415 
Therefore, we have been able to show that with increasing Y~, 
(cru) 9 /G,(t) ts = O(deg -/r*), (3.46) 
where 0 (4og r/r*) denotes terms diminishing as ( fog +)/\ or more 
rapidly.: Ths, we have the asymptotic result, 
Er eH wie itee Ol beg.2-/y").. (3.47) 
We shall find it sufficient to adopt ¢+Was an approximation to @, 
The corresponding approximation to the retarded time TV’ of Eq. 
3.28 then becomes \ 
arn : (3.48) 
alt) 
where the integral is again taken along a path at constant € . The error 
in G(r, t) arising from the use of the approximate [ of Eq. 3.48 can be 
expressed in the following manner. With this definition of t , ( dG/drdy 
is no longer zero but has the value 
OG ity 2664 pal OG f(y 
Ger ae ela OF Yue os wt (3.49) 
where g(r, tT) is given by Eq. 3.46. Since the approximate % becomes equal 
to t when ¥ is equal to a(t) , we obtain by integrating 3.49 along a path 
at constant 
G(r,t) = (It ¢) Galt), 
! a 4 
= —— g(r, ti dr, (3-50) 
G, (t) att) 
We shall find that water is a particularly favorable case for the 
application of the approximate theory. Numerical estimates of an upper bound 
