1531 
regarded as the independent distance variable can no longer 
be treated as such, or associated directly with R. We shall 
use X to represent the "equivalent viscous distance", i.e. the 
distance of propagation which would have produced a given rise 
time with viscous attenuation acting alone. Thus X will be a 
complicated function of R and in the case of compression waves 
will be less than R at any given point because of the restoring 
effect of finite amplitude. The rate of increase of rise time 
with X is obtained by differentiating equation (93), making 
use of the relaticn between a and X in equation (97): 
a) [- iPeeg = / 
4Aard06ssa 3.380 _ 9.655a (— 
Ax vr 2 ex 
4 
\ 
Be) sae) eee 
Re ~ 4.65 (70 IE *| 2x (106) 
The overall rate of change of rise time with R is 
obtained by means of a similar operation: 
EAL 
Be Ae, -4.65 09x" (a & 
eit Ie 
(107) 
We assume that to a first approximation: 
7 an CAP Ge (07a) 
EE Hein a 
and combining (105), (106), and (107), and solving for Ax /AR : 
AR 7 ~ 4.65) ~~ 4.65(0 8)xe | R (108) 
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