431 
From the equation of propagation, 3.32, Oo” and v satisfy the relation, 
Co Ore (I+ Bo), (ee) 
Change of variable from y' to O& in the integral of Eq. 3.48 and use of 
Eqe 5-9 gives 
ae E-ALiao), 
Oo~ ’ 
MpGadod |p?! obo! Len, 
MD = Cy a. 
(5.10) 
6%) a aetay Maia P z 
= Oe [2 La. fe Z. ley = |, 
Mee l//SS.., Ta. = Catt? 
where the subscript a denotes the value of a function on the surface of the 
gas sphere at time 7? . By differentiation of Eqe 5.10, we at once obtain 
the time-spread parameter Y of Eqe 3.35 
“opie eNbeas aienenad 7 aN aie pam ani 2: 
y=i/ Aly Zatl a Gee [tg & (2924 
Gilt.) 2 AG SAG» 
where Z andZ, are defined in Eq. 5.ll as | + (3 and L+ BI, 
respectively. 
J 
To determine the retarded time C, at the wave front, we con- 
sider the time + required for the wave front to reach the point R. 
7) 
R 
t = OE fy J ( ) 
o12 
PT da bene 
where lin) corresponds to a position of the front at point J” . Change 
