413 
ifr cere g |” 
ane ATE 
1G P Sos (3.39) 
9 R-ucrt rcerw) £5 Lemar SY, 
D.&.. EY Os 
Et ; Soha 
A further reduction of g with the aid of Eqs. 3.13, 3.16, 3.17, and 3.24 
yields, 
C+ 3u pie eule*-s, _2a2 
y a eee 2 co) - “=u ee " 
Cen Vis ate 
+ (e-u)| 32" aes eon at (3.40) 
h= S+@ler’, 
IC 
We have already remarked (Eqs. 3.24 and 3.36) that ly vanishes in regions in 
which the flow is either incompressible or acoustial, a circumstance which 
makes the form, Eq. 3.40, especially convenient as an expression for a ° 
From Eqs. 3.23 and 3.26, we remark that OY” and & behave asymp- 
totically as '/p and S as Vy = If € is a continuous function of density, 
we may assume it to be sy analytic function of 0” of the form Q+@¢ O- tere 
Since 4) is equal to cdo » it has the power series oo + ©, v2 Poar ts 
Q 
Thus the sum of the first three terms of the expression for 9 » Eq. 3.40, is 
at most of order & % and thus of order Vraet its asymptotic behavior. In 
26 
