1553 
To calculate the energy dissipated over any arbitrary interval 
between R, and Ry» we would substitute the appropriate values 
of X, and X, into equation (135) and obtain the energy loss by 
taking the difference E(R,) - E(R2). The quantity R” eS 
would be a constant, the value of which would be given by 
Ro” Py”, where Po is the peak pressure of the shock wave at Ro- 
From a slightly different point of viewfor the same 
ideal case,we could consider the rate of energy loss with respect 
to R by differentiating equation (135) in the light of (136): 
- Ir RT,” ¢ [expen , 
ae ec de) Aah | OPO 1a 
og JZ 
Since @& is generally small, the first term in the 
brackets of equation (137) is of the order Ax®, and the ratio 
of this term to the second term is therefore of the order (2 1 )2a 
which is also small. We therefore neglect the first term and 
wite approximately: 
dR re (am)% (138) 
To the degree of approximation involved, this expression gives 
-ll-~ 
