Substitution of equations B-43, B-46, B-51, and B-52 into 111-17 yields: 



U = - ( C ' \ ( 1 - -J! \+ [ 2SC ^a- 1 ) 1 / ""* v" 



^ Po.wa^ V 3p 0a c a 2 a ) [ p 0( p 0a c a 2u)2a<] ^ 2p 0a c Pa ) 



, f co^( Ya -1)K a I r /2s_\ / c pa x » I / 4afv 



+ L 6p 0f 2c fPoa c a 2c pa a2 J L W ; V2p 0a coK a ; J v b3 ; 



+ (p^a) | (~3~) ( 1 "b") + ( 9po, 2 c»2a ) ( 1 " W) 



+ <v- - 1) (^-)T -f) - [-W1 (-feW -5-) 



, riiff(y.-i) i / coK a yy 3 3 \ | 



L3p 0f 2 Cf 2a2 JV2p 0a c Pa / V b3 / J 



+ ' ( 6p 0f 2 Cf a 2 ) ( 1 " 3p 0a c a 2a) ( 1 1 + "F") 



- i f »(Y.-D 1 / a& V 2 /n + *2L\ 



L3po a c a 2p 0f 2c f coa4j V 2p 0a c Pa ; V b3 ^ 



+ ir c ' (Y -- 1)Ka l [i + /Jg-w c p a r 1 



LPo a Ca 2 Po 1 c Pa a2j L V«a 2 / \2p 0a WKj J 



-(■p^r)l(-^r)(\-^) + <v.->(^rrO-T) 



r 2^(Y.-1) 1 / o)K a \ * / _as \ 

 L p 0| coa2 J V2p 0a c Pa / V 1 b3 / 



M 1 -^]fero-£) }■ 



Substitution of equations B-43, B-46, B-53, and B-54 into 111-18 yields: 



W = ( <**—\ (l-*L\ ( - ( 1 ?s_ v r 2s( Y a-1) -| / CQK a v» 



l,3p 0f 2c f a2 M b3 ; | V 3p 0a c a 2a ) L Po a c a 2 coa2 J V 2p 0a c Pa ) 



r 3a^K a ( Ya -i) l r /2s_\ / c Pa v n J 



L 2p 0a c a 2p 0( c f 2c Pa J L Vooa 2 / V 2p 0a coK a / J ) 



. co v ( / oo 2 b v / co 2 ^ 2 b \ / c t a v 

 + ( Po a c a 2 ) 1 V 9Po,c f ) + \ 3p 0f 3c ( 3a2 J ~~ V 3po f b 2 / 



r 0)b(Y a -1) -|/ 0)K a y* 



L 3p 0f c f a Ji2p 0a c Pa j 



r (Q^b(Y a -1) i / Q)K a » _ r C,(Y.-1) l / <*>K a \ l/; 

 L Po, 3 c ( 3 a3 J \2p 0a cJ [ p 0f cob2 J V2p 0a c p J 



45 



