1508 
paths AbB and AB'B is: 
aes ALL Ad = Ab [1- cos(@,- AB) 
CG C, Cc (59) 
where 
Ab = &, sec & (60) 
This expression obviously has a minimum of zero for b = @. 
and AB'B"C is then the least time path as was to be proved. The 
total difference in time of propagation for ABC and AB'B"C is 
now: 
at 
” 
2 a [/- er (OB) 
; (61) 
ere(e-8.) (for small 8-8 ) (62) 
C, 
(Note: in case that h, F# ho, it would be necessary to replace 
AB by % (AB + BC), in this expression.) 
5.5 For the geometry assumed in Figure 4: 
&-@. = .0267 radians 
LNG 
e012 milliseconds 
To see how this affects the reflected wave, we consider a 
particular case where the source is emitting an exponential 
shock wave of time constant .150 milliseconds, which corresponds 
roughly to an explosion of about 0.5 lbs. of TNT. The theoretical 
pressure time curve using the plane wave reflection theory(which 
