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the rate of energy loss with respect to R for the case in which 
viscous effects alone are present. 
13-3 In order to estimate the energy losses in the case where 
we take account of the sharpening effect of finite amplitude, 
we make use of equation (138) as an expression for the rate of 
energy loss, and integrate it over the range under consideration, 
using for X the results of Figure 10 rather than equation 
(136). It would not be correct to evaluate (135) at R, and Ro 
by substituting the corresponding values of X,, and %pg 
from Figure 10 and taking the difference to measure the energy 
loss. This method would not take into account the fact that 
the sharpening effect causes the wave to travel a given range 
with a shorter average rise time, and therefore greater viscous 
dissipation, than it would have had if only viscous effects 
were present. By using (138) as a measure of the rate of dissi- 
pation per foot of propagation for a given value of % , we can 
apply the results of section 9 to estimate the total energy loss. 
There remains the problem of selecting appropriate 
values for the amplitude parameter tas, As indicated above, 
an upper bound can be set by taking TT,, as the peak pressure 
of the wave at some relatively low value of the range, Ro» where 
viscous effects have not appreciably rounded off the front and 
thereafter setting RM, equal to the constant R,P,- This 
method would be strictly correct only for the case in which 
change of shape is due solely to viscous effects. The situation 
- 16 ~ 
