The requirement that T must be zero can be examined by substituting 

 (13) in (23) and rearranging to yield, 



P2h2M2-V(0g2+g^^2)^ (27) 



Using conditions (26a) to (26c), it can be shovm that T vanishes 

 provided that the ratio P2/P1 is constant. Therefore, (25) and (26) 

 assure that (20) and (22) are entirely consistent with T equal to 

 zero and all other terms are identical. These two sets of equations 

 will also be used to determine a and /3. 



From (25a), (25b) and (26a), (26b) we find 



and 



2 _ 



ttg^ = P2r^/p^ii^[iii-^-r^)/(r^-r^)], 

 /3g2 = re/H2[(H2-ri)/(rg-ri)3, 

 H^ = P2ri/€PiHi[(rg-Hi)/(re-ri)], 



(28) 



(29) 



2 _ 



^i^ = ri/€H2[(rg-H2)/(rg-ri)]. 



It is not difficult to show that the ratios (/3/a)g and (/3/a)^ 

 obtained from (28) and (29) are the same as those in (19). If we 

 substitute (16) in (28) and (29), we obtain the relation for a and 

 /3, accurate to order e, in terms of H^^, H2 and D as follows: 



°-e = 1 + 2« - ie(H2/D)2 + O(e^), (30a) 



/Jg = 1- j€(Hi/D)2 + 0(e2), (30b) 



13 



