and v' = £|^ 



Pp 

 The Eq. (i9a) may be written 



B 



492 



