Falttnsen 
and 
16 ce 
mor 
ree l1vax -v J 
I Spee d o*(vt+va) dl oe 
a2 Hee a 
0 
(63) 
a/ 72 
1lvz Veeaal -ivz [Pee 
AES Oe Tee ES TRE) PTY 4, eee 
Uw 2 Uw 2. 
2 
foes f afi ~c +a] Mees -1fr+—2asa) 
g g& 
Here, 6, is some very small positive number. (61) is valid for 
y = 0(1) > 0. We are now going to find a two-term inner expansion of 
the far-field source solution. We then let y be of order e€ , and we 
reorder the terms in (61). The procedure is shown in Appendix D. 
We get 
(64) 
Using (60) and the symmetry properties associated with 
sources, we can now write down a two-term inner expansion of the 
far-field source solution as 
1790 
