892 
De Fail 
5: 
St D2 = S 
(2.2) 
(2,2) 
wy cn, 2) 
° 
26 
vanish on S the integral in 
? 
(1,1) extended over s, aleo vanishes. 
This is true for a point, oe internal 
to S, and also for a point, Fo, ex- 
ternal to 3. Hence the integral over 
S collavses to. one over So, and one may 
write 
i a f ft, As ath, 
(3,) 
z =| fa. ef as 
(S,) 
where ae ig any point inside of 8 and where ¥, is its image 
in 85. Addition of (2,1) and (2.2) gives 
(2.3) 
yd, £) 
dy fle 
The value of this integral is not changed if it is extended 
over all of T, eince [4] vanishes everywhere on T outside of 
55. Note that the gradient is taken opposite to the direction 
in which the wave front advances. (2,3) reauires much less 
knowledge of the boundery conditions than (1,1). 
3. Now divide space intc two nerts, Gand E, by an infinite plane, 
T, on opposite sides of which are the cauge, g, and the source, 
e, of an explosion (Fig 2). 
The explosive weve starts out from 
e, strikes g, and is reflected and diffracted back into E. In 
the acoustic approximation the 
disturbance due to e may be des- 
cribed by a velocity potential, 
vY , from which the pressure, 
2 - 
