the solution of (53) to (55) is 



""'=1 



mnr > ■- 





(57) 



where F- (z) has been expanded in an eigenfunction series according to 



F„-„ (z) 



X^w^r 



(z) 



p/^j ^^ """' ' (58) 



and the functions W- (z), W- Cz), and Wj- (z) are governed by the following equa- 

 tions 



r , p ^ lf_ rn n j i m nl ynX _ r\ 



dz^ 



dz 



(aj„ ± CO J" 



dW- s \k ± k l'^ 



W-= at z = H 



l!!r ^prfw± fgr-K^±a^2]|r^i^j2 



dz^ dz 



raj„± coj^ 



Wr=o 



dW- G- -^-4. fw ±aj J G± 



r ^ mn \ ir/± "'"m '^n' mn 



\_i = 2ii^ \w- 



/-,dz 4(aj„± CO J Z. '" 





at 2 = 



l^T 



at 2 = H 



(59) 



(60) 





dW- g\k ±fe r °4 



W: = at 2 = H 



A- dV/7 



— -"'"-^ -i at 2 = 



2gfe ±fel^ dz 



> (61) 



18 



