energy transfer between modes, and the other terms in (22) are 

 defined as follows: 



T = l/p2[(Mg-Bg/rg) + e(Mi-Bi/ri)+g(^gCe+60q)]. (23) 



Ej^ = l/P2[(M|/rg) + €(M?/ri)], (24a) 



Ep = Up2<3i<l>l + e^i), (24b) 



J = 9/p2<^<t>e^B * «*iMi)f (24c) 



S = l/p2[(Me-Ge/rg)+e(Mi-Gi/ri)], (24d) 



where Gg and G^^ are defined in (31) . 



If (20) and (22) are to be consistent, their corresponding terms 

 must be equal and T must be zero. Inserting (8a) to (8c) in (24a) to 



(24d) it can be shown that the necessary conditions that Ej^ as well 



as S in (20) and (22) are consistent for arbitrary h^^, h2, Ki, and M2 

 are that 



a^^/r^ + ea^^/r^- = l/}i^ip2/p^). (25a) 



^e^/^e ■" ^^^i^/^i = l/"2' (25b) 



a^P^/r^ + ea^fi^/r^ = 0. (25c) 

 It is also necessary, for consistency in Ep and J, that 



Og^ + ea^^ = Pi/P2i (26a) 



/3e^ + e^i^ = 1 , (26b) 



Qg/Jg + €aj_/}i = 1 . (26c) 



12 



