Ill- 111 



where h^ is the mean square wave height, J(-> is the zero order Bessel function 

 of the first kind, and r'^ = ^ + rf . Marsh also shows that Z(-t, m) can be 

 written as 



00 



2^ J 



Z(t,m) = — ^ Z(r')jQ^r'(l - v^)^^ r' dr' (111-145) 



Substituting (111-145) for Z(l,m) in (III-142), and (III- 144) for Z(r'), gives 



1 

 i .(1-m^)' 



I ^ 



-1 -(l-m^)2 



spec u2 





^oyb ' ^^^^''^' ""- ^>]^ r' 



A^(a)) T {r' 1 - v^(-t. - a, m - 3) r }r' duu dt dm dr' (III-146) 



Making the change in variable t = — — and using the identity 



00 00 



jqdq) 



F(t) Jf.(qt) J^ (qp) t dt = F(p) (III- 147a.) 



'0 



with the correspondence 



p=<l- 

 one obtains 



A^[(kgt)^ ] 



^^'^ - 3/2 

 t 



q = r' (III- 147b) 



\){l-a, m- 3) 

 1 (1-m^)^ 





spec ^ J J _>3/^ 



■1 -(l-m^)2 



Arthur Sl.lLittleJnt. 



S-7001-0307 



