- TTpg r (4iR + 2^z' -^J R dz' 



- pTT r il + '^(z' - Zq) - 2 co^Ae^^' cos wt] R^ dz' 



J-H 



or, since 



C{*^''*^'^h'^"* c 



— (R^z') dz' = 

 dz' 



it follows that 

 .0 



i = - P f ii + 4'(z - ^r) - 2oj^Ae^^ cos wt] S(z) dz + 0(R-^ log R) 

 J-H 



[25] 



\where 



i2 



S(z) = TT [R(z)]' 



is the sectional area function. 



In a similar manner we obtain 



,0 



m(C + g) = -pg;S(0)+ pg r S(z)dz + pgA sincot f e^^ ^ d 



J-H •'-H ^^ 



+ 0(R'* log R) [26] 



Iifi =-pg^i I (z - Z(^) S(z)dz 



J-H 



-P f [^ +i[/ (z - Z-) - 2oj^Ae^^ cos cot] (z - z^) S (z)dz 



+ 0(R^ log R) [27] 



11 



