2 

 Upon substituting these approximations and also writing v for - to v 



2 

 and 6 for - u 6, Equations [50a,b] and [U6a,b] divided by k k take the 



approximate forms: 



F = yJlv + i- y£^e ; G = | y£ v + 1- p£^e [62a, b] 



.... 2 . • 



m'v + h'm'e - BS e + (c + BS) v - CSe = [62c] 



h'm'v + lie - LBS^e + LBSv + (c^ + E^S) 6 = [62d] 



where ' 



3 

 12 1 u£ 



m' = m + u£ ; h'm' = hm + - uJi ; I^ = !„ + T [63a,b,c] 



Also, Equations [52a, b] become: 



,2.2 





^2^2 / .,5 3,.,2 



^^ V + 



o 2k2 ^ ..^2 



Treated in the usual way (i.e., equating determinant to zero). Equations 

 [62c, d] give as approximate conditions for harmonic vibration: 



03^ [m'l^ - (h'm')^] - c^C2 - (c^E^ + C2B)S 



- [h'm' + E^ + L (C - m' )] BS^ = [6i+a] 



(/ [(C2 + BS) I' + (cg + \S) m' + h'm'CS - Lh'm'BS] 



+ c^LBS^ = [6i+b] 



These equations are simpler than Equations [53a,b,c,d], especially because 



2 



w affects the coefficients here only through the factor to . The final 



63 



