430 
: at 
Y= Golk : (3.35) 
The asymptotic propagation equation, valid when €)(#¢) can be approximated 
in acoustical form by PZ » has been shown to be 
p= (4,/R) chet Retr), t's 2-409), 
(3.37) 
To) = /2 at ok CEI, 
We remark again that at the shock-front numerical calculation shows 
5 never to exceed a few percent of U. Therefore at the shock front or 
in a region immediately behind it, we can safely approximate 5 by zero and 
u& by & . We shall employ this approximation incalculating te and“ « 
Although the second integral of Eq. 5.7 defining t. » is taken along a path 
extending behind the shock front, it is easy to see that no point of this 
path lies very far behind the front. This is because the shock front RC t) 
moves only slightly more slowly than the wave of constant > > uhati dis; 
the point rit’; Cy) . The time elapsing between the passage of the shock 
front and of the wave of constant (o at any given point r is of the order 
of te or smaller, and for our theory only small values of Ce are important. 
Therefore the Riemann § has no time to build up to appreciable values. 
With the neglect of 5 » we may write, using Eqs. 5.4, 5.5, and 5.6, 
CHIL Vs Ce (1+ 28c) , 
Ie CrGir Bad 
OQ =O, rll+Bo), 
(3 2 Cnei/Ye, ; 
43 
(548) 
